Quote:
Originally Posted by Jam-Fly
He needs 29.4% equity to call (it's £390 to call, pot is £938. 390/(938+390)=0.29367). If his equity is 24%, you want him to call.
Another way of looking at it, if he calls (and has 24% equity), you win a £1328 pot 76% of the time. 0.76*1328= £1009.28. If he folds, you win £938 100% of the time. £1009.28>£938 so you'd rather he calls.
This assumes you somehow know for a fact his equity is 24%. Running it once or twice is irrelevant. The equation for running it twice would be (0.76*664)+(0.76*664)=1009.28. £1009.28>£938 so it's the same thing as above.
The conclusion is correct but I question the EV analysis. You only considered hero's win amount with a call. What about his possible loss?
Prior to hero's raise of 550, the pot was 228 + 160 = 388. If villain calls, adding 390 to hero's potential winnings, hero EV for doing RIT is
EV = 0.76 *778 - 0.24*550 = 459.
This is greater than the 388 pot hero wins if villain folds.
The equation for running it twice is not correct. In its most general comparative EV form it would be
EV = P(W1)*[P(W2|W1)*Pot + P(L2|W1)*Pot/2] + P(L1)*[P(W2|L1)*Pot /2
where Wi and Li are win and lose run i, respectively.
Without knowing the card specifics I don't see how this can be solved, though it's easy to show the EVs for one or two runs are equal.