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I prefer something that intuitively matches up with the $ value of EV for the entire hand - and ignores the previous streets where this is unreliable.
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Sorry, pressed the button by mistake in the middle.
How about a method that weight's previous streets? I think it might be better than both methods.
I'll explain with an example, and I'll take AA against TT instead of AA against KK (cause TT can fold on other flops, KK against AA it usually ends all in always).
Stacks Pre Flop are 1000.
Pre Flop bet is 4BB, $40.
Flop now comes Td7c3h.
Equity on the flop is: 91.41% for TT and 8.59% for AA
Now we calculate the equity pre flop, weighted by the percentage of time TT is going to have EV 91.41% on the flop or better. So, we take it from the following
Equity Distribution Graph for TT againt AA on the Flop
So we aproximate the number that TT has 91.41% EV or more against AA to be 5% (I've seen somewhere that the graph can be obtained as a table, but I don't remember where).
Now we can compute the weighted EV pre flop for TT and AA, and it is -$36 for TT and +$36 for AA.
And, we can compute the weighted EV on the flop for TT and AA, and it is +$39,8496 for TT and -$39,8496 for TT. So, total weighted EV for TT for the hand is $3,8496 and for AA is -$3,8496.
Hand Board Stack Pre Flop Bet Flop % EV Pre Flop Bet % EV Flop Flop Bet EV Flop Bet EV
TT Td7c3h 1000 40 5,00% -36 91,51% 960 39,8496 3,8496
AA Td7c3h 1000 40 95,00% 36 8,49% 960 -39,8496 -3,8496
We can compute in the same way with bets of 20% of the stacks and 80% of the stacks pre flop, and we have EV of +$ 146 and +$711 for AA, as we expect EV grows for AA as more money is put pre flop.
Hand Board Stack Pre Flop Bet Flop % EV Pre Flop Bet % EV Flop Flop Bet EV Flop Bet EV
TT Td7c3h 1000 200 5,00% -180 91,51% 800 33,208 -146,792
AA Td7c3h 1000 200 95,00% 180 8,49% 800 -33,208 146,792
Hand Board Stack Pre Flop Bet Flop % EV Pre Flop Bet % EV Flop Flop Bet EV Flop Bet EV
TT Td7c3h 1000 800 5,00% -720 91,51% 200 8,302 -711,698
AA Td7c3h 1000 800 95,00% 720 8,49% 200 -8,302 711,698