Re: 2+2 Poker Probability Question

From: The Qurqirish Dragon (qurqirishd_at_aol.com)
Date: 03/09/05 

Date: 9 Mar 2005 07:24:07 -0800

Proof that the probability of the next card being the ace of spades is
1/52:

Let us assume that the first ace is at position x, so the card we are
checking is at position x+1.
The probability of it being the ace of spades is:
(52-x)/52 * 1/(52-x) = 1/52

The first term is the probability that the ace of spades is not among
the first x cards, the second is the probability that it is the next
card up (a specific card out of the 52-x remaining)

Technically, you also need a term for "what if the ace of spades IS in
the first x cards," but then the probability that the next card is the
AS is 0, so this term can be ignored.

It is obvious that your 1/68 is incorrect, and here is why:
Assuming your reasoning is correct:
Probability of any specific ace= 1/68
Probability of any other specifc card = 1/51
Probability of ANY card = 3*1/68 + 48/51 < 3/51 + 48/51=1 (note that
there are only 3 aces left, so it is NOT 4*1/68 for the first term,
since one of the aces has probability zero.)

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