poker odds

A few weeks ago a friend of mine drew to an inside straight flush, i was wondering what the odds were of that happening

You’ve asked this already, haven’t you?
Maybethis site helps.

Are you asking the odds for getting the draw, given that he started with the hand? Or do you want the odds for getting dealt the hand and then getting the draw he wanted?

If it’s the former, it’s easy: There was one specific card he wanted, and 47 cards left unaccounted for, so his chances of getting the straight flush were one in 47. If he was willing to settle for a non-flush straight, or a non-straight flush, then there were twelve cards unaccounted for which could give him a hand, for 12 in 47, or a little better than 1 in 4.

Now, what about the odds of getting dealt an inside straight flush in the first place? There are 40 possible straight flushes (high card ranging from 5 to A, in one of four possible suits), and for each of those, there are three possibilities for missing an inside card, so there are 120 possible hands matching your description. There are a total of ([sup]52[/sup] [sub]5[/sub]) poker hands, or 52!/(47!*5!) , which works out to 2598960 (call it two and a half million). His odds of getting dealt the inside straight flush are then 120/2598960 , or one in 21658.

All this is assuming, of course, five cards and nothing wild. Throw in more cards or wild cards, and the odds improve considerably.

Ask your friend. He’s the one who drew to it. :slight_smile:

Ask your friend. He’s the one who drew to it. If he’s like most players, the only thing that would stop him from drawing to that would be if the roof fell in on him while he was pondering the situation. :slight_smile:

There are more than three possibilities for missing an inside card.

Start with, as you say, any of the 40 straight flushes. Take away any one of the three cards and replace it with any of the 47 other cards.

IOW:

2H 3H 4H 6H 2C is a different hand than
2H 3H 4H 6H 3C.

For each one of the three positions there are 47 possibilities in the total ~2.5 million hands.

40347 = 5640 of them, about one out of every 461 hands.