Re: AA hand 2
Good approach, but I'll tweak your numbers. Effectively, the pot is $44.10, and it's $17.60 to call - his stack is bigger, so his all-in is really smaller, making it easier to call.
Using your numbers (which neglect what fimbulwinter said about the pair + straight draw) we get
X * 10% * $44.10 +
X * 90% * (-$17.60) +
(1 - X) * 90% * $44.10 +
(1 - X) * 10% * (-17.60)
which simplifies down to x ~= 77%.
As an exercise, I'll run through the whole thing based strictly off hand frequencies.
AA-JJ - I'll assume I would've either seen a raise or a re-raise.
TT - 6
99 - 6
88 - 6
77 - 3
66 - 3
55 - 6
44 - 3
54 - 3
65 - 3
76 - 2
75 - 3
I'm assuming the connectors must be suited.
2 combinations = 4.5%
3 combinations = 6.8%
6 combinations = 13.6%
(TT) .136 * (.88 * 44.10 + .12 * -17.6) = 4.99
(99) .136 * (.88 * 44.10 + .12 * -17.6) = 4.99
(88) .136 * (.74 * 44.10 + .26 * -17.6) = 3.82
(77) .068 * (.10 * 44.10 + .90 * -17.6) = -0.78
(66) .068 * (.11 * 44.10 + .89 * -17.6) = -0.74
(55) .136 * (.61 * 44.10 + .39 * -17.6) = 2.73
(44) .068 * (.11 * 44.10 + .89 * -17.6) = -0.74
(54) .068 * (.54 * 44.10 + .46 * -17.6) = 1.07
(65) .068 * (.51 * 44.10 + .49 * -17.6) = 0.94
(76) .045 * (.26 * 44.10 + .74 * -17.6) = -0.07
(75) .068 * (.52 * 44.10 + .48 * -17.6) = 0.98
Summing these gives me $17.20 per time I call.
I don't think TT-88 is too reasonable to go all in with, so removing those gives me $3.40, still a reasonable call - every other pair he could have is just gravy.
Can someone better than me at this verify if this is right?
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