Biased Dice: The science begins
May 10th, 2013 at 3:38:25 PM
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Is this your way of suggesting or stating that I am not an experienced craps player? It sure sounds like it. Why would you presume such a thing?Quote: AhighA fact that I believe any experienced craps player should learn if they don't already know.
I assure you that I know the difference between edge per bet made vs. edge per bet resolved vs. edge per roll. The fact that it is "just your way to only use per roll" doesn't make that the best way or the only way. Though it is helpful to be clear so that we are comparing apples with apples.
You said, specifically, If you bet the don't pass with maximum odds on a $5 table, you're edge is 0.40% or $0.02 per roll. I questioned you because that is not a true statement. Even the math alone is wrong.
I also know that the house edge on the don't pass line without any odds is 0.40% per roll. The house edge per roll is obviously much lower than that with "maximum odds" but I don't know what you mean by "maximum odds." It is 0.081% at 3x-4x-5x odds and I believe 0.037% at 10x and I think under 0.020% at 20x.
I also questioned you since I could not believe you were willing to offset the casino's house edge on my average bet by one-half which is what I thought you were saying.
May 10th, 2013 at 4:02:11 PM
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Yeah, the edge on the non free bet, not the combined edge. You are correct. And no I'm not trying to say you're inexperienced. I am trying to say you should recognize 0.4% as the edge per roll on a don't with no odds, though.
Anyway, let's not focus on arguing percentages. The minimum cost is two cents per roll, and I'm offering to lower that minimum cost to $0.01 per roll if they click some buttons.
KISS.
Anyway, let's not focus on arguing percentages. The minimum cost is two cents per roll, and I'm offering to lower that minimum cost to $0.01 per roll if they click some buttons.
KISS.
aahigh.com
May 10th, 2013 at 4:09:09 PM
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I assure you that I recognize and know exactly the house edge on the don't. I also recognize many things in your posts.Quote: AhighI am trying to say you should recognize 0.4% as the edge per roll on a don't with no odds, though.
May 10th, 2013 at 4:11:12 PM
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Quote: JimboI assure you that I recognize and know exactly the house edge on the don't. I also recognize many things in your posts.
I made an mistake saying the edge was 0.4% per roll with max odds. I didn't clarify that this is the edge on the only bet with an edge. The Wizard calculates a "combined edge" but that's more of a weighted formula. But still I made a mistake, alright?
Anyway, as long as we both understand, there's no point to argue about this stuff. I mean I'm offering real money here at a penny a roll. I think everybody gets that, right?
aahigh.com
May 10th, 2013 at 4:13:39 PM
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Quote: JimboThough it is clear from my previous remarks that I believe this endeavor will accomplish nothing, I am curious by your comment. I am a Don't player who is regularly in Vegas. I don't see what you are proposing in the data gathering process that will "cut my edge." (And did you really mean to say that as a Don't player, I have an edge that I am willing to cut?)
Here's where it sounded to me like you thought I was claiming that a don't player has an edge against the house.
This did make me wonder about your experience level FWIW. But just to recap all of this, I'm just trying to offer someone to cover half the minimum cost to be at the table while they are working for me pushing buttons. Basically I'm offering half a cent for each time they press a button. It seems really pragmatic and simple to me, but I know we all get wrapped up in arguments.
Also to recap all of this I absolutely positively do not expect a single other person to be willing to even do this even with my incentive added. People are lazy in general, and this is work, and it doesn't pay much at all.
The only way it might actually happen is if there is someone who really just wants to cut his edge down to the bone at a penny a roll and find a place that offers high max lay odds.
If this were me taking up this offer, I would probably go to Cosmopolitan, LVH, and all Harrah's properties, and maybe some Boyd Properties with higher maximum odds and try to have fun with it. As far as my play time, I would prefer to stay on the do side of things and I generally never want to play at the places I would be going to if I were to be doing this type of sampling myself.
aahigh.com
May 10th, 2013 at 5:55:31 PM
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Can anyone explain how to derive that 0.4% edge? I'm never going to be anywhere near the math elite here, but .014 times $5.00 seems to come out at 7 cents.Quote: AhighI am trying to say you should recognize 0.4% as the edge per roll on a don't with no odds, though. Anyway, let's not focus on arguing percentages. The minimum cost is two cents per roll.
May 10th, 2013 at 5:58:49 PM
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Quote: SanchoPanzaCan anyone explain how to derive that 0.4% edge? I'm never going to be anywhere near the math elite here, but .014 times $5.00 seems to come out at 7 cents.
That's per bet. Divide by 3.375 rolls per bet to get roughly 2 cents per roll.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 10th, 2013 at 6:09:56 PM
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Quote: JimboAhigh, what exactly is the motivation for doing this?
Might it be that certain "dice influencers" need a scapegoat to explain why their technique doesn't work as expected?
I recall one of Ahigh's early Internet TV shows when he was surprised that he was throwing so many 7s and I believe it was Harley who pointed out that the die or dice that Ahigh was using may have been biased. I think that was the genesis of all this, and fueled the biased dice conspiracy theory.
Yes, blaming it on the dice would be a good "way out" for the DIs to explain why their sets and tosses aren't working.
Edited to add: there have also been allegations that dice are changed to a biased set when the table is dumping too much money. I know for a fact that the dice are changed at certain fixed times at Caesars. I know that because when I play there its often for a stretch of hours at a time. I do not know the procedures at other casinos.
And for the record, I have been at tables at Caesars when the same dice from the bowl have been used for monster rolls and for point-7s and dice are NEVER changed while a shooter has them during his hand.
May 10th, 2013 at 6:12:50 PM
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Close, but no cigar
The number of rolls to resolve a pass line or DP is
12/36 (2, 3, 7, 11, 12).
6/36 * 5 (36/9)+1 [4,10]
8/36 * 4.6 (36/10)+1 [5,9]
10/36 * 4.273 (36/11)+1 [6,8]
3.70909 rolls to resolve a pass line / don't pass.
1.364% HA for DP = .368% HA per roll.
1.414% HA for Pass = .381% HA per roll.
The number of rolls to resolve a pass line or DP is
12/36 (2, 3, 7, 11, 12).
6/36 * 5 (36/9)+1 [4,10]
8/36 * 4.6 (36/10)+1 [5,9]
10/36 * 4.273 (36/11)+1 [6,8]
3.70909 rolls to resolve a pass line / don't pass.
1.364% HA for DP = .368% HA per roll.
1.414% HA for Pass = .381% HA per roll.
-----
You want the truth! You can't handle the truth!
May 10th, 2013 at 6:39:34 PM
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Quote: boymimboClose, but no cigar
The number of rolls to resolve a pass line or DP is
12/36 (2, 3, 7, 11, 12).
6/36 * 5 (36/9)+1 [4,10]
8/36 * 4.6 (36/10)+1 [5,9]
10/36 * 4.273 (36/11)+1 [6,8]
3.70909 rolls to resolve a pass line / don't pass.
1.364% HA for DP = .368% HA per roll.
1.414% HA for Pass = .381% HA per roll.
Your equation doesn't yield 3.70909 on my calculator. The formula is right, though.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 10th, 2013 at 6:46:33 PM
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Close, but no cigarQuote: boymimboClose, but no cigar
The number of rolls to resolve a pass line or DP is
12/36 (2, 3, 7, 11, 12).
6/36 * 5 (36/9)+1 [4,10]
8/36 * 4.6 (36/10)+1 [5,9]
10/36 * 4.273 (36/11)+1 [6,8]
3.70909 rolls to resolve a pass line / don't pass.
1.364% HA for DP = .368% HA per roll.
1.414% HA for Pass = .381% HA per roll.
What buttons did you press??
https://wizardofodds.com/ask-the-wizard/craps/probability/
In one of your answers you state that the average number of rolls for a shooter in craps is 8.522551. How is that number obtained?
The Wizard
"So the expected number of throws per round is 1+(2/3)*((3/12)*4 + (4/12)*3.6 + (5/12)*(36/11)) = 3.375758."
Using the perfect 1980 table I also get =557/165
Bet
Pass, come,
Expected Rolls: 3.38
Per Bet Made: 1.41%
Per Roll: 0.42%
Don't pass, don't come
Expected Rolls: 3.38
Per Bet Made: 1.36%
Per Roll: 0.40%
https://wizardofodds.com/games/craps/appendix/2/
More biased dice
biased dice
dice
winsome johnny (not Win some johnny)
May 10th, 2013 at 7:28:55 PM
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Face faces face counts. Round 1
| Face Up | Day #1 |
|---|---|
| 1 | 82 |
| 2 | 56 |
| 3 | 94 |
| 4 | 72 |
| 5 | 85 |
| 6 | 66 |
| Total | 455 |
The opinions of this moderator are for entertainment purposes only.
May 10th, 2013 at 7:32:02 PM
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Interesting, good luck with the task.
I am a robot.
May 10th, 2013 at 7:36:50 PM
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more 7654 roll sample setsQuote: WizardHere is my analysis of the Midgley results.
First, one die at a time.
Die Observations Expected Chi-squared 1 2498 2551.33 1.114885 2 2647 2551.33 3.587188 3 2606 2551.33 1.171327 4 2590 2551.33 0.586012 5 2462 2551.33 3.127951 6 2505 2551.33 0.841434 Total 15308 15308.00 10.428795
The p value for a chi-squared statistic of 10.428795 with 5 degrees of freedom is 0.063958.
Next, the sum of the two dice.
Total Observations Expected Chi-squared 2 210 212.61 0.032067 3 433 425.22 0.142264 4 656 637.83 0.517420 5 858 850.44 0.067125 6 1065 1063.06 0.003557 7 1265 1275.67 0.089191 8 1067 1063.06 0.014636 9 867 850.44 0.322286 10 652 637.83 0.314650 11 399 425.22 1.617048 12 182 212.61 4.407296 Total 7654 7654.00 7.527541
The p value for a chi-squared statistic of 7.527541 with 10 degrees of freedom is 0.674878.
So, these throws look random to me.
would show on average that 67.5% of the results would be equal to or more further from expectation.
Since the observed data was compared to expectations of fair dice, the null hypothesis would be accepted.
That these results came from fair dice.
No eyebrows to even raise.
more
dice
winsome johnny (not Win some johnny)
May 10th, 2013 at 7:38:27 PM
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Quote: onenickelmiracleInteresting, good luck with the task.
No promises =)
The opinions of this moderator are for entertainment purposes only.
May 10th, 2013 at 8:03:58 PM
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Corrected stand I do young Jedi master. 3.375758 rolls it is.
-----
You want the truth! You can't handle the truth!
May 10th, 2013 at 8:12:20 PM
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Tks. I'll stick with the more meaningful original calculation of tosses that cause resolutions of the bets. The intervening tosses of the dice are for all intents and purposes meaningless.Quote: SanchoPanzaCan anyone explain how to derive that 0.4% edge?
Quote: MathExtremistThat's per bet. Divide by 3.375 rolls per bet to get roughly 2 cents per roll.
May 10th, 2013 at 10:51:08 PM
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Quote: SanchoPanzaTks. I'll stick with the more meaningful original calculation of tosses that cause resolutions of the bets. The intervening tosses of the dice are for all intents and purposes meaningless.
That is absolutely true making the assumption that you only have one bet at a time that has an edge!
If you consider the combination of all bets on the table as one bet, the (weighted) edge per roll is the only sane way to proceed. Multiplying the weighted edge per roll by the average bet amount is the best way to calculate average cost for playing the game. And it is a function of the number of rolls, not a function of the number of bets placed unless you always and consistently bet the bet until resolution (something I don't personally do FWIW).
Some examples of bets that I take:
$110 even working. -- combination of buy the 4 and 10 for $25 each and a $30 six and a $30 eight. This combo-bet pays $49 for a four or a ten and $35 for a six or an eight. Each payment costs exactly a $1 vig.
Edge per roll is ( ( 50/110 ) * 0.33 + ( 60/110 ) * 0.46 ) = 0.401 -- better than the pass line with no odds, plus .. compared to the pass line, I am only committed for a single roll.
If I "hit it and quit it" meaning that I bring the bet down on the first hit, it lasts for 1.63 rolls. So the bet that isn't marked on the table that I can roll any even box number before a seven is only a 1/160 edge when I hit a four or a ten and a 1/146 edge when I hit a 6 or an 8. The 4 or 10 is 6/16th of the win events and the 6 and 8 is 10/16th of the win events. So the edge per bet resolved on this bet that I am creating here is ((1/160)*(6/16))+((1/146)*(10/16)) = 0.66% per resolved bet. If you and your thinking that edge per bet resolved is the best way to go, then I advise you to follow through and create some of your own bets and take those bets because you can get a much lower edge by putting more money at risk! I'm pointing out that I don't think that way because looking at edge per bet resolved makes an assumption that you will be done with a single resolved bet. Instead I don't look at it that way. I look exclusively at edge per roll and I try to make the fewest number of bets possible keeping my edge per roll low (minimize hedging) and try to win in as few tosses as possible and go with a profit if I can get it.
Here's another bet that I look at in terms of two bets combined...
Hard 8 for $1 and place the eight for $30:
Edge per roll is ((1/31) * 2.78) + ((30/31) * 0.46) = 0.535% edge per roll -- you can focus on the hard 8 having a high edge, or you can look at the total edge being relatively low. Increasing the edge per roll from 0.46% to 0.53% is a 15% increase in the edge. I consider the combination of these two bets a single bet. That's just how I look at it. Sure it's not on the felt, but I'm betting on the eight, and I get paid a little more if it comes hard.
Now I'm not saying people that don't do this have anything wrong with them, but I am saying that looking at the weighted edge per roll is just another way of analyzing the game where you don't get all upset about one leg of a complex series of bets having a high edge if the weighted average is sufficiently low .. it's a big picture sort of way to look at the game that to me is perfectly sane.
The correlary is that you will never find me betting a single $5 bet on the four on my or anyone else's roll. That's a 6.66% edge and 1.66% edge per roll! TERRIBLE!!!
My cutoff point is 1.00% edge per roll. And generally speaking, I don't usually take bets that sum up to more than 0.8% edge per roll under any circumstances. I have recently made exceptions for playing crapless in order to get bigger pays on crap numbers, which on a regular table, I have no low edge way to get paid on the 12, and the only low edge way to get paid on an ace-deuce is from a DC bet.
aahigh.com
May 11th, 2013 at 10:46:50 AM
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Thanks to face for having the first submission of face counts. I do want to remind everyone to try to document details of the casino and the dice being used. Even if you don't post them on the board, please try to have them handy. I understand folks might not want to reveal their identity, so I can work with those issues.
aahigh.com
May 11th, 2013 at 6:43:08 PM
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Gonna have weird dreams tonight...
| Face Up | Sample #1 | Sample #2 | Running Total |
|---|---|---|---|
| 1 | 82 | 80 | 162 |
| 2 | 56 | 96 | 152 |
| 3 | 94 | 100 | 194 |
| 4 | 72 | 108 | 180 |
| 5 | 85 | 94 | 179 |
| 6 | 66 | 112 | 178 |
| Total | 455 | 590 | 1,045 |
The opinions of this moderator are for entertainment purposes only.
May 11th, 2013 at 9:56:16 PM
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I was at Gold Coast tonight and I was gonna pull out the counter, but I didn't, and instead I did a roll and got up about $60 and figured that was good enough. I ate on a coupon and won another $30 on another shooter before I left.
I did notice that they brought out TK dice with the pink logo and clear (non-frosted) finish (red colored dice). I did not pay attention to the serial number, though.
Thanks for your efforts, Face! I don't know if you tried the spreadsheet I have that lets you put in face counts and calculates house edge for a non-evenly distributed random number generator that matches the frequency of face outcomes, but it might be interesting to make bets according to trends. If you bring a laptop with the spreadsheet you might even be able to poke in some numbers on a break and come back.
Free odds on the 4, 5, 6, 8, 9, 10 look like this for the running total:
-0.9165% -0.5480% -0.1379% 0.4788% 1.6783% 0.9445%
Lay with commission up front looks like this
0.2551% 0.0070% -0.4404% -0.9543% -1.4772% -0.6754%
Passline Don't pass
0.5417% -3.4431%
I did notice that they brought out TK dice with the pink logo and clear (non-frosted) finish (red colored dice). I did not pay attention to the serial number, though.
Thanks for your efforts, Face! I don't know if you tried the spreadsheet I have that lets you put in face counts and calculates house edge for a non-evenly distributed random number generator that matches the frequency of face outcomes, but it might be interesting to make bets according to trends. If you bring a laptop with the spreadsheet you might even be able to poke in some numbers on a break and come back.
Free odds on the 4, 5, 6, 8, 9, 10 look like this for the running total:
-0.9165% -0.5480% -0.1379% 0.4788% 1.6783% 0.9445%
Lay with commission up front looks like this
0.2551% 0.0070% -0.4404% -0.9543% -1.4772% -0.6754%
Passline Don't pass
0.5417% -3.4431%
aahigh.com
May 11th, 2013 at 10:43:03 PM
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Quote: FaceGonna have weird dreams tonight...
Face Up Sample #1 Sample #2 Running Total 1 82 80 162 2 56 96 152 3 94 100 194 4 72 108 180 5 85 94 179 6 66 112 178 Total 455 590 1,635
p value on sample #1 = 0.027238516
p value on sample #2 = 0.256958403
p value on combined sample = 0.274211156
Also, the total of the running total is 1045.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 12th, 2013 at 5:41:29 AM
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I presume the percentages are house edges (since that is in reference to what you are discussing in this particular post). If not, what does this mean?Quote: AhighFree odds on the 4, 5, 6, 8, 9, 10 look like this for the running total:
-0.9165% -0.5480% -0.1379% 0.4788% 1.6783% 0.9445%
Lay with commission up front looks like this
0.2551% 0.0070% -0.4404% -0.9543% -1.4772% -0.6754%
Passline Don't pass
0.5417% -3.4431%
Please help me understand this.
Regardless what your percentages mean, are you saying that you derive conclusions as to the distribution of "dice combinations" from simply the report of individual die face counts??
And you can also derive or determine Passline and Don't Pass results (again, I don't know for certain what your percentages mean, if not house edges) also from simply the individual die face counts??
How???
May 12th, 2013 at 9:35:10 AM
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Quote: JimboI presume the percentages are house edges (since that is in reference to what you are discussing in this particular post). If not, what does this mean?
Please help me understand this.
Regardless what your percentages mean, are you saying that you derive conclusions as to the distribution of "dice combinations" from simply the report of individual die face counts??
And you can also derive or determine Passline and Don't Pass results (again, I don't know for certain what your percentages mean, if not house edges) also from simply the individual die face counts??
How???
An excel spreadsheet. These percentages are based on a continued distribution of face outcomes as observed. With a couple hundred samples, the edges are not very meaningful at all, but with millions of samples, you have a pretty good view on the reality of how the outcomes of the faces are affecting the free odds and free lay odds bets for the average casino die as sampled.
The negative percentages are in the house's favor. The positive percentages are in the player's favor.
The values are calculated using an excel spreadsheet. And yes, I determine the passline and don't passline as well. When you have a flat distribution of face counts, it shows -1.41% and -1.36% in the spreadsheet, and all the odds bets are 0.0000% and the lay with commission up front are all negative edges for the vig. The free lay odds bets are just the negative representation of the odds bets of course.
I think 7craps found one error in the way I calculated the vig in the lay odds with commission, so there may be an error in those percentages, but the free odds and line bet percentages I'm pretty sure are accurate.
aahigh.com
.jpeg "Bohemian"){kind=small}
May 12th, 2013 at 11:12:59 AM
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Quote: AhighThanks for your efforts, Face! I don't know if you tried the spreadsheet I have that lets you put in face counts and calculates house edge for a non-evenly distributed random number generator that matches the frequency of face outcomes, but it might be interesting to make bets according to trends. If you bring a laptop with the spreadsheet you might even be able to poke in some numbers on a break and come back.
Ahigh, where is this spreadsheet for inputting?
May 12th, 2013 at 11:57:43 AM
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Quote: WizardAlso, the total of the running total is 1045.
Fixed. I need a nap...
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May 12th, 2013 at 12:56:48 PM
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I don't claim to know much about math, but how can measuring individual faces be used to figure odds or edge when it takes two dice and a combination of two die faces to come up with a "number"?
May 12th, 2013 at 1:55:19 PM
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Quote: AlanMendelsonI don't claim to know much about math, but how can measuring individual faces be used to figure odds or edge when it takes two dice and a combination of two die faces to come up with a "number"?
This isn't odds or edges, this is biased dice.
We all know that all die must have bias, since the tolerances aren't to aerospace+ standards. However, there are those who say the bias is enough to be exploitable. Not only that, but that the manufacturers and even the casinos are in on it.
I know for a fact every single die is biased. I believe with all my heart that it's not enough to matter. I also believe that even if it was, it would at the very least be difficult to the point of impossibility for someone to identify a bias and take advantage in the lifetime of a stick.
I'm tired of supposition, I'm tired of assumption, and I'm tired of conspiracy theories that are allowed to exist simply because there's been no proof. I'm also too curious for my own good. I'm also foolish enough to believe that once this "prooves" die are fair, that the biased die conversation will never be heard from again =P
In short, I'm fighting a losing battle but am learning enough for it to be worth it. I just wonder if I should be couting the faces of the rolls I see in my sleep...
The opinions of this moderator are for entertainment purposes only.
May 12th, 2013 at 2:16:31 PM
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Quote: Face
I know for a fact every single die is biased. I believe with all my heart that it's not enough to matter. ..
I believe every roulette wheel is biased, but not
enough to matter. In the long run, where the
stats count, its just not enough of a bias to make
any kind of real difference.
"It's not called gambling if the math is on your side."
May 12th, 2013 at 2:22:11 PM
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Quote: AlanMendelsonI don't claim to know much about math, but how can measuring individual faces be used to figure odds or edge when it takes two dice and a combination of two die faces to come up with a "number"?
The concept about which you are asking is very basic and fundamental to probability and gambling.
Let's say that you have a pair of dice, and each die is somehow excessively biased such that the ace is rolled 50% of the time. In that case, snake eyes should appear in 1/4 (25%) of the rolls.
In another example, if one die is biased as above (the ace appears in 50% of rolls) while the other die is unbiased, then snake eyes should happen 1/12th (8.333%) of the time.
In contrast, unbiased, randomly-tossed dice should yield snake eyes 1/36th (2.778%) of the time.
May 12th, 2013 at 2:31:05 PM
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Face, I agree with you. I think that IF a bias is detected the difference won't be much of a difference or won't even make a difference. I also reject the conspiracy theory. But Ahigh (if I read him correctly) appears to be making some sort of statement that by counting individual faces he can determine which numbers are a better bet? Is that right? The way I've been playing the game, it doesn't matter what one die shows a 6 because it matters what the other die is also showing and the two combined show the "roll."
But as I said, I'm not a "math guy" so if I am missing something I'd like to know what it is?
I do understand that if one die is ALWAYS showing a 6 then we will never see a "roll" with a number less than 7. But even if one die was always a 6 we'd still have a distribution of 7, 8, 9, 10, 11, 12.
I guess if you believe in the conspiracy theory, you'll want to justify it by throwing in some math, too.
Face, I don't think you are fighting a losing battle. I think if the "bias dice conspiracy believers" want to make their case, they should be allowed to make it here. At least we'll be able to see their reasons. I'm all for full disclosure even though I don't believe any casino would ever want to use biased dice.
But as I said, I'm not a "math guy" so if I am missing something I'd like to know what it is?
I do understand that if one die is ALWAYS showing a 6 then we will never see a "roll" with a number less than 7. But even if one die was always a 6 we'd still have a distribution of 7, 8, 9, 10, 11, 12.
I guess if you believe in the conspiracy theory, you'll want to justify it by throwing in some math, too.
Face, I don't think you are fighting a losing battle. I think if the "bias dice conspiracy believers" want to make their case, they should be allowed to make it here. At least we'll be able to see their reasons. I'm all for full disclosure even though I don't believe any casino would ever want to use biased dice.
May 12th, 2013 at 2:33:05 PM
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Quote: tuppThe concept about which you are asking is very basic and fundamental to probability and gambling.
Let's say that you have a pair of dice, and each die is somehow excessively biased such that the ace is rolled 50% of the time. In that case, snake eyes should appear in 1/4 (25%) of the rolls.
In another example, if one die is biased as above (the ace appears in 50% of rolls) while the other die is unbiased, then snake eyes should happen 1/12th (8.333%) of the time.
In contrast, unbiased, randomly-tossed dice should yield snake eyes 1/36th (2.778%) of the time.
Okay, I understand that, which is why I wrote above that if a 6 shows up all the time you'd never see a number under 7.
But a die with such a heavy bias isn't really biased... it's loaded for heaven's sake.
Has ANYONE ever seen anything remotely like that at a craps table?
May 12th, 2013 at 2:34:01 PM
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In short... This is an exercise in futility.
"I'm a DO'er and you my friend, are a Don'ter"
-Mark Walberg
pain and Gain
May 12th, 2013 at 2:34:36 PM
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Quote: JimboAre you saying that you derive conclusions as to the distribution of "dice combinations" from simply the report of individual die face counts??
And you can also derive or determine Passline and Don't Pass results .... from simply the individual die face counts??
How???Quote: AhighAn excel spreadsheet.
I assumed it was from an Excel spreadsheet. Thanks for being so illuminating.
Quote: AlanMendelsonI don't claim to know much about math, but how can measuring individual faces be used to figure odds or edge when it takes two dice and a combination of two die faces to come up with a "number"?
This is, Ahigh, my point as well.
You are only furnished with individual die face counts. Nothing more--not the order of the face counts or how the individual die were combined to arrive at a number.
You say you are then able to take that information and determine the numbers of the two dice combinations that actually occurred? And also the order of those two dice combination numbers so as to determine the results of the Pass Line and the Don't Pass Line (i.e. when the sevens occurred in relation to the point number)?
That is an amazing spreadsheet!
I must be missing something.
May 12th, 2013 at 2:50:32 PM
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Quote: AlanMendelsonBut as I said, I'm not a "math guy" so if I am missing something I'd like to know what it is?
You are missing the fundamental concept that enough bias in one or more dice will give certain rolls a greater propensity to appear.
Quote: AlanMendelsonI do understand that if one die is ALWAYS showing a 6 then we will never see a "roll" with a number less than 7. But even if one die was always a 6 we'd still have a distribution of 7, 8, 9, 10, 11, 12.
You have just demonstrated how bias in one of two dice can skew results.
Quote: AlanMendelsonI guess if you believe in the conspiracy theory, you'll want to justify it by throwing in some math, too.
Most here don't believe in "conspiracy theory," and the math is straightforward. The difficulty comes in determining the degree of bias.
Quote: AlanMendelsonI think if the "bias dice conspiracy believers" want to make their case, they should be allowed to make it here.
You make a huge assumption about those who support face counting.
Quote: AlanMendelsonI'm all for full disclosure even though I don't believe any casino would ever want to use biased dice.
Not all on this forum are for full disclosure, but most believe that casino's do not want biased dice.
May 12th, 2013 at 2:56:28 PM
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Quote: JimboYou are only furnished with individual die face counts. Nothing more--not the order of the face counts or how the individual die were combined to arrive at a number. You say you are then able to take that information and determine the numbers of the two dice combinations that actually occurred?
No. What would be the purpose of that?
If the actual combinations were sought, they would simply be recorded. Incidentally, it is easy to simultaneously record individual faces and roll totals.
Quote: JimboI must be missing something.
The roll totals are not imperative in determining bias toward future rolls.
May 12th, 2013 at 2:59:16 PM
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Quote: AlanMendelsonBut a die with such a heavy bias isn't really biased... it's loaded for heaven's sake. Has ANYONE ever seen anything remotely like that at a craps table?
That was a hypothetical scenario, as was your example in which a die always rolled a six.
Nobody is claiming that casino dice are biased that heavily. Please stop jumping to conclusions.
May 12th, 2013 at 3:07:38 PM
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Quote: AlanMendelsonFace, I agree with you. I think that IF a bias is detected the difference won't be much of a difference or won't even make a difference. I also reject the conspiracy theory. But Ahigh (if I read him correctly) appears to be making some sort of statement that by counting individual faces he can determine which numbers are a better bet? Is that right? The way I've been playing the game, it doesn't matter what one die shows a 6 because it matters what the other die is also showing and the two combined show the "roll."
I’m getting out of my area of expertise, but I remember back when I was studying sliding that “killing” certain numbers, that is, sliding so they wouldn’t show, made certain combinations much less likely to appear. In effect, they changed the odds (and damn me for not filing properly, I can’t find my old worksheets)
IF dice were biased to the point that a number was much less likely to appear, I imagine the same concept would apply. I have data of a two hour session that included almost 150 results. Only six of those 150 results were the face of “2”. If that trend was due to bias and it continued for the next 8 hours, then 2 would be much less likely to appear and all dice totals that include one die showing “2” would likewise be less likely to appear.
The opinions of this moderator are for entertainment purposes only.
May 12th, 2013 at 5:11:29 PM
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http://www.goodshooter.com/ahigh/excel/biased_faces_with_line_bet_edges.xlsx
http://www.goodshooter.com/ahigh/excel/crapless_biased_faces_with_line_bet_edges.xlsx
It's entertaining seeing the folks making comments. Here are the spreadsheets. I think 7craps found at least one error in here, so I don't guarantee they are 100% accurate. But yes, in fact, this will tell you that if you intentionally created biased dice with an exact and known bias what you would expect to get in terms of MODIFIED house edges resulting from the theoretically biased dice.
If you're curious how this works, you can easily click and look at the formulas for each cell to see how I am calculating the probability of each of the 21 outcomes from the chance of each face occurring and so on.
http://www.goodshooter.com/ahigh/excel/crapless_biased_faces_with_line_bet_edges.xlsx
It's entertaining seeing the folks making comments. Here are the spreadsheets. I think 7craps found at least one error in here, so I don't guarantee they are 100% accurate. But yes, in fact, this will tell you that if you intentionally created biased dice with an exact and known bias what you would expect to get in terms of MODIFIED house edges resulting from the theoretically biased dice.
If you're curious how this works, you can easily click and look at the formulas for each cell to see how I am calculating the probability of each of the 21 outcomes from the chance of each face occurring and so on.
aahigh.com
May 12th, 2013 at 5:23:00 PM
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I never once suggested otherwise. (By "roll totals" I assume you mean dice combinations.)Quote: tuppThe roll totals are not imperative in determining bias toward future rolls.
I also agree with the other comment in your post in which you stated "if actual combinations were sought, they would simply be recorded." That is also obviously true. I never once suggested otherwise about that either.
BUT--here--the actual dice combinations were NOT recorded.
And--here--Ahigh utilized his "Excel spreadsheet" to arrive at a number of conclusions beyond whether there is simply suspected bias towards future rolls.
My issue is that Ahigh has NOT relied on the dice combinations--but only the individual die faces--in order to determine the house edge for various dice combinations.
Ahigh also determined the results of Pass Line and Don't Pass Line bets, based ONLY on the recording of the individual die faces.
Nothing about dice combinations. Nothing about the order or sequence of the individual die faces. Nothing about the order or sequence of dice combinations.
I still don't understand how that is possible.
May 12th, 2013 at 5:57:35 PM
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The edges are the edges for theoretical dice that are biased according to the face counts. They are nothing more or less and do not reflect the edges present on average for the sessions recorded. Even biased dice can appear 100% fair and fair dice can appear biased. You have to separate the topics.
aahigh.com
May 12th, 2013 at 5:58:03 PM
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Quote: JimboI still don't understand how that is possible.
My guess -
All of the odds of all of the bets on a Craps table are based off the probability of specific dice totals showing. The probability of those specific dice totals showing are based off the probability of the individual die faces showing.
As it stands now, assuming fair die, the probability of the individual faces showing are all 1/6. If a die was biased enough to show up less, it's probability would fall below 1/6, which would cause the die totals that involve said number to fall lower than what they currently are.
Using my example from my previous post, if that "2" stayed at 6/147, the 3, 4, 5, 6, 7 and 8 would all be less likely to appear than they are currently. That changes the odds. If you knew all those numbers were now less likely, wouldn't you bet differently?
The opinions of this moderator are for entertainment purposes only.
May 12th, 2013 at 6:45:28 PM
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If you knew for fact that the dice were biased enough to profit from the bias, the best way to do it would be on the free bets.
This spreadsheet allows you to effectively combat such theoretically biased dice on the fly. All of this is just theory, and as has been pointed out the chance that enough bias is present to take advantage of is impractical unless the bias is very strong.
A simulation could even use the equations to determine exactly how strong a bias would be necessary for a procedural method to be effective at battling such theoretically biased dice.
IE: it should be obvious that 100% bias to the aces would cause aces every roll, and after you rolled aces 12 times in a row, anyone could hop the aces and parlay into retirement.
But if the dice are biased to produce 11 ace faces for every 10 of each other face, it would be very difficult to both see this as well as to know how to profit from it.
The spreadsheet just automates the process of knowing where the largest edges are for any theoretically biased dice. Whether your theoretical dice are created in your mind, or created from looking at actual samples at a particular moment from a real stick of dice at a table, the biased dice don't exist in the real world at all, they are just theoretically biased dice created for the purpose of investigation into what the effects would be for such theoretically biased dice.
But again, you have to realize that all of this is theory. And none of this is showing you actual edges from a session.
This spreadsheet allows you to effectively combat such theoretically biased dice on the fly. All of this is just theory, and as has been pointed out the chance that enough bias is present to take advantage of is impractical unless the bias is very strong.
A simulation could even use the equations to determine exactly how strong a bias would be necessary for a procedural method to be effective at battling such theoretically biased dice.
IE: it should be obvious that 100% bias to the aces would cause aces every roll, and after you rolled aces 12 times in a row, anyone could hop the aces and parlay into retirement.
But if the dice are biased to produce 11 ace faces for every 10 of each other face, it would be very difficult to both see this as well as to know how to profit from it.
The spreadsheet just automates the process of knowing where the largest edges are for any theoretically biased dice. Whether your theoretical dice are created in your mind, or created from looking at actual samples at a particular moment from a real stick of dice at a table, the biased dice don't exist in the real world at all, they are just theoretically biased dice created for the purpose of investigation into what the effects would be for such theoretically biased dice.
But again, you have to realize that all of this is theory. And none of this is showing you actual edges from a session.
aahigh.com
May 12th, 2013 at 7:00:22 PM
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Quote: Jimbo
My issue is that Ahigh has NOT relied on the dice combinations--but only the individual die faces--in order to determine the house edge for various dice combinations.
Ahigh also determined the results of Pass Line and Don't Pass Line bets, based ONLY on the recording of the individual die faces.
Nothing about dice combinations. Nothing about the order or sequence of the individual die faces. Nothing about the order or sequence of dice combinations.
I still don't understand how that is possible.
It relies on a pretty big assumption, namely that all dice have the same bias. If not true, which is exceptionally likely, the conclusions are invalid. Averaging biases across multiple dice is a flawed methodology.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
May 12th, 2013 at 7:06:10 PM
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This is why it's good to keep all the samples separate too. Also, knowing the manufacturer of the dice and other details is very important.
I have no idea how far this is going to go as it is a ton of work relative to the value of these samples (I'm putting a value of half a cent per sample).
But if there is a bias that is consistent across all casino dice, I do believe it will be visible.
I am actually of the opinion that any bias is going to be pretty small, but my mind is open to other possibilities.
I have no idea how far this is going to go as it is a ton of work relative to the value of these samples (I'm putting a value of half a cent per sample).
But if there is a bias that is consistent across all casino dice, I do believe it will be visible.
I am actually of the opinion that any bias is going to be pretty small, but my mind is open to other possibilities.
aahigh.com
May 12th, 2013 at 7:13:34 PM
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Quote: MathExtremistAveraging biases across multiple dice is a flawed methodology.
...and, on that note...
| Face Up | Sample #1 | Sample #2 | Sample #3 | Running Total |
|---|---|---|---|---|
| 1 | 82 | 80 | 63 | 225 |
| 2 | 56 | 96 | 55 | 207 |
| 3 | 94 | 100 | 56 | 250 |
| 4 | 72 | 108 | 67 | 247 |
| 5 | 85 | 94 | 59 | 238 |
| 6 | 66 | 112 | 69 | 247 |
| Total | 455 | 590 | 369 | 1,414 |
The opinions of this moderator are for entertainment purposes only.
May 12th, 2013 at 7:19:22 PM
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Quote: Face...and, on that note...
Face Up Sample #1 Sample #2 Sample #3 Running Total 1 82 80 63 225 2 56 96 55 207 3 94 100 56 250 4 72 108 67 247 5 85 94 59 238 6 66 112 69 247 Total 455 590 369 1,414
p values:
Sample 1: 2.72%
Sample 2: 25.70%
Sample 3: 74.25%
Running Total: 31.06%
So far I've seen no evidence to support the loaded dice conspiracy.
Also, just out of curiosity, if a casino were inclined to introduce loaded dice to the tables, what would be the revenue-maximizing way to bias them?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
May 12th, 2013 at 7:19:28 PM
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So, when the two faces are recorded after a throw, are they each assigned to an individual die? How do you keep track of the results after the dice are returned to the bowl prior to a new shooter's come out?
Or are you just recording results from any of the five dice in the stick, without regard to which die generated the result?
Or are you just recording results from any of the five dice in the stick, without regard to which die generated the result?
May 12th, 2013 at 7:19:31 PM
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Thank you, MathExtremist, for putting this so succinctly.Quote: MathExtremist...the conclusions are invalid. Averaging biases across multiple dice is a flawed methodology.
May 12th, 2013 at 7:20:40 PM
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To be a little more clear (this time) for theoretically biased dice that produced randomly 225/1414 ace faces, 207/1414 two faces, 250/1414 three faces, 247/1414 four faces, 238/1414 five faces and 247/1414 six faces the following would be the modified edges for such theoretically biased dice. This has nothing to do with actual edges present during the collection of this data, except that such theoretically biased dice (which also do not exist) are modeled from the outcome from the samples provided by the forum member, Face.
Free odds edges: (4, 5, 6, 8, 9, 10)...
-1.1245% -0.5605% -0.3477% 0.2770% 1.4217% 1.2075% (fair dice are 0%)
Passline/don't
-0.0266% -3.0248% (fair dice are -1.41% and -1.36%)
Field:
-1.5942% (fair is -2.78%)
Free odds edges: (4, 5, 6, 8, 9, 10)...
-1.1245% -0.5605% -0.3477% 0.2770% 1.4217% 1.2075% (fair dice are 0%)
Passline/don't
-0.0266% -3.0248% (fair dice are -1.41% and -1.36%)
Field:
-1.5942% (fair is -2.78%)
aahigh.com
