GT-NO: Sometimes You Always Fold

Regular readers of mine may have noticed that I have many times warned against tough, aggressive opponents who will bluff a lot on the flop and, if called, will sometimes, but not always, continue bluffing on the turn, and, if called, give up on even more of those bluffs on the river, but not all of them.

Our new book talks about this a lot. And it goes on to say that when you are playing against someone like that (decidedly NOT the typical opponent we are trying to help you beat) you should often fold to his first bet even if you think your chances of having the best hand is a bit over 50% (unless it doesn’t cost you too much to move in on his first bet.)

To show why this could happen, I will continue with the lesson I started last column about the GTO strategy when one hand falls into the category of being either great or terrible with nothing in between (polarized), while the other one is merely good.

When not playing the river, this precise situation will very rarely occur, but sometimes spots can come close. (Perhaps someone flopping a small flush in pot-limit Omaha, while the other player has at least the ace of that suit, but may or may not have the ace high flush.)

For the sake of simplicity, I will specify that all bets are pot sized. Recall that GTO requires that the bettor should bluff the size of the pot half as often as his value bets when he bets the river against one opponent.

Because that opponent is getting 2:1 and you want him to be “indifferent” as to whether to call or not, he cannot exploit you when you bet in this fashion. Meanwhile, the caller who is playing GTO should flip a coin to decide whether to call because the bettor is getting exactly even money on his pot-size bluffs.

Keep in mind though that if the bettor is using GTO you would do equally well no matter how often you called or folded. This is worth knowing because, as we will see in a moment, it is often easier to do more complex calculations under the assumption that the GTO bet produced a fold. (Note however that if the bettor is more than two-thirds to have it, he should always bet, and the other player should now fold 100% since he is more than a 2:1 underdog.)

But things change if there is more than one round of betting left. If the ensuing cards make almost no difference, the bettor’s GTO strategy is to bluff A LOT on that first round. 

Suppose that the chances that the bettor has a real hand is 24%. If there was only one round of betting he would bet 36% of the time. So if there was $100 sitting in the pot his EV would be $36 while the opponent’s would be $64 regardless of how the opponent played.

But what if there were three rounds of betting? If it gets to that third round, the bettor would again bet only 36% of his total hands. But here is the thing. On the turn the caller knows (GTO assumes he knows) that he is facing a bet that will result in him folding 36% on the river. That means that if the bettor bets a total of 54% (36% plus half of that) the caller may as well fold to that bet.

Which means that on the flop, the bettor can be betting 54% plus 27% to make the caller indifferent as to calling that bet.

We can thus conclude that the caller can’t improve on the strategy of always folding (which means that his EV in this case was only 19%).

Still skeptical? Let’s see how he would do if he never folded.

24% of the time he would lose 100 + 300 + 900 which is an EV of (-$312)
12% of the time he would win the $1,300 total bet plus the original $100 which is an EV of $168.
18% of the time he would win 100 + 300 + 100 which is an EV of $90
27% of the time he would win 100 + 100 which is an EV of $54.
19% of the time he would win 100 which is an EV of $19.

This is the same plus $19 EV as would accrue to the player who just folds right away.

(I will leave it as an exercise for the reader to verify that it is also the same EV for the caller who gives up calling on the second or third round.)

Don’t worry if you can’t completely follow the above. Just realize that in this hypothetical scenario the bettor can bet hands that are known to be 24% to be best (and will remain best), up to 81% of the time, and the caller (who can’t easily move all in), should fold and be satisfied with the $19 EV he picks up when the bettor checks the flop.

Notice also that if that 24% was 30%, the aggressor should bet 45% on the river, 67.5% on the turn, and 100% on the river. So theoretically the other player should always fold to that first bet. 

Hopefully you see one of the main reasons you want to try to avoid playing heads up against one of these GTO types, especially out of position with a big stack. ♠

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].