when giving free cards is better than betting vulnerable hands

[ceczar]

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a+b+c

0,19*-57K+0,12*138K+0,69*300K = +234,390$ which is actually 9000$ less than going all in on the turn.

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using your formulation of the problem, but converting it to 2+2 favored form (where fold = 0) and correcting mistakes (i think):

108,000 in pot on turn. he has 97k left
if you get it in now, you gain 205k 77.27% of the time and lose 97k 22.73% of the time = 136.31k EV

if you check:
22.73% of the time you have to fold river = 0 EV
63.63% of the time you get allin on river = 205k EV
13.63% of the time a Q or J comes = X

here's the indifference equation:
22.73% * 0 + 63.63% * 205k + 13.63% * X = 136.31k
130.45k + 13.63% * X = 136.31k
X = (136.31k - 130.45k) / 13.63%
X = 43k

43k = 108k + BetSize * Call%

based on these numbers, even if he folded every time on the river you would gain money by checking the turn.

another way to put it:
by checking:
63.63% of the time all the money goes in anyway
22.73% of the time you save your remaining 97k
13.63% of the time you lose his remaining 97k when the scare card hits

clearly even if you check behind on the river when the Q or J comes you're better off by checking the turn