No Limit Bet Sizing: The Payoff Factor

This article is about bet-sizing in No Limit Hold’em. It is specifically about how to size your bet with a made hand against draws and the adjustments you have to make based on whether or not you’ll have to pay off if your opponent hits. In this article I will use constantly, and only briefly explain the concepts of pot and implied odds. The key to bet sizing against a draw is giving reasonable but negative implied odds to your opponents. It is easiest to just work from examples, and the concepts should become clear.

It’s a 9 person game with blinds of $0.50 and $1. Each player has $75. You hold KQ on the button. Two early position players limp in and you make a small raise, to 4X the big blind. The blinds fold and the early limpers both call. The flop comes K Q 4. It’s checked to you and you bet $9. One opponent folds and the other calls, making the pot $31.50. The turn comes 3, a total blank. It’s checked to us and we have to decide how much to bet.

First we’ll imagine that we know he has a flush draw and thus we can fold if another spade falls. In this case we can use simple pot odds to determine the minimum size of our bet. His chance of hitting a spade on the river is 9/44, roughly 1/5.  His expected value if he calls our bet = (amount of pot + our bet)(his chance of winning) – (our bet)(his chance of losing). We’ll start by finding out the breakeven point, where his expected value of calling is $0. Then we’ll know we have to bet more than that; deciding how much more is more of an art than a science.

The size of the pot is $31.50, his chance of winning is 1/5, and therefore his chance of losing is 4/5 so,

0 = (31.5+our bet)(1/5) – (our bet)(4/5)
0 = 6.3 + (1/5)(our bet)-(4/5)(our bet)
3/5(our bet) = 6.3
our bet = 10.5

Therefore, we must bet more than $10.50 in order for his expectation to be negative (meaning we make a profit). Let’s check and make sure. What is his expectation if we bet $15?

His expected value = (31.5 + 15)(1/5) – (15)(4/5)
= 46.5/5 – 60/5
= 9.3 – 12
=  -2.7

On average, he loses $2.70 if he calls our $15. We should bet as much as we think our opponent will call, as long as it’s more than $10.50, his breakeven point. If he’ll call all in, then we should bet all in. In real life we rarely know for sure what he has, so in the next example we’ll assume we have no idea at all what he has (although he still has the same flush draw).

In this example we’ll look at how much we have to bet on the turn if we’re going to have to payoff an all in bet if he hits. In this case,

His expected value = (amount of pot + our stack)(his chance of hitting) – (our bet)(his chance of missing)

Again, we’ll first find his breakeven point. “Our stack” is the only different value from the first example. In this case it’s $75 - $4 - $9 = 62. If both we and our opponent had larger stacks we would replace the term “our stack” with “our bet + his river bet”. The point is to include what we lose by paying off another bet when he hits.