GT-NO: The Math Of Blocking Bets

Blocking bets are smallish bets you should sometimes make when heads up on the river when you are first to act and your chances of having the best hand are not high.

They are a well-known option among experienced players and should theoretically be done when the EV of that play is higher than checking and calling, checking and folding, or bluffing.

Almost always they are made with the intention of folding when raised. Except of course when the bet is a fake blocking bet with a good hand that doesn’t mind being raised.

As always, there is a GTO solution as to the size and frequency of a blocking bet but, as always, you can improve on the GTO recommendation if you have a pretty good idea of the various probabilities and the various proclivities involved in a specific hand.

For instance, let’s make the following assumptions…

There is $100 in the pot.
Your chances of having the best hand are X. 
You are first to act and are thinking of betting $20 rather than checking.
You think that if you check and he bets it will be a bet of $100.
He will never fold when he has the best hand, will sometimes raise when he does and never raise when he doesn’t.
You will never call a raise (except when it was a fake blocking bet with a good hand.)
His chances of calling and winning is Y.
His chances of calling and losing is Z.
His chances of folding (which he will never do when his hand is best) is (1-x z)
His chances of raising is 1 (the three chances above). 

Now let’s fill in the variables with an example.

You think there is a 25% chance you have the best hand. You think that if you bet $20, he will raise 50%. He will call another 25% with the best hand. He will also call with 10% of the 25% when your hand is best while folding the remaining 15% of his hands (all losers). 

Your EV is calculated as:

15% of the $100 pot (when he folds) plus 10% of $120 (when he calls) minus 75% of $20. Thats an EV of $12.

If you check, you only win the pot when he checks behind you. Say that happens 10% of the time. He is not bluffing as much as GTO recommends but it is still enough to cut your EV down to 10% of the pot since you can’t call him. That’s $10 EV, which makes the blocking bet better.

But it wouldn’t take much to change that. If he almost never bluffs if you check, your EV shoots up to almost $25 if you check. If he will sometimes raise bluff your blocking bet, that EV goes down. It also goes down if he would almost never call your bet with a worse hand.

The bottom line, for those who don’t want to follow the math, is that the decision as to whether to make a blocking bet, while depending on several factors, should mainly be based on whether it tends to turn an opponent into a bad (i.e. timid) bluffer when he would otherwise be a good one. ♠

David Sklansky is the author of The Theory of Poker, as well as nearly two dozen other guides on gambling, poker, and other games. The three-time WSOP bracelet winner’s latest book, Small Stakes No-Limit Hold’em: Help Them Give You Their Money, is now available on Amazon. You can contact Sklansky at [email protected].