BAD DICE: the saga CONTINUES
February 24th, 2013 at 10:58:29 PM
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Well, I have been the champion of the idea that bad dice are as much of a fantasy as pixie dust and fairy tales.
But today, I found myself betting max Passline bets ($250) at the Fiesta, and after seeing an extraordinarily large number of aces and twelves running into my bets (and losing several hundred bucks) I decided to use the remaining $800 I had on the rail to do some counting.
For every roll, I counted the faces that appeared (two faces occur per roll).
130,125,108,125,119,142
When one die flew off the table, I still recorded the die that resolved on the felt. So this was face counts from approximately 370 rolls (yes I realize the count is odd).
This graph shows 200,000 samples with randomly generated outcomes from the faceweights from the 370 or so rolls (749 samples) of outcomes.
The findings from these samples that I took personally today match the claims that Harley has been making. I have historically been the lead critic of how ridiculous it is to consider that this is happening, but it appears to be happening.
After I compiled this simulation, I made several very large field bets and had fun with it (since I haven't played the field in years, it was actually kind of fun). I hit a $60 aces! And the best part was that I was just betting on random shooters. The aces and twelves just kept coming.
During the samples, there was a set of three hard 8's that came back-to-back, and there were plenty of other unusual things that happened. But I tried to be diligent in collecting as many samples as I could.
I took samples all from random finger snappers at the table .. with no discernable pattern at all from one of their rolls to the next. Just the "come on dice" followed by snapping of the fingers.
I was betting max bets on the passline before I started smelling something fishy in the outcomes and started counting and stopped playing.
After I started counting, and then I went back in heavy, I had a host assigned to me and she hugged me and gave me all kinds of peace-and-love and we all love you so much Aaron kind of stuff.
But they knew what I was doing, and I had my laptop out in the Keno area plotting out charts to see.
It's a long path to grind out a profit in the field, and obviously there is always risk of losing even if the theory is all on target and the player does have an edge.
But it absolutely forced me to reconsider the idea that bad dice could be a very real phenomenon.
On the subject of how I did the recording of the faces, I had six stacks of chips. I added two singles to the stack according to the outcome. I would then exchange five singles for a nickel, and five nickels for a quarter. After I had a common chip among all six stacks, I made a seventh stack that was a common count that was to be added to each of the six stacks.
I honestly hate the idea that I found this to be happening. 6-1 seven-outs were everywhere.
The chart above shows the passline and the dont passline with no odds and the field bet all of them grinding on $5 bets. You can see the pass and the don't pass line has a reduced edge and the passline has an increased edge and the field bet has massive exposure. This exposure could be a reason why LVH and Cosmopolitan have moved to only paying double on the 12.
I still have a lot more investigating to do into this. And frankly, I am NOT excited about it. It makes me very sad that I can't just say "what a bunch of bullshit all this biased dice theory."
Especially since I have been the poster-boy for there is no such thing as biased dice.
This is not enough samples to come to a conclusion, but I have seen enough to warrant further investigation into this subject.
And on that note, if there are any casinos who wish to be on the up-and-up and want to help me get to the bottom of this and take the position that they are not using what I would call "unfair dice" please let me know. I fully do not expect ANY cooperation at all as the casino pit crews that I have talked to on this subject have all clammed up pretty quickly leading me to be even MORE suspicious.
If you do think that you have bad dice on a table, and especially if you see a lot of aces and twelves, I say start doing a count, and if you have got really heavy six faces, go for it on the field and reverse martingale their asses. It would fucking HURT if there is any truth to this and if any of these places are going overboard on the heavy six faces like what it looks like may be the case.
It's ridiculous for them to consciously be exposing themselves on the field. The only thing saving them may be that most people with big bankrolls are too "smart" to play the field!
But today, I found myself betting max Passline bets ($250) at the Fiesta, and after seeing an extraordinarily large number of aces and twelves running into my bets (and losing several hundred bucks) I decided to use the remaining $800 I had on the rail to do some counting.
For every roll, I counted the faces that appeared (two faces occur per roll).
130,125,108,125,119,142
When one die flew off the table, I still recorded the die that resolved on the felt. So this was face counts from approximately 370 rolls (yes I realize the count is odd).
This graph shows 200,000 samples with randomly generated outcomes from the faceweights from the 370 or so rolls (749 samples) of outcomes.
The findings from these samples that I took personally today match the claims that Harley has been making. I have historically been the lead critic of how ridiculous it is to consider that this is happening, but it appears to be happening.
After I compiled this simulation, I made several very large field bets and had fun with it (since I haven't played the field in years, it was actually kind of fun). I hit a $60 aces! And the best part was that I was just betting on random shooters. The aces and twelves just kept coming.
During the samples, there was a set of three hard 8's that came back-to-back, and there were plenty of other unusual things that happened. But I tried to be diligent in collecting as many samples as I could.
I took samples all from random finger snappers at the table .. with no discernable pattern at all from one of their rolls to the next. Just the "come on dice" followed by snapping of the fingers.
I was betting max bets on the passline before I started smelling something fishy in the outcomes and started counting and stopped playing.
After I started counting, and then I went back in heavy, I had a host assigned to me and she hugged me and gave me all kinds of peace-and-love and we all love you so much Aaron kind of stuff.
But they knew what I was doing, and I had my laptop out in the Keno area plotting out charts to see.
It's a long path to grind out a profit in the field, and obviously there is always risk of losing even if the theory is all on target and the player does have an edge.
But it absolutely forced me to reconsider the idea that bad dice could be a very real phenomenon.
On the subject of how I did the recording of the faces, I had six stacks of chips. I added two singles to the stack according to the outcome. I would then exchange five singles for a nickel, and five nickels for a quarter. After I had a common chip among all six stacks, I made a seventh stack that was a common count that was to be added to each of the six stacks.
I honestly hate the idea that I found this to be happening. 6-1 seven-outs were everywhere.
The chart above shows the passline and the dont passline with no odds and the field bet all of them grinding on $5 bets. You can see the pass and the don't pass line has a reduced edge and the passline has an increased edge and the field bet has massive exposure. This exposure could be a reason why LVH and Cosmopolitan have moved to only paying double on the 12.
I still have a lot more investigating to do into this. And frankly, I am NOT excited about it. It makes me very sad that I can't just say "what a bunch of bullshit all this biased dice theory."
Especially since I have been the poster-boy for there is no such thing as biased dice.
This is not enough samples to come to a conclusion, but I have seen enough to warrant further investigation into this subject.
And on that note, if there are any casinos who wish to be on the up-and-up and want to help me get to the bottom of this and take the position that they are not using what I would call "unfair dice" please let me know. I fully do not expect ANY cooperation at all as the casino pit crews that I have talked to on this subject have all clammed up pretty quickly leading me to be even MORE suspicious.
If you do think that you have bad dice on a table, and especially if you see a lot of aces and twelves, I say start doing a count, and if you have got really heavy six faces, go for it on the field and reverse martingale their asses. It would fucking HURT if there is any truth to this and if any of these places are going overboard on the heavy six faces like what it looks like may be the case.
It's ridiculous for them to consciously be exposing themselves on the field. The only thing saving them may be that most people with big bankrolls are too "smart" to play the field!
aahigh.com
February 24th, 2013 at 11:32:07 PM
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"If there's somethin' strange in your neighborhoodQuote: AhighWell, I have been the champion of the idea that bad dice are as much of a fantasy as pixie dust and fairy tales.
But today, I found myself betting max Passline bets ($250) at the Fiesta, and after seeing an extraordinarily large number of aces and twelves running into my bets (and losing several hundred bucks) I decided to use the remaining $800 I had on the rail to do some counting.
For every roll, I counted the faces that appeared (two faces occur per roll).
130,125,108,125,119,142
Who ya gonna call?
If it's somethin' weird an' it don't look good
Who ya gonna call?"
Man, nothing strange or weird...
You are just watching the variance from a multinomial distribution unfold. Cool!
Casino Craps dice do show wear during their run on the felt.
where is your chi-squared test results?
Mine shows a 5.12 statistic with 5 DoF
That is a p-value of 0.401710642
Yahoo!
That means we'd end up with a result this skewed or more 40% of the time we rolled the die 749 times, if it were completely fair.
The bottom line is while these results are more skewed than would be expected,
they are not skewed enough to raise any eyebrows in such a small sample
I ain't afraid o' no ghost
I ain't afraid o' no ghost
winsome johnny (not Win some johnny)
February 24th, 2013 at 11:41:17 PM
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There were some strange things going on. Maybe it's just Harley getting into my head, and I respect your analysis and opinion, 7craps. I hadn't run a chi-squared on the faces yet.
I am still no chi-squared expert, but if you're saying this trend of the field wasn't likely to hold up, I think I understand that position, and I do tend to agree with you because I don't want to believe that the trend could continue, but man, it was very consistent. Those 6 faces stayed ahead and were leading the way throughout the count. And the three faces just way behind.
And it's not just that it fell outside of random, it's that it matched the theoretical desirable profile for what I characterized as the sort of "ideal" bad dice.
I think over the longer term the heavy 6-1 seven out might fade, but that would be more desirable. They don't want exposure in the field, and they ABSOLUTELY had it during the rolls that I recorded.
And after recording, I was rolling 12's like CRAZY and a field better on the opposite end of the table went from a couple hundred to a couple thousand with big bold field bets with tons of hi's and lo's (IE: AFTER I stopped recording and I was rolling).
I don't even want to believe this is happening, so I hope that if I kept recording it would balance out, but I just have to do more digging. It just matches too closely what Harley has been saying all along, and I want to close the door on the possibility, but I owe it to Harley to keep pursuing this until I find out for sure what the truth is.
And right now I don't know. I mean I just don't know. It really stinks to me.
And just LAUGHABLE that there can be exposure on the field. The only other bet that is exposed is a buy on the ten (they do automatic buys). All the other place bets and other bets in general are getting KILLED with these face weights.
I am still no chi-squared expert, but if you're saying this trend of the field wasn't likely to hold up, I think I understand that position, and I do tend to agree with you because I don't want to believe that the trend could continue, but man, it was very consistent. Those 6 faces stayed ahead and were leading the way throughout the count. And the three faces just way behind.
And it's not just that it fell outside of random, it's that it matched the theoretical desirable profile for what I characterized as the sort of "ideal" bad dice.
I think over the longer term the heavy 6-1 seven out might fade, but that would be more desirable. They don't want exposure in the field, and they ABSOLUTELY had it during the rolls that I recorded.
And after recording, I was rolling 12's like CRAZY and a field better on the opposite end of the table went from a couple hundred to a couple thousand with big bold field bets with tons of hi's and lo's (IE: AFTER I stopped recording and I was rolling).
I don't even want to believe this is happening, so I hope that if I kept recording it would balance out, but I just have to do more digging. It just matches too closely what Harley has been saying all along, and I want to close the door on the possibility, but I owe it to Harley to keep pursuing this until I find out for sure what the truth is.
And right now I don't know. I mean I just don't know. It really stinks to me.
And just LAUGHABLE that there can be exposure on the field. The only other bet that is exposed is a buy on the ten (they do automatic buys). All the other place bets and other bets in general are getting KILLED with these face weights.
aahigh.com
February 25th, 2013 at 3:14:44 PM
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Quote: AhighThere were some strange things going on.
And after recording, I was rolling 12's like CRAZY and a field better on the opposite end of the table went from a couple hundred to a couple thousand with big bold field bets with tons of hi's and lo's (IE: AFTER I stopped recording and I was rolling).
I don't even want to believe this is happening, so I hope that if I kept recording it would balance out, but I just have to do more digging. It just matches too closely what Harley has been saying all along, and I want to close the door on the possibility, but I owe it to Harley to keep pursuing this until I find out for sure what the truth is.
And right now I don't know. I mean I just don't know. It really stinks to me.
And just LAUGHABLE that there can be exposure on the field. The only other bet that is exposed is a buy on the ten (they do automatic buys). All the other place bets and other bets in general are getting KILLED with these face weights.
Don't you set your dice on boxcars? If you were getting alot of 6-1s it's because of your pitch of the dice when it makes "the turn" on the pyramids...
When the dice are made... They are balanced, but after they are engraved with the logo of the casino... There goes the balance... I have some old treasure island dice and no one can tell me that the big ass TI on the side does not make a difference.. The corner of the 6 and two seems to be more dense than the other side.
Or maybe... Just maybe... You had a bad day... you dice guys are gonna learn.. The moment you stop all the one leg leaning throws, you might actuallly start shooting better... Embrace random and it will embrace you.. (I'm just poking fun) but honestly if your setting box cars and you've been getting 6-1 all day, why not just flip one Die and shoot from 6-1. Don't get stuck in your practice set... All that practice doesn't mean anything if you can't make a slight adjustment in live action.. You know exactly what faces are falling, so make that slight adjusmentt and get back to good shooting...
I don't know if you will take my advice, but I hope you do. I just want to see players win. But some people are so blinded by over-complicated lies, and they will laugh at a very simple truth.
There arre unbalanced dice. It might just be a problem at that location and I would just stop going there..
"The math guys always say the "dice do not have a memory"... But if you've seen the cracks and edges on a pair of dice after being thrown all day, they sure look like they have some memory to me..."- Wolf
"I'm a DO'er and you my friend, are a Don'ter"
-Mark Walberg
pain and Gain
February 25th, 2013 at 3:16:47 PM
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Quote: AhighI took samples all from random finger snappers at the table .. with no discernable pattern at all from one of their rolls to the next. Just the "come on dice" followed by snapping of the fingers.
Every single roll was recorded from other people random shooting. There was absolutely no controlled shooters at ALL that got recorded. Sorry if I didn't make it clear. Those dice were flying and pretty fast at that.
Please PLEASE try to actually read the posts, people.
In addition, I have posted it multiple times, but I have been using 4242 set since September. Six on the left axis and aces on the right side of the axis. Backspin, three finger GTC style. But to reiterate none of it has relevance to the data I collected in this instance.
aahigh.com
February 25th, 2013 at 3:56:45 PM
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Ahigh,
I am a PhD student who has taught undergraduate and graduate level statistics. The textbook formula are fresh in my mind. 7craps is right, the chi-squared test is very important.
The question is: "is it possible the face counts recorded come from FAIR dice?"
Chi-Squared test says YES.
The test is very powerful, and very simple. 40% of 370 dice samples you collect in the same way could have face count results this wonky or worse. The conclusion you must draw is there is no evidence the dice are biased.
-----
If you make the mistake of assuming the face counts you observed represent the true bias of the dice, then you WILL see weird results in a simulation. Unfortunately, all your simulation results are essentially worthless, because they arise from this mistake.
I am a PhD student who has taught undergraduate and graduate level statistics. The textbook formula are fresh in my mind. 7craps is right, the chi-squared test is very important.
The question is: "is it possible the face counts recorded come from FAIR dice?"
Chi-Squared test says YES.
The test is very powerful, and very simple. 40% of 370 dice samples you collect in the same way could have face count results this wonky or worse. The conclusion you must draw is there is no evidence the dice are biased.
-----
If you make the mistake of assuming the face counts you observed represent the true bias of the dice, then you WILL see weird results in a simulation. Unfortunately, all your simulation results are essentially worthless, because they arise from this mistake.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
February 25th, 2013 at 4:12:26 PM
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I was thinking much the same... if you poked in any 370 roll set of data and analyzed it over a monte carlo, given that distribution, you'd find all sorts of cool patterns to bet on.
I've fallen into the trap before. Assess the null hypothesis first (how likely is this to have happened by chance).
I've fallen into the trap before. Assess the null hypothesis first (how likely is this to have happened by chance).
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 25th, 2013 at 4:21:16 PM
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I agree with 7craps' Chi Squared analysis, and the binomial distribution shows the 6 at .95 and the 3 at .05, but really not anything out of the ordinary.
Please understand the math. Your chart over 200,000 rolls only extends the variance out to show that if the dice remain that way, this is how the result will end up.
Except you don't know that the dice will remain that way.
Please understand the math. Your chart over 200,000 rolls only extends the variance out to show that if the dice remain that way, this is how the result will end up.
Except you don't know that the dice will remain that way.
-----
You want the truth! You can't handle the truth!
February 25th, 2013 at 4:29:09 PM
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Quote: dwheatley
The conclusion you must draw is there is no evidence the dice are unbiased.
That is correct. But I am guessing you meant to write there is no evidence the dice are biased. I would add the word conclusive before evidence. If you roll the dice once and record a boxcars, that is 'evidence' that 6's are favored. Quite weak evidence, of course. If it happens 10 times in a row the first boxcars was the first peice of evidence.
February 25th, 2013 at 4:32:33 PM
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Quote: thecesspitI was thinking much the same... if you poked in any 370 roll set of data and analyzed it over a monte carlo, given that distribution, you'd find all sorts of cool patterns to bet on.
I've fallen into the trap before. Assess the null hypothesis first (how likely is this to have happened by chance).
dwheatley and thecesspit - not so fast my friends .... if you for a second doubt AHigh's results as chance or just a pattern, then you have to concur that I am a better prophet than Nostradamus because I told AHigh before he even walked into that casino what the results would be biased to ...
Believe me, I am not Nostradamus, but I can predict with almost 99% accuracy what the dice results are going to be after 30 rolls --- and they will continue to be that same Bias for 500 or 600 rolls which is all we care about because they change dice every 8 hours in Vegas (except Caesar's which will keep them for up to 24 hours on a table)
.... that is simply my opinion ....
Ciao,
Harley ...
Link = http://crapsadvantageplayers.blogspot.com/
February 25th, 2013 at 4:34:36 PM
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Stats don't lie, only people using stats lie. Show us the data, or exploit it yourself, whatever works for you.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
February 25th, 2013 at 4:35:12 PM
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Quote: Harleydwheatley and thecesspit - not so fast my friends .... if you for a second doubt AHigh's results as chance or just a pattern, then you have to concur that I am a better prophet than Nostradamus because I told AHigh before he even walked into that casino what the results would be biased to ...
Believe me, I am not Nostradamus, but I can predict with almost 99% accuracy what the dice results are going to be after 30 rolls --- and they will continue to be that same Bias for 500 or 600 rolls which is all we care about because they change dice every 8 hours in Vegas (except Caesar's which will keep them for up to 24 hours on a table)
I look forward to seeing this feat in person.
February 25th, 2013 at 4:50:21 PM
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Quote: boymimboI agree with 7craps' Chi Squared analysis, and the binomial distribution shows the 6 at .95 and the 3 at .05, but really not anything out of the ordinary.
Please understand the math. Your chart over 200,000 rolls only extends the variance out to show that if the dice remain that way, this is how the result will end up.
7craps and boymimbo ... I take exception with your chi-squared analysis as I am not sure you have considered your calculation correctly ? ...... Craps is based on the outcome of 2 dice .... combining the results of 2 biased dice would exponentially advance the deviation ......
Quote: boymimbo...Except you don't know that the dice will remain that way.
boybimbo .... you can doubt all you wish .... I see the same bias after 500 rolls as I do after 30 to 50 rolls more than 80% of the time ..... you can't argue with Mother Nature - gravity is going to conquer in the short run and the long run
Quote:There are 3 classes of people:
- Those who see;
- Those who see when they are shown;
- Those who do not see; ...
.... that is simply my opinion ....
Ciao,
Harley ...
Link = http://crapsadvantageplayers.blogspot.com/
February 25th, 2013 at 4:58:21 PM
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.... just look in the mirror after you chart 500 rolls and compare it to what the Pyramid Distribution was after 30 rolls, again after 50 rolls and again after 100 rolls ...... If you have fair dice, randomness will occur, however if you have biased percentage dice the same pattern will occur over and over .... that's why they call it biasQuote: SOOPOOI look forward to seeing this feat in person.
Don't believe me or even Ahigh or anyone else that knows Biased dice exist --- do the test yourself like Ahigh did
.... that is simply my opinion ....
Ciao,
Harley ...
Link = http://crapsadvantageplayers.blogspot.com/
February 25th, 2013 at 5:09:43 PM
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Quote: Harley7craps and boymimbo ... I take exception with your chi-squared analysis as I am not sure you have considered your calculation correctly ? ...... Craps is based on the outcome of 2 dice .... combining the results of 2 biased dice would exponentially advance the deviation ......
The dice are not correlated. If each dice is independent, then 370 separate events will be the model for chi-square analysis.
Quote:boybimbo .... you can doubt all you wish .... I see the same bias after 500 rolls as I do after 30 to 50 rolls more than 80% of the time ..... you can't ague with Mother Nature - gravity is going to conquer in the short run and the long run
Depends how you are measuring the 'same bias'... do you mean the side that is ahead stays ahead? Or something else.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 25th, 2013 at 6:04:52 PM
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If you'd like, I can translate the chi square and standard deviation for your data in a heartbeat, and tell you whether or not it statistically relevant. I can also provide you with a comprehensive mathematical breakdown of exactly how you should bet any bias that you find with dice. All you need to do is provide a data stream, or the number of times each face of the dice have shown. (And NO, I'm not selling anything)
-Keyser
-Keyser
February 25th, 2013 at 6:13:05 PM
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Does the fact that the 370 observations were among 5 dice make any difference? Each shooter got to pick two from the bowl.
Another thought... How is it that the six-one would show up more than normal? These two faces are opposites, so what hypothetical bias would cause this to occur?
Another thought... How is it that the six-one would show up more than normal? These two faces are opposites, so what hypothetical bias would cause this to occur?
Simplicity is the ultimate sophistication - Leonardo da Vinci
February 25th, 2013 at 6:20:49 PM
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deleted
DUHHIIIIIIIII HEARD THAT!
February 25th, 2013 at 6:41:43 PM
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Quote: Harley7craps and boymimbo ... I take exception with your chi-squared analysis as I am not sure you have considered your calculation correctly ? ...... Craps is based on the outcome of 2 dice .... combining the results of 2 biased dice would exponentially advance the deviation ......
boybimbo .... you can doubt all you wish .... I see the same bias after 500 rolls as I do after 30 to 50 rolls more than 80% of the time ..... you can't ague with Mother Nature - gravity is going to conquer in the short run and the long run
Uh huh. I won't argue with statistical analysis. Good thing you're not a medical researcher. Good luck.
-----
You want the truth! You can't handle the truth!
February 26th, 2013 at 2:01:29 AM
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Quote: HarleyI told AHigh before he even walked into that casino what the results would be biased to ...
If you know that, why can't you exploit the bias?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
February 26th, 2013 at 5:09:48 AM
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Like so many other threads, the meme here that's common:
1) I do hours of work
2) I publish my work
3) People do minutes of math
4) People tell me my work is worthless
5) Some people tell me that I'm not as smart as them
Here is my suggestion. If you truly doubt Harley do the work and publish your results.
Not all dice are unfair! I was counting faces last night at Mandalay Bay SPECIFICALLY after a new table was opened and overhearing the guy handing the dice over that "there are a lot of advantage players here tonight." I asked the boxman what dice were being put on the table and taken off and he told me the dice were Bee dice were being put in, and they had just taken Bud Jones dice off the table. The Bee Dice were looking pretty darn fair.
As I am doing this work, the Wizard himself walks up behind me, and I veered off my dice counting plan to show him my shot.
Then the Wizard and I went to talk about a few things.
I grow very weary about people who say with such certainty what they know without doing the work. I have been Harley's biggest critic. One of the Wizard's comments when I told him what I was doing (and these dice were fair after counting) with respect to Harley is "maybe he is pulling your leg."
I said, "yeah maybe." I went on to tell him that Harley is a modest guy.
As Harley's biggest critic for over a year now, dismissing his claims as ridiculous, the very FIRST time I did what it would take to look at the potential for bias after observing what appeared to be the conditions that Harley described for such biased dice, it came up the way that Harley suggested.
So it's not just that the Chi-squared was 40% that mattered, it was the fact that the ones and sixes were heavier than the 2, 3, 4, and 5. Those who are only looking at the 40% number aren't looking at the shape of the face outcomes (heavy on the sixes and heavy on the ones) which is the consistent read that Harley is making a claim that he continues to see.
Now my eyes start to glaze over when Harley goes into the details of various dice. And I *LOVE* talking about dice. I make Tungsten dice, and I have had my own custom dice made that I designed myself. But when he starts talking about the details of the fonts and the frost and the color and all those details, *I* get bored. And that's not a slight to Harley, it's to his credit. He knows his damn dice better than anybody else I have ever met.
So if you numbers guys want to focus on a single 40% number as a method of rejection, then who is using statistics for a light post and who is using it for illumination in this instance?
It's convenient to reject Harley's hypothesis, yes. But I don't enjoy doing this work either. But I must also admit that my very first session recording faces (and it took more than an hour sitting there recording faces) led to exactly what he was suggesting.
Yesterday, I sent a private message to the Wizard for the first time ever and said "we should arrange to meet." Then randomly he finds me playing craps at the M last night. And he said, "what are the odds?"
So these kinds of rare events do happen where you have to say "what are the odds?"
But if you just walk away thinking "random stuff happens sometimes" and "I like math" as you push up your glasses and dismiss any meaning to the event, you are living a much duller life than I.
For the record, the dice that I recorded the results on at Fiesta Rancho were brand new and fresh dice when I started recording as well, and I generally only think it makes sense to record starting with a fresh stick!
1) I do hours of work
2) I publish my work
3) People do minutes of math
4) People tell me my work is worthless
5) Some people tell me that I'm not as smart as them
Here is my suggestion. If you truly doubt Harley do the work and publish your results.
Not all dice are unfair! I was counting faces last night at Mandalay Bay SPECIFICALLY after a new table was opened and overhearing the guy handing the dice over that "there are a lot of advantage players here tonight." I asked the boxman what dice were being put on the table and taken off and he told me the dice were Bee dice were being put in, and they had just taken Bud Jones dice off the table. The Bee Dice were looking pretty darn fair.
As I am doing this work, the Wizard himself walks up behind me, and I veered off my dice counting plan to show him my shot.
Then the Wizard and I went to talk about a few things.
I grow very weary about people who say with such certainty what they know without doing the work. I have been Harley's biggest critic. One of the Wizard's comments when I told him what I was doing (and these dice were fair after counting) with respect to Harley is "maybe he is pulling your leg."
I said, "yeah maybe." I went on to tell him that Harley is a modest guy.
As Harley's biggest critic for over a year now, dismissing his claims as ridiculous, the very FIRST time I did what it would take to look at the potential for bias after observing what appeared to be the conditions that Harley described for such biased dice, it came up the way that Harley suggested.
So it's not just that the Chi-squared was 40% that mattered, it was the fact that the ones and sixes were heavier than the 2, 3, 4, and 5. Those who are only looking at the 40% number aren't looking at the shape of the face outcomes (heavy on the sixes and heavy on the ones) which is the consistent read that Harley is making a claim that he continues to see.
Now my eyes start to glaze over when Harley goes into the details of various dice. And I *LOVE* talking about dice. I make Tungsten dice, and I have had my own custom dice made that I designed myself. But when he starts talking about the details of the fonts and the frost and the color and all those details, *I* get bored. And that's not a slight to Harley, it's to his credit. He knows his damn dice better than anybody else I have ever met.
So if you numbers guys want to focus on a single 40% number as a method of rejection, then who is using statistics for a light post and who is using it for illumination in this instance?
It's convenient to reject Harley's hypothesis, yes. But I don't enjoy doing this work either. But I must also admit that my very first session recording faces (and it took more than an hour sitting there recording faces) led to exactly what he was suggesting.
Yesterday, I sent a private message to the Wizard for the first time ever and said "we should arrange to meet." Then randomly he finds me playing craps at the M last night. And he said, "what are the odds?"
So these kinds of rare events do happen where you have to say "what are the odds?"
But if you just walk away thinking "random stuff happens sometimes" and "I like math" as you push up your glasses and dismiss any meaning to the event, you are living a much duller life than I.
For the record, the dice that I recorded the results on at Fiesta Rancho were brand new and fresh dice when I started recording as well, and I generally only think it makes sense to record starting with a fresh stick!
aahigh.com
February 26th, 2013 at 7:23:06 AM
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" dismissing his claims as ridiculous "
This is known as a " LUCID INTERVAL " !
This is known as a " LUCID INTERVAL " !
Shed not for her
the bitter tear
Nor give the heart
to vain regret
Tis but the casket
that lies here,
The gem that filled it
Sparkles yet
February 26th, 2013 at 7:45:42 AM
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Energy folks, ENERGY! It is as real as the energy that fires up your wireless phones and computers.. You cant see it, hear it, smell it, taste it, or feel it... but it is real. It cant be proven scientifically, which makes it a moot point with the very scientifically smart people on this board, but once you understand the dynamics of it, you will have a significant edge in the game.
February 26th, 2013 at 8:09:22 AM
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You don't need hours of work to analyze dice. You need to know basic statistical analysis which is available online and known to 10th graders. Everything else is just fluff, sorry to say.
Energy, folks? Ghosts, hobgoblins, and Santa Claus.
Show my work?
ChiSquare = sum of ((actual - expected)^2) / expected for each dice face. Add it up. Divide by degrees of freedom = 5. Calculate the P-value (most people use a chart or Excel.
Binomial Distribution in excel = BINOMDIST (actual, #trials, 1/6, false) gives me a p value.
Done.
I don't need a long chart extrapolating to xxx,xxx trials. It's meaningless. It's like extrapolating a poll of 700 people to the election results across the state. If boxcars appear 3% of the time over 700 trials, it's going to appear 3% of the time over 200,000 trials from your charts. So yeah, your charts, while pretty, are meaningless.
There's no new math to exploit, no new theorems. Harley claims he sees bias after 30-50 rolls. Well, it's not mathematical bias. It's just a feeling.
If Harley wants to show mathematical bias, then he would:
(1) make a claim (ie I see a bias after 30 - 50 rolls).
(2) test the claim (for n trials of 30 - 50 rolls, show that without a doubt, that the next 450 - 770 rolls show the same bias) over a number of trials.
(3) determine whethe the claim is true or within the realms of variance (luck).
If Harely wants to show emotional bias, well then, that's fine.
Energy, folks? Ghosts, hobgoblins, and Santa Claus.
Show my work?
ChiSquare = sum of ((actual - expected)^2) / expected for each dice face. Add it up. Divide by degrees of freedom = 5. Calculate the P-value (most people use a chart or Excel.
Binomial Distribution in excel = BINOMDIST (actual, #trials, 1/6, false) gives me a p value.
Done.
I don't need a long chart extrapolating to xxx,xxx trials. It's meaningless. It's like extrapolating a poll of 700 people to the election results across the state. If boxcars appear 3% of the time over 700 trials, it's going to appear 3% of the time over 200,000 trials from your charts. So yeah, your charts, while pretty, are meaningless.
There's no new math to exploit, no new theorems. Harley claims he sees bias after 30-50 rolls. Well, it's not mathematical bias. It's just a feeling.
If Harley wants to show mathematical bias, then he would:
(1) make a claim (ie I see a bias after 30 - 50 rolls).
(2) test the claim (for n trials of 30 - 50 rolls, show that without a doubt, that the next 450 - 770 rolls show the same bias) over a number of trials.
(3) determine whethe the claim is true or within the realms of variance (luck).
If Harely wants to show emotional bias, well then, that's fine.
-----
You want the truth! You can't handle the truth!
February 26th, 2013 at 8:55:45 AM
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Actually, no-one rejected your work. People were trying to WORK with you (as you keep asking for) to show you how to IMPROVE your results. I thought you wanted feedback and constructive criticism? I think it is interesting, but non-conclusive.
There's no rejection of the hypothesis, just pointing out -by itself- 370 rolls is no enough to prove a bias (1-6 or otherwise). Of course what was biased towards matters... chi-squared takes that into account my assessing the null hypothesis. You could repeat the same work by taking a chi-squared where you assume a bias towards the 1-6 (you'd have to state what the extent was, but with the prior work you can make an estimate of what you think the dice IS doing) and test that hypothesis.
As ever, the more unlikely the claim, the more evidence is required. If you repeated again for another 370 rolls, and got the same sort of distribution, chi-squared returns about 0.05 (or so).
Note, if you are selecting the dice to test based on the first 30-50 rolls, you have to ignore those rolls when testing the hypothesis (e.g. you can't pick and choose to include the 'selection' set, as you'd introduce bias into your sample set by only choosing sets where the first 30-50 rolls were heavy on the 1-6, which obviously can happen by chance).
There's no rejection of the hypothesis, just pointing out -by itself- 370 rolls is no enough to prove a bias (1-6 or otherwise). Of course what was biased towards matters... chi-squared takes that into account my assessing the null hypothesis. You could repeat the same work by taking a chi-squared where you assume a bias towards the 1-6 (you'd have to state what the extent was, but with the prior work you can make an estimate of what you think the dice IS doing) and test that hypothesis.
As ever, the more unlikely the claim, the more evidence is required. If you repeated again for another 370 rolls, and got the same sort of distribution, chi-squared returns about 0.05 (or so).
Note, if you are selecting the dice to test based on the first 30-50 rolls, you have to ignore those rolls when testing the hypothesis (e.g. you can't pick and choose to include the 'selection' set, as you'd introduce bias into your sample set by only choosing sets where the first 30-50 rolls were heavy on the 1-6, which obviously can happen by chance).
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 26th, 2013 at 9:50:14 AM
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Quote: thecesspitNote, if you are selecting the dice to test based on the first 30-50 rolls, you have to ignore those rolls when testing the hypothesis (e.g. you can't pick and choose to include the 'selection' set, as you'd introduce bias into your sample set by only choosing sets where the first 30-50 rolls were heavy on the 1-6, which obviously can happen by chance).
I was conscious of this and did not start recording at a convenient time to support the hypothesis. To be specific, I did start recording after a boxcar, and I did not count that boxcar knowing that it would skew the results.
I appreciate all your input. I am trying to remain neutral on the theory. If anything I don't want to believe it because it's not really that fun counting faces and doing this stuff and I would rather work on throw-related bias.
aahigh.com
February 26th, 2013 at 10:12:17 AM
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Quote: AhighI was conscious of this and did not start recording at a convenient time to support the hypothesis. To be specific, I did start recording after a boxcar, and I did not count that boxcar knowing that it would skew the results.
Cool. data mining can be dangerous. I've been caught by it before, and will probably do so again.
Yeah, this is why I want to Understand harley's comments about knowing the bias continues after 30-50 rolls. If you add in those first 50 rolls, then add 350 more, the distribution that you first noted will still be there to some effect.
Quote:I appreciate all your input. I am trying to remain neutral on the theory. If anything I don't want to believe it because it's not really that fun counting faces and doing this stuff and I would rather work on throw-related bias.
Model a biased dice (18/16/16/16/16/18 for example), test your rolls against that and the null hypothesis.
You'd need the null hypothesis chi value to be very small before you could decide how good the model of bias was (else your fitting your results to a small observation, the model above give a chi-square of ~0.8 on the 370 rolls). But then you could take the biased model forward. But you need to be applying a quantative value to the bias to be able to show any effect mathematically.
---
And as boymimbo says, you can do this by feel if you desire. Just realize there's plenty of Maths Geeks(*) here who won't take that as evidence, and if that's frustrating, then it's part of the nature of the community here. (This comment is not aimed at AHigh but more generally to the 'energy and feel' guys, who I find just as mystical and frustrating as they probably find the 'Math Guys').
(*) No insult intended. That's a compliment in my world.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 26th, 2013 at 10:19:23 AM
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Ahigh
The casinos don't have to worry about anybody placing bets that would take advantage of those dice you were seeing.
So there are going to be some finger snappers playing the field, that don't have the bankroll they need to do so. You also have to remember that they will be placing every other stupid bet they can make. Now I'm not saying that the field is a stupid bet if it pays 3 to 1 on the 12. It's all those other prop bets they make that will kill them.
Then you have all those guys that only bet the inside numbers that are getting killed. The next on the list is the guys that are betting the don't because of all the come out 7's. You even got the guys that are going to bet the don't come because of all the PSO's.
Now what does that leave, you have the guys that have the brains to bet the outside numbers, but there are a very are few of those at any table. Now lets get back to you sitting there with a lap top recording rolls. I don't know how you managed to pull that one off, but most casinos won't let you get anywhere near the table games with a lap top. The other thing is how long did it take you before you said to yourself, I think I might be on to something here, let me see if I bet this way what would happen?
The outside points can be a goldmine at time, if you have the brains to bet them, it's funny as hell when you see the don't players getting killed on laying the 4's and 10's and nobody is betting them! Back when I was working I saw a homeless guy make $13,000 just betting the crap numbers at the Plaza, it had to be one of the funniest things that I've seen on a craps table, now the reason I said that was because one of his buddies came to the table and needed a beer, so he tell his buddy I can roll those numbers too, how about putting me on the table and I'll shoot, that way I can get my beer, you got plenty of chips!
When the one guy did seven out, the new guy starts to make nothing but craps numbers too; they kicked these guys off the table and banned them from playing in the Plaza. They banned two of the most random rollers on this earth. The only difference was that the one guy had the brains to bet what he was seeing happening on the table.
The guy that taught me how to play craps would tell me all the time that he had been playing craps for 45 years and he would never bet a 5 or 9, he only bet on the 6 and 8! He always said I can't understand it you are always winning and he was not. When I would tell him to bet the outside numbers he would laugh at me and tell me how bad of bets those were. I've always tracked the table from the first time I picked up the dice and would even show him what was happening on the tables and he would still only bet the 6 and 8 and lose. It wasn't till a year before he passed away that when he came back to Vegas that he finally changed how he was betting and for once started to win at the craps tables! He was just like everybody else they loved to play the game but couldn't change what they are doing to win, they are only playing for the fun of it.
There are the days that the 6's and 8's will be showing but not like they should. When RaleighCraps was here at the first of the year, we had stopped at a off strip casino and I told him to bet the field and leave his chips in the field for three rolls or more, because of all the crap numbers and outside number that were being rolled. That is how he got most of his bankroll back; we didn't have the time to exploit what was happening, as I had to get him back to his hotel to catch a flight out of here.
I say if you don't want to believe they are using cheap dice, and you will stay a true follower of out great fiction writers, more power to you, we always need losers on the tables, thanks for not seeing what is happening right in front of you!
Ahigh I will give you all the credit in the world, for being a man about the whole thing on the bad dice or cheap that they are now using in the different casinos. I never thought that you of all people would say hey, wait a minuet Harley is right about these dice. The test of any man is when there comes a time to admit he was wrong, it can go either two way, you bury your head in the sand and say its not true, just so you can be right, or you man up and say look guys, I put all this time and work into finding out for myself and I made a mistake thinking along the lines of everybody else.
Now for our great fiction writers and the guys that are in craps only to sell their classes, I feel for their followers, but that's their problem for reading fiction. This information has been around for a few years now and they couldn't figure out how to make money on it, so all they did was to call Harley names!
What started out as just a warning about what was being seen in Vegas on the weekends and when big conventions where in town now has spread around the country, because of all the pencil pushers buying the cheapest dice they can buy! Yes you may be one of the lucky ones that you local casinos are still buying quality dice, but if you're not just remember you will never be at any craps table for 10,000 rolls of the dice.
Then for all you guys that say if I knew that there were these cheap dice on the table I would be a millionaire playing the don't, think about what you are saying, because you too are going to get killed on the come-out rolls with the 7's. Then I know you would play the don't come avoiding the come-out rolls only to get killed on the PSO's!
I have never seen any system that will work all the time, or betting strategy that can win all the time, even knowing that you have cheap dice on the table is not a guarantee that you are going to win by changing what you are doing on the table. The one thing it does do is to get you off a table when you are seeing things that shouldn't be happening on the table, if you can't adapt to what is happening!
The casinos don't have to worry about anybody placing bets that would take advantage of those dice you were seeing.
So there are going to be some finger snappers playing the field, that don't have the bankroll they need to do so. You also have to remember that they will be placing every other stupid bet they can make. Now I'm not saying that the field is a stupid bet if it pays 3 to 1 on the 12. It's all those other prop bets they make that will kill them.
Then you have all those guys that only bet the inside numbers that are getting killed. The next on the list is the guys that are betting the don't because of all the come out 7's. You even got the guys that are going to bet the don't come because of all the PSO's.
Now what does that leave, you have the guys that have the brains to bet the outside numbers, but there are a very are few of those at any table. Now lets get back to you sitting there with a lap top recording rolls. I don't know how you managed to pull that one off, but most casinos won't let you get anywhere near the table games with a lap top. The other thing is how long did it take you before you said to yourself, I think I might be on to something here, let me see if I bet this way what would happen?
The outside points can be a goldmine at time, if you have the brains to bet them, it's funny as hell when you see the don't players getting killed on laying the 4's and 10's and nobody is betting them! Back when I was working I saw a homeless guy make $13,000 just betting the crap numbers at the Plaza, it had to be one of the funniest things that I've seen on a craps table, now the reason I said that was because one of his buddies came to the table and needed a beer, so he tell his buddy I can roll those numbers too, how about putting me on the table and I'll shoot, that way I can get my beer, you got plenty of chips!
When the one guy did seven out, the new guy starts to make nothing but craps numbers too; they kicked these guys off the table and banned them from playing in the Plaza. They banned two of the most random rollers on this earth. The only difference was that the one guy had the brains to bet what he was seeing happening on the table.
The guy that taught me how to play craps would tell me all the time that he had been playing craps for 45 years and he would never bet a 5 or 9, he only bet on the 6 and 8! He always said I can't understand it you are always winning and he was not. When I would tell him to bet the outside numbers he would laugh at me and tell me how bad of bets those were. I've always tracked the table from the first time I picked up the dice and would even show him what was happening on the tables and he would still only bet the 6 and 8 and lose. It wasn't till a year before he passed away that when he came back to Vegas that he finally changed how he was betting and for once started to win at the craps tables! He was just like everybody else they loved to play the game but couldn't change what they are doing to win, they are only playing for the fun of it.
There are the days that the 6's and 8's will be showing but not like they should. When RaleighCraps was here at the first of the year, we had stopped at a off strip casino and I told him to bet the field and leave his chips in the field for three rolls or more, because of all the crap numbers and outside number that were being rolled. That is how he got most of his bankroll back; we didn't have the time to exploit what was happening, as I had to get him back to his hotel to catch a flight out of here.
I say if you don't want to believe they are using cheap dice, and you will stay a true follower of out great fiction writers, more power to you, we always need losers on the tables, thanks for not seeing what is happening right in front of you!
Ahigh I will give you all the credit in the world, for being a man about the whole thing on the bad dice or cheap that they are now using in the different casinos. I never thought that you of all people would say hey, wait a minuet Harley is right about these dice. The test of any man is when there comes a time to admit he was wrong, it can go either two way, you bury your head in the sand and say its not true, just so you can be right, or you man up and say look guys, I put all this time and work into finding out for myself and I made a mistake thinking along the lines of everybody else.
Now for our great fiction writers and the guys that are in craps only to sell their classes, I feel for their followers, but that's their problem for reading fiction. This information has been around for a few years now and they couldn't figure out how to make money on it, so all they did was to call Harley names!
What started out as just a warning about what was being seen in Vegas on the weekends and when big conventions where in town now has spread around the country, because of all the pencil pushers buying the cheapest dice they can buy! Yes you may be one of the lucky ones that you local casinos are still buying quality dice, but if you're not just remember you will never be at any craps table for 10,000 rolls of the dice.
Then for all you guys that say if I knew that there were these cheap dice on the table I would be a millionaire playing the don't, think about what you are saying, because you too are going to get killed on the come-out rolls with the 7's. Then I know you would play the don't come avoiding the come-out rolls only to get killed on the PSO's!
I have never seen any system that will work all the time, or betting strategy that can win all the time, even knowing that you have cheap dice on the table is not a guarantee that you are going to win by changing what you are doing on the table. The one thing it does do is to get you off a table when you are seeing things that shouldn't be happening on the table, if you can't adapt to what is happening!
Note, all my post start with this is just my opinion...!
You do good brada ..!
superrick
Winning comes from knowledge and skill when your betting and not reading fiction
http://procraps4u2.myfanforum.org/index.php
...
February 26th, 2013 at 11:53:09 AM
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Does not this puts more weight on a 1 and 6 face.Quote: thecesspitModel a biased dice (18/16/16/16/16/18 for example), test your rolls against that and the null hypothesis.
Is not the claim from the "percentage dice sect" that faces 5 & 6 are heavier than the others?
If true, that would make them less likely to end facing up on any one roll with any number of dice thrown.
at least this (17,17,17,17,16,16)
AlanM even asked about this and was brushed off.
Weighted 5 and 6 faces shows more 1s and 2s.
A 10 year old easily knows this.
I asked one.
"Scratch down the pips, not all the way down so you can see the solder from another side,
fill almost level with solder, paint over, sand and you have your weighted die."
LOL
of course there are NO 21 year olds or older that are smarter than any 10 year old today
winsome johnny (not Win some johnny)
February 26th, 2013 at 11:57:44 AM
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Quote: 7crapsDoes not this puts more weight on a 1 and 6 face.
Yes, and the claim was 1's and 6's turn up more often.
Quote:
Is not the claim from the "percentage dice sect" that faces 5 & 6 are heavier than the others?
If true, that would make them less likely to end facing up on any one roll with any number of dice thrown.
at least this (17,17,17,17,16,16)
AlanM even asked about this and was brushed off.
Weighted 5 and 6 faces shows more 1s and 2s.
A 10 year old easily knows this.
I asked one.
"Scratch down the pips, not all the way down so you can see the solder from another side,
fill almost level with solder, paint over, sand and you have your weighted die."
LOL
of course there are NO 21 year olds or older that are smarter than any 10 year old today
What ever you want to model, you can then test the claim versus the null hypothesis. No specific claim of the percentages of the 1/6 biased dice has been made exactly, so I guesstimated as an example.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 26th, 2013 at 12:10:32 PM
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Quote: 7crapsIs not the claim from the "percentage dice sect" that faces 5 & 6 are heavier than the others?
Depends on the density/weight of the pip material. If the pip material is less dense than the body of the die, then faces 5 and 6 would be lighter.
Quote: 7crapsIf true, that would make them less likely to end facing up on any one roll with any number of dice thrown.
Not necessarily.
The heaviest face might also be predisposed to land face-up more than the lighter "side" faces, due to the extra momentum carrying that face up when turning in that portion of the rolling arc. Of course, the heavier face would tend to land face down more often, reducing the relative number of "side" faces that land face up.
February 26th, 2013 at 12:19:38 PM
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OK.Quote: thecesspitYes, and the claim was 1's and 6's turn up more often.
No specific claim of the percentages of the 1/6 biased dice has been made exactly, so I guesstimated as an example.
The one's that claim more 1s and 6s from heavier faces of 5s and 6s have shown the bias as percentages from actual casino dice rolls,they were there,
of course no data has been shown here except by Ahigh,
and one even claims before going into the casino, how the 1s and 6s will do.
probably knows the manufacture of the dice that the particular casino uses.
So their hypothesis is simply more 1s and 6s will roll, from certain dice manufacturers,
because the faces 5&6 are heavier than the others.
IOW, the more heavier faces 5 and 6 are, the more 1s and 6s will end facing up after a roll.
This is great stuff.
How about a water test??
Would a stick of dice from one manufacturer that are NOT biased
displace less water in a container than from stick of dice that are biased???
Damn, 10 year olds these days know everything!
Hey, we just had an earthquake jolt
winsome johnny (not Win some johnny)
February 26th, 2013 at 12:33:58 PM
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Well you got me on that one.Quote: tuppThe heaviest face might also be predisposed to land face-up more than the lighter "side" faces, due to the extra momentum carrying that face up when turning in that portion of the rolling arc.
I guess my intuition let me down. I am not at all versed in physics.
so now you say in a series of dice rolls, the heavier side of the dieQuote: tuppOf course, the heavier face would tend to land face down more often, reducing the relative number of "side" faces that land face up.
(and we know there are actually 2 heavy sides next to each other on each die)
would face down more as a percentage vs. the other faces.
I got the relative probabilities.
Thanks.
Sounds like a closed case to me.
winsome johnny (not Win some johnny)
February 26th, 2013 at 12:34:31 PM
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Quote: 7crapsHow about a water test?? Would a stick of dice from one manufacturer that are NOT biased displace less water in a container than from stick of dice that are biased???
Not sure if this comment is serious, but displacement and weight are two different properties. Displacement is directly related to an object's volume, unless the object is bouyant enough to float on top of the medium.
In regards to the water test, I had always thought that one uses a tall glass or vase filled with water, and one merely drops the die into the vase to see if one side consistently lands up/down.
February 26th, 2013 at 12:38:43 PM
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Quote: 7crapsI guess my intuition let me down. I am not at all versed in physics.
[snip]
Sounds like a closed case to me.
Not sure what is meant by that last comment, but, yes, a significant part of physics is "non-intuitive."
February 26th, 2013 at 1:32:18 PM
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Quote: 7crapsOK.
The one's that claim more 1s and 6s from heavier faces of 5s and 6s have shown the bias as percentages from actual casino dice rolls,they were there,
of course no data has been shown here except by Ahigh,
and one even claims before going into the casino, how the 1s and 6s will do.
probably knows the manufacture of the dice that the particular casino uses.
Some people claim they do know all these details (shrug). Not defending or attacking them, just pointing out how they -could- test for it.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
February 26th, 2013 at 2:39:07 PM
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Here's my original post where I talk about generating random data samples from a biased random number generator given six face weights.
https://wizardofvegas.com/forum/gambling/craps/12748-so-unbalanced-dice-everywhere-or-not/16/#post215753
https://wizardofvegas.com/forum/gambling/craps/12748-so-unbalanced-dice-everywhere-or-not/16/#post215753
aahigh.com
February 27th, 2013 at 9:07:41 AM
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Then one must pay a DI for a lesson on what set to use when percentage dice (biased) are suspected being used in a casino, how to spot percentage dice and run away if you are not a DI.Quote: thecesspitSome people claim they do know all these details (shrug).
Not defending or attacking them, just pointing out how they -could- test for it.
That gives this group of DIs a leg up on all the other DI lesson sellers.
Casinos know they could be using biased dice, because they are cheaper to buy.
Sounds good to me. More to study.
Go Ahigh, but do not let small sample sizes prove anything just because the results from the sample fit your hypothesis. (more 6-1 7s )
==========================
Hey thecesspit
you see this
http://aleph.sagemath.org/
try this R code in it (or another code)
(just a sample from fair (150) and biased dice (60))
die.fair = sample(1:6,150,p=c(1,1,1,1,1,1)/6,replace=T)
die.bias = sample(1:6,60,p=c(2,1,1,1,1,2)/8,replace=T)
res.fair = table(die.fair);res.bias = table(die.bias)
rbind(res.fair,res.bias)
chisq.test(rbind(res.fair,res.bias))
works just like my R program
slick!
winsome johnny (not Win some johnny)
February 27th, 2013 at 9:24:52 AM
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The idea of an influenced throw added in with theoretically biased dice is interesting.
I should make the point that I do not currently believe that biased dice exist. I am merely not rejecting the notion as firmly as I was before, and some data has supported the underlying theory.
I should make the point that I do not currently believe that biased dice exist. I am merely not rejecting the notion as firmly as I was before, and some data has supported the underlying theory.
aahigh.com
February 27th, 2013 at 10:22:00 AM
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I believe they exist.Quote: AhighI should make the point that I do not currently believe that biased dice exist.
I am merely not rejecting the notion as firmly as I was before, and some data has supported the underlying theory.
I have seen bad dice brand new. Many others have too.
I have also seen fair dice after 8 hours of use very biased, but normally from edges and side wear.
Many others have see this also.
Being it would be extremely costly to make a perfectly true and fair die, let alone 5 at a time, bias has to exist.
But to what degree and can it be proven to any degree of confidence?
It is easy to load a die but a casino would not willingly want that,
but does the material for the pips really differ in weight that much from the material removed to cause more bias?
winsome johnny (not Win some johnny)
February 27th, 2013 at 10:51:02 AM
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To me, it is not a matter of whether bad dice exist, but whether they are common or if some casinos purposefully use them. This last is the charge being made I believe.
Nothing should make a player happier than to know that there are biased dice being used, and biased in what way.
Nothing should make a player happier than to know that there are biased dice being used, and biased in what way.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
February 27th, 2013 at 4:29:32 PM
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You know I challenge any critics to do face counts. Six piles of chips. Add two chips per roll and color up as needed.
I made a seventh stack that represented an amount to add to each of the other six stacks.
You only need about $200 (about $25 in singles, $80 in nickels, and $75 in quarters). You can also just use pocket change instead of casino chips to make it cheaper, but they might frown a little more if you are using pocket change in the rail.
One person at least imagined me with my laptop in the rail of the craps table. I used the laptop away from the craps table. Specifically in the chair in front of Keno and later at Gardunio's restaurant. It would probably be wise in the future to do laptop stuff in the car where nobody can see what you're doing, but I didn't care!!
The serial number on the dice at Fiesta Rancho was 1199. If you get a similar serial number, it might be worth doing your own counts, or risking $100 to $200 in the field..
They SHOULD be scared if they know their dice are bad. Maybe they don't know. Maybe it's just randomly fitting what Harley described. Maybe they have plan to put in place once I start betting the $250 max in the field. They brought these dice out when I put $250 max on the passline though. That I can tell you for sure.
There were people with earpieces and people from security watching me as I had a whole lot of action on that table relative to what they were used to.
If I had went to grinding $250 in the field, I am pretty certain I would have won a lot of money, but like a dope, I did all that work and then went back to my normal play strategy and ended up losing a couple hundred bucks and left. The money I lost absolutely reflected the fact that I was doing big passline bets running into aces, ace-deuce and boxcars!
I made a seventh stack that represented an amount to add to each of the other six stacks.
You only need about $200 (about $25 in singles, $80 in nickels, and $75 in quarters). You can also just use pocket change instead of casino chips to make it cheaper, but they might frown a little more if you are using pocket change in the rail.
One person at least imagined me with my laptop in the rail of the craps table. I used the laptop away from the craps table. Specifically in the chair in front of Keno and later at Gardunio's restaurant. It would probably be wise in the future to do laptop stuff in the car where nobody can see what you're doing, but I didn't care!!
The serial number on the dice at Fiesta Rancho was 1199. If you get a similar serial number, it might be worth doing your own counts, or risking $100 to $200 in the field..
They SHOULD be scared if they know their dice are bad. Maybe they don't know. Maybe it's just randomly fitting what Harley described. Maybe they have plan to put in place once I start betting the $250 max in the field. They brought these dice out when I put $250 max on the passline though. That I can tell you for sure.
There were people with earpieces and people from security watching me as I had a whole lot of action on that table relative to what they were used to.
If I had went to grinding $250 in the field, I am pretty certain I would have won a lot of money, but like a dope, I did all that work and then went back to my normal play strategy and ended up losing a couple hundred bucks and left. The money I lost absolutely reflected the fact that I was doing big passline bets running into aces, ace-deuce and boxcars!
aahigh.com
February 27th, 2013 at 4:53:04 PM
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Ahigh I don't doubt your research at all. In a random situation -- what happens from the rolling of two dice in a random way -- you could see any multitude of results or patterns.
However, this doesn't mean your results can ever be duplicated by anyone else.
You talk about the dice having a bias, but what about your throw? What about your grip? What about your delivery? And you set your dice too, don't you? So where is the bias? Is the bias in the dice, in the throw, the grip, the bounce?
My point is this: publishing your "findings" will do nothing but spur debate and criticism. If you find that you can detect a bias, your next steps would be:
1. try to isolate the factor causing the bias
2. use the bias you detected to make more money playing craps
Arguing it here is useless. I don't know if the dice are biased or if your "set" or your "grip" or your "toss" creates the bias. On the other hand, putting biased dice in the hands of someone who throws the dice in a particular way could offset or cancel out the bias.
This is becoming a chicken or egg debate.
By the way, which came first, the chicken or the egg?
However, this doesn't mean your results can ever be duplicated by anyone else.
You talk about the dice having a bias, but what about your throw? What about your grip? What about your delivery? And you set your dice too, don't you? So where is the bias? Is the bias in the dice, in the throw, the grip, the bounce?
My point is this: publishing your "findings" will do nothing but spur debate and criticism. If you find that you can detect a bias, your next steps would be:
1. try to isolate the factor causing the bias
2. use the bias you detected to make more money playing craps
Arguing it here is useless. I don't know if the dice are biased or if your "set" or your "grip" or your "toss" creates the bias. On the other hand, putting biased dice in the hands of someone who throws the dice in a particular way could offset or cancel out the bias.
This is becoming a chicken or egg debate.
By the way, which came first, the chicken or the egg?
February 27th, 2013 at 5:01:40 PM
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Alan .... AHigh said his results came from 370 tosses of random rollers ... various rollers with the same biased variance existing throughout various subtotals of the 370 total ........... which just happens to be what I told him would happen --- I did not tell AHigh which casino to go to do this test .... I did say Saturday night would be a good time to test "Saturday night specials"
And his results are somewhat consistent with over 10,000. of our rolls gathered by at least 12 different dice charters
Anyone including the "Great Frank Scoblete" (retired) can become a victim of biased dice and Mother Nature unless they compensate for the imbalance
And his results are somewhat consistent with over 10,000. of our rolls gathered by at least 12 different dice charters
Anyone including the "Great Frank Scoblete" (retired) can become a victim of biased dice and Mother Nature unless they compensate for the imbalance
.... that is simply my opinion ....
Ciao,
Harley ...
Link = http://crapsadvantageplayers.blogspot.com/
February 27th, 2013 at 9:34:01 PM
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AlanMendelson
You got to love a gambler, even when you tell them there could be something wrong with what is happening, they will defend the casinos that are taking their money! They basically don't want to win anyway; they won't take the time to learn the games they play. They love the fiction they read, where you have a fiction writer, writing they are taking hundreds of thousands of dollars off the tables every year playing craps. These fiction writers will post photos of all the high end cars that they make like they are theirs, then you have the photos of the best restaurants, videos of all the places they write about, that they pull off places like YouTube, that are not theirs!
When you have players from all around the country saying the same thing about the cheap dice that are now in use, everybody that wants their money making machine to continue will write that there is no such thing and call Harley a nut case. They after all don't want that money making machine to dry up!
This all goes back to a warning that Harley put out about the dice and that was all it was, at the time! Then everybody that didn't want to see anything change, that owned a craps board or a school came out and changed what he was saying to make everybody think the dice were loaded or shaved, also saying the casinos wouldn't cheat, well sorry to say in this day and age just about every corporation cheats some how if the think they can get away with it!
There isn't a day that goes by that you couldn't pick up a news paper and find an article in it about them cheating in some way shape or form. Scandals run rampant now days, from the most trusted organization “The Church” to the people that are to protect us “The Police”! Gambling in this country is all about the money it generates for taxes. Here in NV, what is supposed to protect the players, the gaming board has no rules on what the casinos can use as dice. Basically they can do anything they want too, if you are stupid enough to play in their casino. There are no shortages of stupid players out there, which only play in a casino to have fun.
It's all entertainment to them, they come into Vegas with a gambling budget that they are going to lose, they are never at the tables long enough to see anything out of the ordinary. To them they just had a bad day at the casino, it didn't occur to them that just about all the 7's were coming the same way, they were just so happy to be at the tables having fun, hoping for the big score, that they have read about on the different craps boards, nor did it occur to them the reason why they were getting hassled when they missed the back wall one time if they were setting the dice. Could it have been because of all our great fiction writers on the game of craps, that write some of the best stories you ever wanted to read if you’re into fiction!
These guys that write all this BS has done more damage to the rest of the players that play craps, maybe that's why you have players that hate to see a so-called DI on the tables. Now days they get hassled too because they are getting lucky and are on a roll, I've seen true random rollers have the dice taking away from them, only because they were getting lucky. I've seen the same thing on the BJ tables, when you had a player that didn't even know that there was such a thing as card counting, it all goes back to the BS we all read about gambling!
Remember what Abert Einstein said; "If I can't picture it, I can't understand it."
99% of all the players can't picture it, can you?
The one that can are trying to do something about it, by posting what they have found!
You got to love a gambler, even when you tell them there could be something wrong with what is happening, they will defend the casinos that are taking their money! They basically don't want to win anyway; they won't take the time to learn the games they play. They love the fiction they read, where you have a fiction writer, writing they are taking hundreds of thousands of dollars off the tables every year playing craps. These fiction writers will post photos of all the high end cars that they make like they are theirs, then you have the photos of the best restaurants, videos of all the places they write about, that they pull off places like YouTube, that are not theirs!
When you have players from all around the country saying the same thing about the cheap dice that are now in use, everybody that wants their money making machine to continue will write that there is no such thing and call Harley a nut case. They after all don't want that money making machine to dry up!
This all goes back to a warning that Harley put out about the dice and that was all it was, at the time! Then everybody that didn't want to see anything change, that owned a craps board or a school came out and changed what he was saying to make everybody think the dice were loaded or shaved, also saying the casinos wouldn't cheat, well sorry to say in this day and age just about every corporation cheats some how if the think they can get away with it!
There isn't a day that goes by that you couldn't pick up a news paper and find an article in it about them cheating in some way shape or form. Scandals run rampant now days, from the most trusted organization “The Church” to the people that are to protect us “The Police”! Gambling in this country is all about the money it generates for taxes. Here in NV, what is supposed to protect the players, the gaming board has no rules on what the casinos can use as dice. Basically they can do anything they want too, if you are stupid enough to play in their casino. There are no shortages of stupid players out there, which only play in a casino to have fun.
It's all entertainment to them, they come into Vegas with a gambling budget that they are going to lose, they are never at the tables long enough to see anything out of the ordinary. To them they just had a bad day at the casino, it didn't occur to them that just about all the 7's were coming the same way, they were just so happy to be at the tables having fun, hoping for the big score, that they have read about on the different craps boards, nor did it occur to them the reason why they were getting hassled when they missed the back wall one time if they were setting the dice. Could it have been because of all our great fiction writers on the game of craps, that write some of the best stories you ever wanted to read if you’re into fiction!
These guys that write all this BS has done more damage to the rest of the players that play craps, maybe that's why you have players that hate to see a so-called DI on the tables. Now days they get hassled too because they are getting lucky and are on a roll, I've seen true random rollers have the dice taking away from them, only because they were getting lucky. I've seen the same thing on the BJ tables, when you had a player that didn't even know that there was such a thing as card counting, it all goes back to the BS we all read about gambling!
Remember what Abert Einstein said; "If I can't picture it, I can't understand it."
99% of all the players can't picture it, can you?
The one that can are trying to do something about it, by posting what they have found!
Note, all my post start with this is just my opinion...!
You do good brada ..!
superrick
Winning comes from knowledge and skill when your betting and not reading fiction
http://procraps4u2.myfanforum.org/index.php
...
February 27th, 2013 at 10:24:00 PM
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If you go and bet the table max on the passline at a place that normally runs a $3 game and has lots of finger snappers hanging around, you might be able to coerce out a stick of these dice yourself.
I had over four figures in the rail at a place where most people had $20 in the rail. And as soon as I started betting $250 passline bets, these dice came out and got swapped into the game.
I'll give them credit for not taking them OFF the table after I blatantly TOLD them the face counts gave a 2% per roll exposure to the player if the weights continued as they had been recorded.
The table dumped over $1,000 to a guy who was listening to me and bet the field for $100 while I rolled multiple twelves, aces, and many other field rolls into his bets. He even threw me red chips and I accepted them. Something that hasn't happened for years. I was very explicitly telling everyone at the table that the field had a player advantage. I meant it sort of as a joke to the casino and in jest, but it absolutely held true.
I made my money back rolling max odds on a four point. It's easier to roll fours and tens with heavy aces and sixes, and I hit the four to make back a nice little chunk.
If you are familiar with this casino, ask Vern about the event. He's a dealer there that I was telling him what I was doing as I was doing it, and he witnessed the crazy field betting afterwards. He said he also plays at the Cosmo himself, so he's a player too.
Sam assigned herself as my host after this took place, and I think Harry was also behind the pit watching some of this stuff. Feel free to ask about it: it all happened on Sunday Feb 24th, 2013, from around noon all the way until 9:00pm.
But you guys who don't even read all the details of this and come in with your comments, how about you do the work. I busted my ass all day long doing this specifically on Harley's information that he shared with me the day before. And as it turns out, I experience EXACTLY the profile that he described in SPITE of the fact that I thought it would HIGHLY UNLIKELY and in fact the EXPOSURE IN THE FIELD from what he described was something I already knew about from my models, so it wasn't a surprise that the field was exposed, it was only a surprise that it was successfully exploited WHILE TELLING THE CASINO WHAT WAS BEING DONE WHILE DOING IT.
A casino that is on the up-and-up would allow us to collect more samples on this stick of dice and dig deeper into this issue. However, I have not received any cooperation from any casinos in terms of helping reveal what might be going on with regards to any of this stuff. They all clam up and claim that the information is secret.
But let me ask a question: why does it need to be a secret? What is being hidden? Why can't I put these dice in my balance and test them myself? Why will the casinos not tell me more information about this issue?
Harley brings up these questions, but unlike other aspects of the game, the details about the dice are only known by a very small group of people. The dealers, for example, don't do anything put take the dice and put them on the table. Lots of stuff is being done to decide when new dice go in and which dice go in and on what basis. These details should be explained, and players should have the option to have assurances that the dice are fair, and currently they generally do not.
Truly, there is no excuse for not keeping statistics on the dice for all players to see. A distribution for face outcomes has got to be the simplest thing to do for a stick man or a box man. There's really no excuse for not keeping track of it even for the casino's benefit. If the dice are failing a chi-squared test on the faces, why continue to have them in play? Randomness is fairness when it comes to dice outcomes.
I had over four figures in the rail at a place where most people had $20 in the rail. And as soon as I started betting $250 passline bets, these dice came out and got swapped into the game.
I'll give them credit for not taking them OFF the table after I blatantly TOLD them the face counts gave a 2% per roll exposure to the player if the weights continued as they had been recorded.
The table dumped over $1,000 to a guy who was listening to me and bet the field for $100 while I rolled multiple twelves, aces, and many other field rolls into his bets. He even threw me red chips and I accepted them. Something that hasn't happened for years. I was very explicitly telling everyone at the table that the field had a player advantage. I meant it sort of as a joke to the casino and in jest, but it absolutely held true.
I made my money back rolling max odds on a four point. It's easier to roll fours and tens with heavy aces and sixes, and I hit the four to make back a nice little chunk.
If you are familiar with this casino, ask Vern about the event. He's a dealer there that I was telling him what I was doing as I was doing it, and he witnessed the crazy field betting afterwards. He said he also plays at the Cosmo himself, so he's a player too.
Sam assigned herself as my host after this took place, and I think Harry was also behind the pit watching some of this stuff. Feel free to ask about it: it all happened on Sunday Feb 24th, 2013, from around noon all the way until 9:00pm.
But you guys who don't even read all the details of this and come in with your comments, how about you do the work. I busted my ass all day long doing this specifically on Harley's information that he shared with me the day before. And as it turns out, I experience EXACTLY the profile that he described in SPITE of the fact that I thought it would HIGHLY UNLIKELY and in fact the EXPOSURE IN THE FIELD from what he described was something I already knew about from my models, so it wasn't a surprise that the field was exposed, it was only a surprise that it was successfully exploited WHILE TELLING THE CASINO WHAT WAS BEING DONE WHILE DOING IT.
A casino that is on the up-and-up would allow us to collect more samples on this stick of dice and dig deeper into this issue. However, I have not received any cooperation from any casinos in terms of helping reveal what might be going on with regards to any of this stuff. They all clam up and claim that the information is secret.
But let me ask a question: why does it need to be a secret? What is being hidden? Why can't I put these dice in my balance and test them myself? Why will the casinos not tell me more information about this issue?
Harley brings up these questions, but unlike other aspects of the game, the details about the dice are only known by a very small group of people. The dealers, for example, don't do anything put take the dice and put them on the table. Lots of stuff is being done to decide when new dice go in and which dice go in and on what basis. These details should be explained, and players should have the option to have assurances that the dice are fair, and currently they generally do not.
Truly, there is no excuse for not keeping statistics on the dice for all players to see. A distribution for face outcomes has got to be the simplest thing to do for a stick man or a box man. There's really no excuse for not keeping track of it even for the casino's benefit. If the dice are failing a chi-squared test on the faces, why continue to have them in play? Randomness is fairness when it comes to dice outcomes.
aahigh.com
February 27th, 2013 at 10:43:31 PM
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For those of you who believe in biased, weighted, unfair dice -- how much of a weight differential is needed to influence the appearance of one face over another?
If there were biased dice, could a shooter simply take some extra time to choose the two dice prior to his first roll and discover the weighted side by casually rolling the dice in front of him -- as shooters normally do?
Harley, what percentage weight difference do you suppose there is with the 6 and 5 faces over the other faces of the dice? And if true, why should I fear rolling a 7? If all 6s and 5s are heavier I should be making a fortune on betting just the top half of the horn!
So my question is -- and this goes to all of you who believe the dice are not fair -- how much of a difference does the difference make? Under what circumstances does the difference have a bigger impact? Does the bias show up more from SR1 or from straight out? Does the bias show more with a backspin or a throw to the center of back wall?
If there were biased dice, could a shooter simply take some extra time to choose the two dice prior to his first roll and discover the weighted side by casually rolling the dice in front of him -- as shooters normally do?
Harley, what percentage weight difference do you suppose there is with the 6 and 5 faces over the other faces of the dice? And if true, why should I fear rolling a 7? If all 6s and 5s are heavier I should be making a fortune on betting just the top half of the horn!
So my question is -- and this goes to all of you who believe the dice are not fair -- how much of a difference does the difference make? Under what circumstances does the difference have a bigger impact? Does the bias show up more from SR1 or from straight out? Does the bias show more with a backspin or a throw to the center of back wall?
February 27th, 2013 at 11:20:00 PM
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Quote: AlanMendelsonIf all 6s and 5s are heavier I should be making a fortune on betting just the top half of the horn!
The 6 and 5 faces could also be the lightest sides, depending on the pip density relative to the density of the dice body material.
Also, if such an imbalance were true, the heaviest face would show a propensity to land face-up, as well as the lightest face.
Quote: AlanMendelsonSo my question is -- and this goes to all of you who believe the dice are not fair -- how much of a difference does the difference make?
I don't think that all dice are necessarily significantly unbalanced, but, apparently for Ahigh, a possible unbalance made this much difference.
It is all in the OP, if you would take time to read it.
February 28th, 2013 at 12:04:37 AM
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Actually tupp its not all in the original post. What about the uneveness of the felt on the table, the unevenness of the bounce and the back wall, the unevenness of the random throws.
Lets get back to my question:
How much of a difference is the difference? Will I be able to detect the bias by rolling the dice in front of me a few inches, or by bouncing them in my hands? Will the bias be more apparent after throwing the dice four feet or eight feet? Will the bias show up more with a hard throw or a soft throw? What if I use a cross sixes set -- will that offset the bias enough?
come on, I want some specifics, not just pretty charts of numbers that showed up.
I want to see the evidence -- the proof that the dice are biased. Someone cut up the dice, weigh and measure each section. Give me the proof.
None of this is proof that dice are biased-- weighted, shaved or otherwise.
Lets get back to my question:
How much of a difference is the difference? Will I be able to detect the bias by rolling the dice in front of me a few inches, or by bouncing them in my hands? Will the bias be more apparent after throwing the dice four feet or eight feet? Will the bias show up more with a hard throw or a soft throw? What if I use a cross sixes set -- will that offset the bias enough?
come on, I want some specifics, not just pretty charts of numbers that showed up.
I want to see the evidence -- the proof that the dice are biased. Someone cut up the dice, weigh and measure each section. Give me the proof.
None of this is proof that dice are biased-- weighted, shaved or otherwise.
February 28th, 2013 at 12:39:10 AM
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Quote: AlanMendelsonActually tupp its not all in the original post. What about the uneveness of the felt on the table, the unevenness of the bounce and the back wall, the unevenness of the random throws.
Those characteristics are irrelevant, because all of the shooters were random -- as was mentioned in the original post.
Quote: AlanMendelsonLets get back to my question: How much of a difference is the difference?
That question is already answered in the OP (and in the very chart that I linked): 130 1s; 125 2s; 108 3s; 125 4s; 119 5s; and 142 6s. That is "how much of a difference is a difference." According to Ahigh, folks made a decent profit off of that difference.
Quote: AlanMendelsonWill I be able to detect the bias by rolling the dice in front of me a few inches, or by bouncing them in my hands? Will the bias be more apparent after throwing the dice four feet or eight feet? Will the bias show up more with a hard throw or a soft throw? What if I use a cross sixes set -- will that offset the bias enough? come on, I want some specifics, not just pretty charts of numbers that showed up.
Again, the shooters were random (as mentioned in the OP), so any questions about attempts to influence the rolls is immaterial.
Quote: AlanMendelsonI want to see the evidence -- the proof that the dice are biased.
No doubt that you do, but evidence and proof are two different things. The evidence has already been presented.
Quote: AlanMendelsonSomeone cut up the dice, weigh and measure each section. Give me the proof.
Perhaps you could go to the actual casino where these rolls took place and make such demands.
Quote: AlanMendelsonNone of this is proof that dice are biased-- weighted, shaved or otherwise.
Of course, these results are not proof. Nobody claimed that they are proof. However, these results are evidence.
