Very simple math question, but I need help
I was playing 10/20 hold'em at Greektown Casino in Detroit last night when a simple probability question came up. I flopped top set, and lost to a flopped straight. I grumbled to my friend about how I never make my 2-1 dogs one out of three times. The guy on the other side of me said, 'You're a way bigger dog than that, you're at least 3.1 to 1 to make a full house or better by the river.' Clearly this is absurd, and I wagered $1000 with this man that I was better than a 2.8 to 1 dog, and he agreed that HEPFAP would be the source used for the correct answer. I consulted the book today, and although I won the bet, I want to know where my math went wrong.
On page 310 the book states that if you flop trips, you will make a full house or better 33% of the time. My math came up with 36.632%. Here's how I got that answer, and can someone please show me where I erred, as I would trust Sklansky and Malmuth over myself.
My hand:AA
Flop A23
47 unseen cards, 7 give us a FH or better. 7/47=14.893%
Turn A237, 46 unseen cards, 10 give us a FH or better 10/46=21.739%.
14.893%+21.739%=36.632%
That's a 3.632% difference from HEPFAP. Is my math right, and the book worded wrong, or is my math wrong? Thanks
|