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Bluffing, Part 1

02/05/2019 by Steve Blay

Now that I’ve finished my six part series on playing draws (whew!), I want to do a series on bluffing and semi-bluffing. This three-part series will only scratch the surface of this complicated topic, but I plan to address some of the most common mistakes I see made in this area.

In this first part, I’m going to give a high-level overview of the math behind bluffing. In part 2, I’ll talk about what hands you should bluff with. Finally, in part 3 we’ll look at some practical tips and examples. Ready?

So let’s take a quick look at bluffing from a game theory perspective. “How often should I bluff?” is a common question heard by poker coaches. To answer this, first we have to know that game theory tells us to make our opponent indifferent to bluff catching.

What exactly does that mean? Well, it means that whether they choose to bluff catch or not, they win or lose the same amount of money. So, in essence we’ve taken them out of the equation. They can’t influence their own destiny.

Sounds good, doesn’t it? But can we really do that? Yes, we can - let’s take a example and assume we’re on the river with $100 in the pot. We decide we want to bet another $100, a pot-sized bet, and we want to know how often to bluff.

Looking at this from our opponent’s perspective, there is now $200 in the pot (including our pot-sized bet). To bluff catch, it is costing our opponent $100, to potentially win $200. Would everyone agree that if our opponent wins 1 out of 3 times, he will break even? Sure – he wins $200 once, but he loses $100 twice. Therefore if we are bluffing one out of three times, our opponent breaks even. And that’s the answer. No matter how often he decides to bluff-catch, he will always break even in the long run.

To be more concrete about it, let’s suppose our opponent decides to “bluff catch” with a medium strength hand (say, a medium pocket pairs that didn’t improve). When we have a real hand (a set, top pair, etc), he loses $100. That will happen twice, so he loses $200 overall. 1 out of 3 times, we are actually bluffing (remember, we are going to have a legitimate hand twice as often as we bluff). This time he catches us, and wins his $200 back. So he broke even.

So, to truly play game-theory optimally, we should make sure we are bluffing about 1 out of 3 times when making a pot-sized river bet. What if we decide to bet half the size of the pot ($50)? Now there is $150 in the pot (after our bet), and it only costs our opponent $50 to call. Therefore, in this case we need to have 3 legitimate hands for every one bluff. Makes sense?

So we’ve now determined how often, in the long run, we should be bluffing. So, if you generally make pot-sized value bets on the river with your premium hands, and you don’t feel like you’re bluffing the river at least half as often, you aren’t bluffing enough (by theoretically optimal play – more on that later).

Note that so far we’ve specifically been talking about pure bluffs on the river, as opposed to semi-bluffs on earlier streets. While beyond the scope of this article, a mathematical study of poker-like games reveals that you should be bluffing even more often on the turn, and even more often than that on the flop! Part of this is due to the fact that your bluff hands on the flop and turn are actually semi-bluffs in general, and those have some equity. Whereas your river bluffs (if you’re doing it right) are “pure bluffs” with no equity. So since your flop bluffs are not actually pure bluffs, you need more of them to balance out your value hands. That isn’t a mathematically rigorous explanation, nor is it the whole story, but just suffice it to say that you need to semi-bluff on the flop a lot more than you bluff the river. In fact, you should be semi-bluffing on the flop significantly more often than you value bet, possibly more than a 2 to 1 ratio of semi-bluffs to value bets. Most players don’t semi-bluff often enough on the flop.

That’s a quick introduction to the theory behind bluffing. In part 2, I’ll talk about hand selection when it comes to bluffing opportunities.