by Aisthesis » Thu Sep 15, 2005 3:04 am
Taking another step on this whole issue, let me go for another example. Let's say at a 2/5 NL game, you can get 2 callers typically with a $20 raise UTG, and you have AK.
Ok, now if you raise here, you'll have a pot of $60, of which you yourself have contributed $20. Let's also say that your continuation bet of $50 has a probability p of taking down the pot. What's your EV on making the raise and continuation bet (with or without improvement)?
You make $40 net p times, with or without the best hand. You hit 1/3 of the time, and I'm just going to assume that you always have the best hand there (if p is low, you probably actually do). But 1-p times, you get a caller, who bets the turn if you check it but lays down if you bet again (again an oversimplification, but should be roughly accurate).
So, with a probability of 1-p, the following happens: 2/3 of the time, you lose $70, and 1/3 of the time, you win $90. So, we have here an EV of (p-1)*16.5 (which is a minus).
The total EV is thus: 56.5*p - 16.5. For this to break even, p can still be quite low. In fact, a success rate of 1/3 is profitable, with 1/4 being just barely in the red.
Now, let's look at another oversimplification: Let's say you limp your AK, 5 more limpers for a flop pot of $32 (I'm subtracting the rake at the casino where I play). You win this pot 1/3 of the time, and lose your $5 2/3 of the time. So, your EV here is something like $7.
So, now we can solve for p to see when the continuation bet is better (aside from all my oversimplifications): We need 7 < 56.5*p - 16.5.
Hence:
23.5 < 56.5*p
Basically, if p > 50%, then the continuation bet is better according to that calculation, which I think is really pretty realistic. If they fold at least half the time, you're better of making it. If they call the continuation bet more than half the time, then just forget about raising AK.