# you sure of that, Mr S?

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Posted by Denis Borris on October 15, 2002 at 15:30:40:

In Reply to: Re: Poker Problem - 10/08/02 posted by Soroban on October 15, 2002 at 13:11:08:

: But this requires a re-reading of the problem itself. If it said that
: it is GIVEN that we didn't get 4-kind on the 1st draw, we're done.
: But if it said something like, "What is the probability that we don't
: get a 4-kind on the first try, and succeed in the second try?", then
: we'd multiply by the probability of failing on the first try.

Deck is shuffled.
9 cards (max) taken from top and laid down in order.
Do we have 4 same?

3 3 4 5 6 3 4 4 3 : NO (3's have to be in cards 6-8
3 3 4 5 6 3 4 3 4 : YES

3 3 3 3 4 5 6 7 8 : YES
3 3 3 4 3 5 6 7 8 : YES

3 3 3 4 5 5 6 3 7 : NO (3 has to be cards 6 or 7)
3 3 3 4 5 5 3 6 7 : YES

Ran quick simulation on a million tries: 2750 times.

It doesn't matter if 9 cards are dealt even if first 4 are the same;
the deck is reshuffled before each try.

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