V
viking999
Visionary
Silver Level
Okeydokey - J2 redone (which does assume we go broke if a 2 is turned to be fair/in-keeping with the QhTh assumption):
<J2, flat-call flop> = 13/45*30.50 + 32/45*58.50 + (2/45)*(41/44)-43
<J2, flat-call flop> = 8.81 + 41.60 - 1.78
<J2, flat-call flop> = $48.63
<J2, shove flop> = 2/45*-43 + 2/44*-43 + (43/45)*(42/44)*58.50
<J2, shove flop> = 53.36 - 1.91 - 1.95
<J2, shove flop> = $49.50
Much, much, much, much closer than previously calculated. Even if this and K2 are 12x more likely hands than QhTh you gain more than 25x the amount in QhTh option by flat-calling than you lose by flat-calling the J2 so the flat-call is correct. Yippee!
Now for that pesky 22...
Ok, here's my figuring, including our full house redraws (king or jack).
scare = non-J heart, K, or A
<J2, flat-call flop> = P(turn scare) * 30.50 + [P(turn J) + P(turn 2, river K/J) + P(turn not scare/J/2, river not 2)] * 58.50 - [P(turn 2, river not K or J) + P(turn not scare and not J, river 2)] * 43.00
<J2, flat-call flop> = (13/45) * 30.50 + [(1/45) + (2/45 * 3/44) + (29/45 * 42/44)] * 58.50 + [(2/45 * 41/44) + (31/45 * 2/44)] * 43.00
<J2, flat-call flop> = (0.2889) * 30.50 + (0.6404) * 58.50 + (0.0727) * 43.00
<J2, flat-call flop> = $49.40
<J2, shove flop> = [P(no 2) + P(turn K or J, river 2) + P(turn 2, river K or J)] * 58.50 - [P(turn 2, river not K or J) + P(turn not K or J, river 2)] * 43.00
<J2, shove flop> = [(43/45 * 42/44) + (3/45 * 2/44) + (2/45 * 3/44)] * 58.50 - [(2/45 * 41/44) + (42/45 * 2/44)] * 43.00
<J2, shove flop> = (0.9182) * 58.50 - (0.0838) * 43.00
<J2, shove flop> = $50.11
So not much different, as is expected because full house redraws aren't a big deal.
Update: So, that took a looooong time. That's probably why people don't realistically compute this stuff when playing.
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