Re: Probability to ponder...

"Wayne Vinson" <a7a88fc@xxxxxxxxxxxxxxx> wrote in message news:hgktd5xtqe.ln2@xxxxxxxxxxxxxxxx
Everyone knows that the odds of being dealt aces in holdem are slightly
worse than 200:1 against. And therefore the odds of being dealt them
twice in a row are slightly worse than 40,000:1 against. So, if you play
a session of say 100 consecutive hands, what are the odds that there will
be dealt aces twice (or more) in a row? Close to 400:1 against, or 800:1
against?

Here are two sample arguments:

A: Starting with each individual deal, the next two deals constitute a
opportunity to have aces hit twice. There are 99 such opportunities, so
the odds are roughly 400:1 against.

B: A is an idiot. Every time a non-ace hand hits, it ruins not one, but
two different possible chances to get consecutive aces. In other words,
the trials are not independent. If trial N fails (not repeat aces), then
we know either trial N+1 or N-1 failed as well. This means that in effect
there are half as many trials, and the odds are about 800:1 against.

A's rebuttal: B has his head stuck up his ass - he's clearly got cause and
effect confused. The idea that trial N+1, in the future, is going to come
back in time and ruin trial N is absurd. This is poker, not a James
Cameron flick. Starting on every hand, there's a full 40,000 to 1 chance
that aces will hit for the next two hands. That's a fresh slate, and
nothing else alters it. You get 100 such opportunities. Do the math.

So who's right, A or B?

Wayne Vinson
http://cardsharp.org/
http://cardsharp.org/?p=34 (Pot Limit & No Limit Poker reviewed)
Wayne (dot) Vinson (at) gmail (dot) com

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A. When A's fail to hit that only ruins 1/2 of a possible pair of consecutive hits, of any group of 4 unique cards, not only A's.


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