# cbloom rants

## 3/05/2006

### 03-05-06 [poker]

Let's consider limping vs. raising small pockets, playing for sets. You flop a set about 1/7 times. Assume you always have the best hand if you hit your set, and don't if you don't. Half of the time you hit your set you get action, and in that case you win 10X the pot size on the flop.

If you limp for 1 BB , say you see a flop and the pot has 5 BB in it. No set, you lose -1BB. If you hit a set, half the time you bet and just take down the pot = +4BB. When you get paid, you make +49 BB. Net EV =

-1 + (1/7) * ( 0.5 * 5 + 0.5 * 50 ) = + 2.93

If you come in for a raise for 4BB, assume just 1 caller and the pot has about 13 BB in it. No set, you will continuation bet and take down the pot about 50% of the time, 50% you also lose your cbet. When you hit your set, 50% of the time you just get the 13 BB pot, and the other half you get 10*13 BB, but we'll cap that at 100 BB because that's the usual full stack (we use 104 below because you also get your 4 BB back). Assume your cbet is 9 BB, then Net EV =

-4 + (6/7)*(-9 + 0.5*(13+9)) + (1/7) * ( 0.5 * 13 + 0.5 * 104 ) = + 6.07

So, definitely better, but not 4X better. We can see the key benefit is that by building the pot early, it scales up the sizes of everything which allows us to win a much bigger pot when we hit. The cbet factor is actually not necessary for this to be profitable, but it does give us a nice extra bit of value.