[StellarWind]

These raise-to-isolate/call-for-overcalls decisions with flush draws that include either ace-high or a small pair seem to come up a lot. I need to sit down sometime and do a complete EV computation for a couple of them. I think it would be very educational.

For now I've made a small start at considering the situation.

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2) There's no guarantee that they *aren't* going to cold call two bets, and Hero gains immediate equity on the raise once one of them does.

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This is not always true. Suppose we have a 40% chance of winning the hand and SB will always call the raise.

1. If both the players behind us coldcall we gain (4 * 40%) - 1 = 0.6 SB.

2. If one player coldcalls and one player was never calling we gain (3 * 40%) - 1 = 0.2 SB

3. If one player coldcalls and one player is forced out we lose (2 * 40%) - 1 = -0.2 SB

4. If one player was never calling and one is knocked out we lose (1 * 40%) - 1 = -0.6 SB.

5. If we knock out both overcallers we lose (0 * 40%) - 1 = -1.0 SB

6. If no one was ever calling we lose (2 * 40%) - 1 = -0.2 SB

In each case the computation is gain of raising compared to just calling. The overcalls we lose when we force players out count as negative bets. Once we knock a single player out the direct EV from the raise is always negative.

Knocking players out also reduces your implied odds when you make your flush, reduces the number of players available to share the drawing cost on the turn, and exposes you to a possible -EV 3-bet.

It's pretty obvious to me that raising a better hand is quite a bit more than a tiny mistake. I'm not ready to believe -0.1 BB or anything like it.

On course successfully isolating a drawing hand is a coup. About 1/3 of the time you will win the hand because of this. [The rest of the time you would have won anyway by making your hand or he makes at least a pair.] That gives you an extra 1/3 claim on a final pot worth about 7 BB. That's more than 2 BB.

It's interesting that it is a considerably bigger achievement to trap a dominated flush draw than a straight draw. The straight draw has more independent outs and a much better chance of winning when you don't improve.