Poker odds and the distribution of cards

[Airhog]

This question was asked in a different thread.

Originally posted by sooner333
btw, if you have 4 of the same suit on the flop what are your odds of winning the pot? I'm sort of beginning and playing a lot by feel here, but I enjoy it.

This was an anwser to the problem.

Originally posted by MattJones4Heisman
According to Brunson's Super System it's 1.86 to 1 against and 34.97% to complete your flush if you flop four suited (page 577).

This got me thinking, and I think it raises a valid question about the distribution of cards, and the reasoning behind the 34.97% chance of another card coming up that is the same suit.

I think that this number is way to high. If you have 10 players at a table. 20 cards are dealt out, and then 3 cards are dealt for the flop. One card is also burned before the flop. That means that 24 cards are in play. Now you know that you have 2 spades, and the board has two spades. That seems to me, that the best possible odds you could have is the remaining 9 cards are still in the deck of 28 cards left. This is right at 32.14% Im not sure how the book arrives at 34.97%.

However this is just the best possible odds. It all reality some of those spades were dealt. Since 25% of all cards are spades. One can reason then that approximately 6 cards were dealt out. We have seen four of those cards. So it stands to reason there are approximately 7 cards left in the deck that are spades instead of nine. the new percentage would be 25.5%. I think this percentage is more accurate since it refeclts the distribution of cards more realisticly. I would much rather base my decision on odds that accurately reflect the distribution of cards, rather then the best odds one could hope for.

[Airhog]

Feel free to prove my math wrong. I definately have weak math skills

[MJ4H]

I think you need to remember there are 52 cards and you know exactly five of them. The odds are then 9 in 47 and then 9 in 46. I don't know the proper way to figure out exactly what that is, but that seems to be pretty accurate.

[RPI-Fan]

The fact that some cards have been distributed does not matter, at all. Those cards are still unknown, and thus must be calculated that way.

Therefore, you just calculate the odds of NOT hitting the flush, or...

38/47 * 37/46 = .651

1 - .651 = .349

or

34.9%

[korme]

How is it even higher than 25%? With 4 suits that should cut down your chances measurably.

[RPI-Fan]

Because you get two cracks at it, Shorty.

[Airhog]

thanks for explaining how he gets the percentage. Once again I was using the wrong numbers