On the surface, the protection bets are very simple. You think you have the best hand so you bet or raise. Hmm, well I guess that’s it?

Hardly. The beauty of games like NL Holdem lie in the control a player has over bet sizing. This little feature actually allows the poker player to manipulate the fundamental math of the situation and thereby having a control over his destiny in a way that tamer versions of poker don’t allow. 

So the real question is how to size protection bets and why. Lets ignore the facts as to whether the villain actually folds or not. Lets say the fish always calls. That is, our protection always fails. Why? Well because the math is interesting.

Lets set up the scenario. We have a pair of 33 and our villain probably some crazy donkey hand. The betting action pre-flop thins the field to heads up and we are out of position to the villain. The flop comes 3h 4h 9c. We have made bottom set, which is great. But there is a flush, straight and even a straight flush draw out there, which is bad. Its time to consider our protection bet options. First, we do a quick count of the pot and find there is $100 in the pot. Second, we have a look at our stacks and see that we both have around $300. Third, we glance at the villain and we honestly do not know what this crazy person could be holding. This third point is important, protection bets are not about playing psychic poker, they are all about changing the odds of the situation. To illustrate lets consider some different bet sizes for our protection bet.

Protection Bet $20

A protection bet of $20 – apart from being pathetically weak – actually gives our villain the right odds to draw for a huge range of hands. Our villain will in effect be given a 6 : 1 proposition to call. That is, on a flush or open ended straight draw, our villain has positive expected value in calling. The only draw that becomes a mistake is the gut shot, which has a 11 : 1 chance of hitting on the turn. The important point is that we are giving a chance for a villain to make a good decision.

Protection Bet $50

A little more standard, lets say we make a half-pot sized protection bet. In this case, our villain will be facing a 3 : 1 proposition to call. If the villain has a flush draw, his real odds are 4.2 : 1 to make it by the turn. If villain is on an open ended straight draw, his real odds are 4.9 : 1 to make it by the turn. In both these cases, even if he does call, the important thing is that suddenly fishing for those draw cards becomes a mathematically incorrect decision.

Lets complicate things, what about implied odds? Say there was a glint our eyes that gave away that we had a big hand. The villain cunningly considers that even though the pot odds are incorrect to call, the implied odds he is getting is actually $400 : $50 or 8 : 1 (The pot of $150 + our remaining stack $250 : the call $50). This gives the villain positive implied odds, which makes it arguably correct to call. The villain has been bluffing a lot of pots from us and thinks that we probably won’t be able to lay down trips even if the straight or flush hits on the turn. So regardless of the pot odds and in consideration of positive implied odds the villain is correct to call if he is on the flush or straight draw. 

Protection Bet $100

Okay, lets get aggressive, lets make a pot sized protection bet of $100. We already know any bet above $50 will give the villain negative pot odds. Lets see if the $100 bet has changed the implied odds. In effect the villain is now getting $400 : $100 or 4 : 1. Our villain is now getting negative implied odds on both the flush and straight draw. This is EVEN IF his assumption that we would pay off the flush or straight are correct. The important point is that our villain has only one mathematically correct decision, fold. To call and chase is completely mathematically wrong. 

So who cares? Well its not so much that the math is fundamentally interesting as that the math fundamentally affect who wins over the long run. Aggression is not merely about chest beating alpha monkey dancing. It is not just about getting the other man to lay down. It is about forcing his choices to become losing choices. So protection bets are an example but this is a mental framework you should take to all your betting strategies. 

Good Luck