Pos EV on HU one-bet bluff?

[LinusKS]

I have a question about the one-bet bluff from the sb position heads-up.

Here's the set-up.

You make the one-bet bluff, but you will fold to any re-raise. How often does this bluff have to work to turn a profit? (By "work" I mean - your opponent folds - leaving aside the cases where he might just call, for the moment.)

[Ezcheeze]

It depends on the size of the pot. If there is X times the bet you are making in the pot then your probability of success has to be greater than 1/(X+1) to show a profit.

-Ezcheeze

[LinusKS]

Well, the size of the pot is his big blind (bb) + your small blind (.5bb). When you bet, you're adding another 1.5bb to the pot.

So how often does your bluff have to work?

It sounds like you're saying it has to work half the time to break even.

I think it's more than that.

[MisterKing]

It has to work more than 50% of the time. Here's why:

You are risking 1.5 SB (your raise) to potentially win 1SB (the other guy's BB payment). Thats a 3:2 risk/reward. Leaving aside the times he calls, which is a huge caveat, you need this play to work 6 times in 10 to break even, with the math being:

Win 1 SB by raising x 6 times = 6 SB profit.
Lose 1.5 SB when re-raised x 4 times = 6 SB loss.

This assumes there is no rake on small pots (1.5 SB in this case), which may or may not be true depending on where you're playing. I think on Party there is no rake in this situation. If you do add a rake, you're going to need to win there and then more often to justify the raise.

[Ezcheeze]

Your .5 SB already in the pot is dead money. You are risking 1.5SB to win 1.5SB thus you need to win 50% of the time to break even and greater than 50% to turn a profit.

-Ezcheeze

[LinusKS]

That was my initial thought as well.

But consider this - when you win this bluff, you win 1.5 big blinds (bb) - his big blind plus the small blind you contributed to the pot.

When you lose this bluff, your opponent wins 3 big blinds. Your bluff (1.5 bb) plus the money that was originally in the pot.

How can you break even winning just half the time, when he scores twice as much every time he beats you?