Originally Posted by Dan Druff View Post
Alan, I sincerely doubt the claim that 18 Yos (elevens) were rolled in a row in craps.

The odds of one Yo is 1/18 -- or 5.6%.

Now, let's throw out the first one, because a Yo will eventually be rolled. So the question is -- what are the odds of 17 more consecutive Yos being rolled right after that?

Well, that math problem is easy. You take 1/18 and make it to the power of 17. So it's (1/18)^17.

And the answer? 1 in 2185911559738696531968.

Approximately 1 in 2 sextillion.

How long are those odds?

Let's say a craps roll occurs every 10 seconds. It doesn't (because the game pauses far more often than that), but let's go with that number.

At that rate, you would see 17 Yos in a row once every 692 trillion years. And we're talking about 17 Yos in a row. Change it to 18, and that goes up to once every 12 quadrillion years.

Needless to say, Alan has never seen 18 Yos in a row, nor has anyone anytime anywhere.

Unless the dice were loaded.

Dan, you kind of ruined the surprise component of an article I was planning called "The Case of the 18 Yos."

I have the rights to www.TheSkepticalGambler.com, and this is going to be a lead article when I get it up and running.

I'll give the readers here a preview. Basically (and I know nothing about craps at all; I never play), it comes down to this. The math guys can be right, and Alan can also be right. How can this be? Well, ask yourselves, what is more likely, that 18 Yos happened with fair dice, or that a pair of dice that was supposed to be set aside somehow got mixed into the game? The answer presents itself.

Now that opens all the arguments about casinos never cheating and all that, which I find ludicrous from a pragmatic and historical perspective. Rigged dice exist. Thirty years ago, they were not uncommon. Is it really likely they are extinct? C'mon, people, this is the real world.

The most likely explanation, the Occam's Razor explanation, is that a pair of dice that should not have been in the game, somehow got mixed with the other dice by mistake and inserted into the game. Whether it was 15 Yos or 16 yos or whatever, that is the most logical, elegant explanation.