Flop = T♥ 7♥ 6♥
Player 1 = 4♠ 3♥
Player 2 = 5♥ 2♠
Whats the equity of Player 1 on this flop ?
Equity calculators give it 43.54% (18.5% for tie and 25.04% for win). No matter how hard i tried to break it down on simple probabilities and try to reach to the win equity of 25% i failed, closest i got was at 25.55% with rather spooky and most probably incorrect use of maths.
Here is my best try:
- Player 1 wins IF 4 or 3 or 5 comes (not 4h) on turn or river AND avoid a heart on river AND avoid both 4 AND 3or8 on turn and river.
This breaks down in 3 probabilities: PA = 4 or 3 or 5 comes on turn or river (not 4h) = 8outs = 8/45 + 8/44 - 8*8/(45*44) = 32.73%
PB = not a heart on river = 1-8/44 = 0.8182
PA * PB = 26.777 % So this is presumably the probability that one of the 8 outs comes for Player 1 and avoids a heart on the river (now why to avoid a heart only on river i really dont know so thats why i think the calculation is not correct, but that was the only way to reach close to 25% if both turn and river were asked for i was getting a Probability of win close to 21% only)
PC = turn or river 4 AND 3or8 ( not 8h) That was another problematic probability that i was not sure how to handle. The way i decided to handle it is the following:
- 8outs on turn and IF 8 or 3 then 2outs on river, or-else if 4 on turn 6 outs on river
PC =(8/45) X [(6/8)X(2/44)+(2/8)X(6/44)] = 0.01212
Hence Pwin of player 1 = PA*PB-PC = 26.777-1.212 = 25.56%
Is this correct ? Most probably not. What am i missing ? What would be an easy way to calculate correctly this?