Even if the sevens are equally distributed at 13.33% probability each, the expected return on each of the 1-6, 2-5, and 3-4 hop bets, assuming a win of 15 to 1, would be 0.1333*15 + 0.8667*-1 = 1.1333. In other words, a player advantage of 113%.

When is the next flight?

Nah, I think I'll just stay here and play 8-5 Bonus Poker and let Mickey besmirch my reputation.

Exactly what they told you:Quote:BohemianWhat are they trying to hide.

Duh.Quote:Bohemianthey said that would not be fair to each casino's proprietary information.

They have no business releasing proprietary property specific information, and you have no right to have it, which is why you don't, and won't.

Your entire response makes the point very well: You have absolutely no sensible basis to be making the assertion that they are

"using shaved dice." Here is a more likely conclusion: they are dice, behaving like dice do.

Quote:ThundershockWith regulation almost non-existent now, I have noticed some casinos aka Caesars have been flouting the rules. When I played craps there this past weekend, I noticed a huge amount of 7's being thrown despite the randomness of the throwers and on multiple tables too. I'm well aware of variance and everything but when I see sevens or craps thrown on over 40% of the throws (no exaggeration) I have to wonder. This was further confirmed upon inspecting the dice as the edges were worn down. (They were whitish instead of the blue color of the dice)

I've read this thread and I was wondering which edge(s) should be shaved to create an edge for the #7 being thrown.

Which edges were worn down? The edge(s) between 1/2, 1/3, 1/4, 1/5, 2/3, 2/4, 2/6, 3/5, 3/6, 4/5, 4/6, 5/6.

Were there more than one edge worn down?

Quote:FleaStiffOh, so the bias of a shaved die can show up on the first roll but moderate itself on subsequent rolls?

Oh my! :)

That made me laugh so hard tears came to my eyes. I really needed that.

Thanks!

You know, when I taught probability and statistics (at the graduate level) I used to give all sorts of interesting homework assignments to my students that they always thought I designed to drive them crazy (until they realized why I assigned them). One of my favorites (and fairly standard): I'd tell them to all take a regular coin, and flip it 100 times, and record the results on a sheet of paper and turn it in the next class. "H" for heads, and "T" for tails. I'd wait a few seconds for a look of despair at such a boring assignment. Then I'd say, "Well, okay, if you want, you can fake it instead of flipping the coin. Just hand in the paper, and please, everyone, write down on a separate sheet of paper whether you faked it or not: write "fake" or "flip" on it depending on what you did. But don't hand in that second sheet of paper to me -- just bring it along and don't show it to me unless I ask!"

They'd come the next class, hand in their papers with 100 letters on them (and their names, etc.), and I would (for a class of about 20 students) run through the pile of sheets in about a minute (2 max), sorting them into two piles. One big pile of faked results, and the smaller pile of real flips. I could spot the fakes right away. then I'd announce the fakes and real ones by name. I never got one wrong.

Anyone who knows advanced probability and statistics knows how I spotted the fakes vs. the real ones. Which allowed me to give a really nice lecture on the Law of Large Numbers which suddenly had their full attention.

Humans don't do very well with randomness. Our brains evolved to spot patterns so we could survive to reproduce: even where no patterns got generated. And even when the randomly generated patterns can in no way predict future performance.

A respected (by me) colleague asked me yesterday for my definition of "randomness" by the way (not pseudorandomness!). I suppose he considered me an expert on the subject for some reason. I can't tell you why he needed it, but it involves resilient computer systems for the U.S. Department of Defense, and if *he* got discombobulated by the subject then I think the average person at a craps table doesn't have a chance. (He doesn't know information theory though; most statisticians don't, but they should -- and I wish almost everyone would stop using "entropy" as a synonym for "random" but I digress.)

Hell, I've noticed that the average pit boss at a craps table doesn't understand basic probability! Long story involving my last trip when I won an awful lot; I don't want to bore you all.

Quote:Concinnity

Hell, I've noticed that the average pit boss at a craps table doesn't understand basic probability! Long story involving my last trip when I won an awful lot; I don't want to bore you all.

I'd bet on a "random" person pulled off the street over a craps pit boss on basic probability problems.

Can you tell the difference between a Electronic Roulette and Live roulette set of numbers like EvenBob? Or is he just super special?Quote:ConcinnityOh my! :)

That made me laugh so hard tears came to my eyes. I really needed that.

Thanks!

You know, when I taught probability and statistics (at the graduate level) I used to give all sorts of interesting homework assignments to my students that they always thought I designed to drive them crazy (until they realized why I assigned them). One of my favorites (and fairly standard): I'd tell them to all take a regular coin, and flip it 100 times, and record the results on a sheet of paper and turn it in the next class. "H" for heads, and "T" for tails. I'd wait a few seconds for a look of despair at such a boring assignment. Then I'd say, "Well, okay, if you want, you can fake it instead of flipping the coin. Just hand in the paper, and please, everyone, write down on a separate sheet of paper whether you faked it or not: write "fake" or "flip" on it depending on what you did. But don't hand in that second sheet of paper to me -- just bring it along and don't show it to me unless I ask!"

They'd come the next class, hand in their papers with 100 letters on them (and their names, etc.), and I would (for a class of about 20 students) run through the pile of sheets in about a minute (2 max), sorting them into two piles. One big pile of faked results, and the smaller pile of real flips. I could spot the fakes right away. then I'd announce the fakes and real ones by name. I never got one wrong.

Anyone who knows advanced probability and statistics knows how I spotted the fakes vs. the real ones. Which allowed me to give a really nice lecture on the Law of Large Numbers which suddenly had their full attention.

Humans don't do very well with randomness. Our brains evolved to spot patterns so we could survive to reproduce: even where no patterns got generated. And even when the randomly generated patterns can in no way predict future performance.

A respected (by me) colleague asked me yesterday for my definition of "randomness" by the way (not pseudorandomness!). I suppose he considered me an expert on the subject for some reason. I can't tell you why he needed it, but it involves resilient computer systems for the U.S. Department of Defense, and if *he* got discombobulated by the subject then I think the average person at a craps table doesn't have a chance. (He doesn't know information theory though; most statisticians don't, but they should -- and I wish almost everyone would stop using "entropy" as a synonym for "random" but I digress.)

Hell, I've noticed that the average pit boss at a craps table doesn't understand basic probability! Long story involving my last trip when I won an awful lot; I don't want to bore you all.

That's interesting.Quote:ConcinnityOh my! :)

That made me laugh so hard tears came to my eyes. I really needed that.

Thanks!

You know, when I taught probability and statistics (at the graduate level) I used to give all sorts of interesting homework assignments to my students that they always thought I designed to drive them crazy (until they realized why I assigned them). One of my favorites (and fairly standard): I'd tell them to all take a regular coin, and flip it 100 times, and record the results on a sheet of paper and turn it in the next class. "H" for heads, and "T" for tails. I'd wait a few seconds for a look of despair at such a boring assignment. Then I'd say, "Well, okay, if you want, you can fake it instead of flipping the coin. Just hand in the paper, and please, everyone, write down on a separate sheet of paper whether you faked it or not: write "fake" or "flip" on it depending on what you did. But don't hand in that second sheet of paper to me -- just bring it along and don't show it to me unless I ask!"

They'd come the next class, hand in their papers with 100 letters on them (and their names, etc.), and I would (for a class of about 20 students) run through the pile of sheets in about a minute (2 max), sorting them into two piles. One big pile of faked results, and the smaller pile of real flips. I could spot the fakes right away. then I'd announce the fakes and real ones by name. I never got one wrong.

Anyone who knows advanced probability and statistics knows how I spotted the fakes vs. the real ones. Which allowed me to give a really nice lecture on the Law of Large Numbers which suddenly had their full attention.

Humans don't do very well with randomness. Our brains evolved to spot patterns so we could survive to reproduce: even where no patterns got generated. And even when the randomly generated patterns can in no way predict future performance.

A respected (by me) colleague asked me yesterday for my definition of "randomness" by the way (not pseudorandomness!). I suppose he considered me an expert on the subject for some reason. I can't tell you why he needed it, but it involves resilient computer systems for the U.S. Department of Defense, and if *he* got discombobulated by the subject then I think the average person at a craps table doesn't have a chance. (He doesn't know information theory though; most statisticians don't, but they should -- and I wish almost everyone would stop using "entropy" as a synonym for "random" but I digress.)

Hell, I've noticed that the average pit boss at a craps table doesn't understand basic probability! Long story involving my last trip when I won an awful lot; I don't want to bore you all.

Do you think could do the same thing with a group of more astute forum members?

Or if one individual did all 20 sheets 10 real 10 fake?

Quote:ConcinnityYou know, when I taught probability and statistics ...

In 100 flips you would expect a reversal of the previous result 50 times. I would imagine that fake results would have more such reversals, in an effort to appear random. Just off the top of my head, I'd suspect a number of reversals outside of 40 to 60 to be faked.

Not sure how many times he did this. I assume 98% of the students just made up fake results. Who wants to flip a coin 100 times especially when they can have a shot at fooling a teacher?Quote:WizardIn 100 flips you would expect a reversal of the previous result 50 times. I would imagine that fake results would have more such reversals, in an effort to appear random. Just off the top of my head, I'd suspect a number of reversals outside of 40 to 60 to be faked.

I'm surprised no one actually flipped "fake looking results"

I'm sure at least a few students lied and claimed they actually flipped the coin. So how does that affect the %100 accurate results?

Quote:AxelWolf

I'm sure at least a few students lied and claimed they actually flipped the coin. So how does that affect the %100 accurate results?

I thought the same.

The 100% accuracy only means that those caught by him were indeed fake. But he couldn't prove those not caught were non-fake.