Posted by Dr Fro 1:39 PM
How much do I bet?

In limit poker, the only consideration is if you raise/bet, call/check, or fold. In NL and PL, there is the other consideration: how much to bet. This is by no means a science, but I would like to give a quick quantitative analysis of one fairly simple situation, and perhaps this will provide a framework for you to begin to answer the question in the more difficult real-life situations.

Suppose you have top two pair and "he" has a flush draw on the turn. Specifically, You hold AKo, he holds 2h,Qh and the turn shows Ah,Kh,10c,4s. You win as long as none of the 9 remaining hearts don't come, 35 out of 44 times.

The pot is $100 and he checks to you. How much do you bet?

For starters, no matter if you bet $1 or $999999999, you still have "the best of it" You still have a positive EV. As a matter of fact, the EV is positively correlated with the size of the bet, so the more you bet, the better off you are (assuming he calls). But you can't bet a trillion dollars, because you increase the risk of him folding, which would make your return only the $100 already in the pot.

Let's consider what the highest amount is that would get a call. It is $34.62. This is simply 9/44 * ($100 + $34.62) - 35/44 * ($34.62) which equals $0. Any higher bet from us gives the other guy a negative EV. Any lower bet from us gives him positive EV.

Now this assumes you know what he holds and he knows what you hold, and this should never happen. However, you are often put in a situation where it seems quite apparent that you have a made hand and he is on the come.

So, again how much do you bet? Certainly not less than $34.62 as that is leaving money on the table. Bet a minimum of $34.62. You go up from there depending on the likelihood of a call. A rational player should not call > $34.62, but players aren't rational. Worst case scenario, he folds and you get the $100, which is no worse than your EV if you had bet exactly $34.62.

The problem is that most new, inexperienced players will bet something like $20 "becuase if I bet more, he would have folded...I was trying to squeeze more money out of him" Jokes on you, Jack, he would be squeezing money out of you if you bet $20! Specifically, he would have an EV of $8.64 if you bet $20. Bet $34.62 or more and he has an EV of $0 or worse.

What is a good back of the envelope calculation? You don't need one. You know the rule of thumb for flushes (above), and straight draws are typically 8 outs, so the amount is roughly the same. When in serious doubt, though, you know that you should err on the side of an overbet, lest you give EV away.

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