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#2
09-25-2005, 11:31 PM
 AaronBrown Senior Member Join Date: May 2005 Location: New York Posts: 505
Re: Fastest way to figure out redraw pot odds

First of all, a card can only be an out for one player. For example, if T[img]/images/graemlins/heart.gif[/img] is still in the deck, it is an out for villain, not hero.

If there are no overlaps, so there are 10 cards that win for villain, 15 cards that win for hero but only if none of the villain's 10 show up; and if none of the 25 cards appear on the turn or river villain wins then:

10*9/2 + 10*35 = 395 times villain gets at least one good card and wins
15*14/2 + 15*20 = 405 times hero gets a good card and villain doesn't, hero wins
20*19/2 = 190 times neither player gets a good card and villain wins

That adds up to 990, the number of possible combinations of turn and river cards. 405 of them win for hero and 585 win for villain. The exact answer is either 399 (4 or 7 on the flop is not a heart) and 417 (T on the flop is not a heart) wins for hero.