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Here’s a URL (Probabilities) that’ll help you get the formulas to work it out on your own, but (now that my hangover’s gone) here goes (if I screw up on the math somewhere then please correct me):
The probability of flopping a flush 118/1, FD is 8.4/1 and completing by river is 15/1. Flopping trips is 73/1; and two pair (using both of your hole cards) is 49/1. I left out the straight because I had difficulty finding odds of flopping a straight or SD and completing.
So, we’ve got flopping a flush or 2 pr or trips or completing a flush given that a FD flops, or:
1/49 + 1/73 + 1/118 + ((1/15)/ (1/8.4)) = X
1/49 + 1/73 = 73/3577 + 49/3577 = 122/3577 = 1/29.32
1/29.32 + 1/118 = 118/3459.76 + 29.32/3459.76 = 147.32/3459.76 = 1/23.48
1/23.48 + ((1/15)/ (1/8.4)) = 1/23.48 + ((8.4/126)/ (15/126)) = 1/23.48 + 8.4/15 = 15/352.2 + 197.23/352.2 = 212.23/352.2 = 1/1.66
Unless I did something wrong the probability is 1.66 to 1 against one of the above things happening but you’ve also got to compare it to the probability of his AA improving by the river:
4.2 to 1 against making a set or better by the river; 5/1 that a pr flops; that the board pairs by the river about 2/1. I’d imagine that his odds greatly reduce your odds of winning.
1/4.2 + 1/5 + 1/2
1/4.2 + 1/5 = 5/21 + 4.2/21 = 9.2/21 = 1/2.28
1/2.28 + 1/2 = 2/4.56 + 2.28/4.56 = 4.28/4.56 = 1/1.06 or basically 1.06 to 1 against his AA improving by the river.
It looks to me like he has a greater chance of improving, which would imply that in the long run playing 63 is a losing proposition.
If I did screw up the math somewhere would someone please correct it? It’s been a really long time since I’ve done probability statements.
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