Hold'em Brain: Semi-Bluffing

Although the term semi-bluff or semi-bluffing is now used universally in the poker world, it was first used by David Sklansky. The idea is that you bet or a raise with the hopes that your opponent will fold, but if they do not, you still have a chance to win the hand with other cards to come. This allows you two ways to win, via a fold by your opponent or getting lucky on a future round. If there is no chance that the opponent will fold, then it is just a bluff, not a semi-bluff.

Semi-Bluff Raising on the Turn

There are times when you should raise even if you do not have the best cards at the moment. You are hoping that your opponent will fold a better hand, but even if he calls, you will still have a chance of improving to beat him.

Example:

Your hand: A♠K♠

On the Turn, the board is: J♠5♣6♦Q♠

Lets assume you know your opponent has J♣9♣, and he is currently ahead of you with a pair, but you have many outs. Any A, K, T or spade gives you the winning hand. There are a total of 44 unknown cards (52 cards in the deck, minus 2 in your hand, minus 2 in your opponents hand, minus 4 on the board), and 18 cards will win the pot for you (3 A's, 3 K's, 4 T's, and 8 remaining spades, note that a ninth Spade has already been counted). This means you will win 18 out of 44 times. Normally we would use 46 unknown cards on the Turn, but in this case we are assuming we know our opponents hand.

To make this demonstration simpler, lets assume that if you do not make your hand on the River, you will simply fold, and that if you do hit your hand on the River, your opponent will call your bet half the time.

On the Turn, the pot contains 5 big bets, and your opponent bets into you, thus making it 6 big bets in the pot.

If you call here, you expect to hit your hand 18 out of 44 times, and make 6.5 big bets when you do win (remember we assumed that if you hit your hand on the River that your opponent will call you half the time but will not pay you off the other half of the time). You also expect to lose 1 big bet 26 out of 44 times. The expected value in this case would be 2.07 big bets to make this call, so it is worthwhile to at least play and stay in the hand to see the River card.

Expected Value of Calling = (18/44 x 6.5 big bets) + (26/44 x -1 big bet) = 2.07 big bets

Instead of calling, you could consider raising. Suppose if you raise, there is a 20% chance that your opponent folds right there on the spot, with the Q on the Turn, that is not altogether unlikely. If he calls you on the Turn, you realize he is definitely going to call again on the River if you do not hit your hand (so you cannot bluff on the River), but he will not call if you do hit your hand since the combination of your raise on the Turn and the scary board will now be too much for him. Now is it better to raise or just call?

Expected Value of Semi-Bluff Raising = (20% x 6 big bets) + (80% x 18/44 x 7 big bets) + (80% x 26/44 x -2 big bets) =2.55 big bets

The EV of the semi-bluff raising play is greater than the EV of calling with these numbers that we used, which means we should raise instead of just call.

But what if you had estimated his folding percentage incorrectly? What if instead of having a 20% chance that he folds on the Turn, this guy will actually never fold. Well now you have cost yourself money with a raise in this spot, because you are more likely to lose than win and you have put more money in the pot.

Expected Value of Semi-Bluff Raising if your opponent will never fold on the Turn = (0% x 6 big bets) + (100% x 18/44 x 7 big bets) + (100% x 26/44 x -2 big bets) = +1.68 big bets

With that adjustment, it is clear that a semi-bluff raise against this opponent is not a good idea, as it lowers your expectancy from 2.07 from calling down to 1.68. This is the main reason why the semi-bluff can sometimes be a useless concept in the lower limit games. Since the players in the low limit games are much more likely to call than players in the middle or higher limit games, players who use the semi-bluff raise too often in the low limit games will find that they are costing themselves money by making this play.

The math shows the breakeven point of the semi-bluff is for your opponent to fold 9% of the time. At that rate, your expected value of the semi-bluff raise would be 2.07, which was the same as just calling.

EV against a player who folds 9% of the time: (9% x 6) + (91% x 18/44 x 7) + (91% x 26/44 x -2) = 2.07

As you can see by this demonstration, whether a semi-bluff raise is correct or not depends on the frequency that your opponent will fold a made hand. This is a nice example of how combining the mathematical side of the brain with the social side of the brain can result in a correct analysis. If we just used the math side, we are still at a loss as to whether or not a raise is correct since we do not have an accurate assessment of his folding percentages. If we just used the social side, we are at a loss as to whether or not a raise is correct since we do not have an accurate assessment of the value of a possible fold compared to the negative value of a call by the opponent and losing more money when we lose. It is only when we combine both sides of the brain that we can make it all work.

Unless you are very good with math, or an idiot savant like the character that Dustin Hoffman played in Rain Man, you will not be able to do the math in your head. Even if you understand the concept, it is completely irrational to think anyone can do these calculations in the heat of the battle. But it is still useful to play with the spreadsheet and the math so you can have some idea of certain situations when you are at the table. In this case, you will notice that it takes the opponent's folding rate to be only 9% of the time for a semi-bluff to be a breakeven play when you have a 18 out of 44 chance of winning and an EV of 2.07 big bets when calling. Anything higher than a 9% folding rate makes the semi-bluff a positive expectancy play. Since most players will fold more than 9% of the time in a situation like this, you can keep in mind the strategy of the semi-bluff Turn raise when you have so many outs, and the opponent may only have second pair.

Raising on the Turn for a free showdown

Another way to semi-bluff is when you have a decent hand on the Turn and raise for a "free" showdown. Actually, the showdown is not free at all since you are committing the two bets on the Turn, but in the spirit of the free card raise on the Flop that really saves a half a bet, lets call this a free showdown raise.

Here are the issues to consider regarding a free showdown raise.

1. Your hand has a chance to win a showdown on the River
2. If you are behind, you have some possible outs
3. There is a chance that your opponent will fold
4. The chance that your opponent will re-raise you on the Turn is low

Lets take a look at each issue closely

1. Your hand has a chance to win a showdown on the River

The reason this factor is important is because you do not want to be putting in any extra bets if you are an underdog and your opponent is likely to call. If you had called the Turn and would not have called the River if your opponent had bet on the River, then you should not consider raising here unless the other factors are very extreme towards raising. You want to have a hand that you would have been willing to call a Turn bet and a River bet anyway. Thus if you do lose this hand, you do not lose any more. In the previous section, I described a semi-bluff raise on the Turn, but that example is a bit different in that your hand has almost no chance of winning a showdown if it is unimproved on the River.

2. If you are behind, you have some possible outs

Having a chance that you are ahead is important, but sometimes you are wrong and you are actually behind. In those cases, you want to have as many outs as possible so that if you are behind you still have a chance of catching up and giving your opponent a bad beat. For example, if you have KQ and the board on the Turn is K983, you may have the best hand, but you are not so sure. Your opponent could have KJ or KT and you are raising for value, or your opponent could have AA, AK or K9 and be ahead, in which case you have 3 outs to catch up. With KQ you would have been willing to call the Turn and River anyway, so you do not mind committing those bets on the Turn. If your opponent calls, you may decide to exercise the option of betting the River only if a Q or K comes.

3. There is a chance that your opponent will fold

Whether or not your opponent has a better hand, if he folds to your raise on the Turn, it is normally a good thing. If he is ahead, you win a hand that you were an underdog to win. If he is behind, you win a hand right there on the Turn and do not give him a chance to give you a bad beat on the River. The only time when it would be bad for your opponent to fold if you raised is if he was drawing dead or drawing relatively thin. For example, maybe he only has two outs, in which case you are hoping he calls. But notice that even in a case like that you would prefer to raise because you would not want to give him a free look at the River if you did not think he was planning on betting or calling the River unless he caught. Typically, the higher the chances of your opponent folding when he has outs, the better a Turn raise will be.

4. The chance that your opponent will re-raise you on the Turn is low

If your opponent re-raises you, then he has completely foiled your strategy if he is ahead. If you still plan to call the River, now you have cost yourself two full bets with the free showdown raise strategy. It would be best to put yourself in the position where you know a re-raise on the Turn is a sign that he has a great hand and is very unlikely to be a bluff. This way you could safely fold a marginal hand. For example, you have AT and on the Turn, the board is AKJT of four different suits, any Q would make a straight. You decide to raise for a free showdown, but your opponent, normally a passive player re-raises. If the pot odds warrant it, you may still want to call this raise and see if the River brings you a full house. If the pot odds are not there, then you can safely fold without fearing you folded to a bluff.

An Expected Value analysis on whether or not to raise on the Turn for a free showdown could be used, but the problem is that there are too many variables to show with one example and often when this play is made, the raiser does not even know if he is ahead or behind.

When the opponent's semi-bluff or free card draw has hit

There are times when you think the other player is bluffing or semi-bluffing and you do not mind letting him bet as you are likely ahead. However, there are situations when you have to rearrange your thoughts based on cards that hit the board. This can happen when a dangerous card comes and if your opponent was betting or raising with a semi-bluff, he would have gotten there. If he was not semi-bluffing to begin with, he may already have been ahead. In either case, you are much more likely to be behind now and should seriously consider giving up on the hand.

Here's an example:

You are in late position with K♠T♠. It is folded to you and you raise. The small blind and the big blind call. There are three players and 3 big bets in the pot.

Flop: J♠T♣3♦ rainbow

Both blinds check to you and you bet. The small blind folds and the big blind check-raises. You know the big blind is a good aggressive player. You also know that the big blind knows that you are a good player that have the ability to lay down a hand like A5. There are a myriad of hands that the big blind could be raising with, they include: any J, any T, JT, Q9, KQ, 98, A3, 33. Many of these hands you can beat, and you do not mind calling his raise and you do. There are now two players and 5 big bets in the pot.

The Turn is a 5♣

The big blind bets and you call. The 5 should not change anything except the unlikely case that the big blind has T5, 53 or 55, which all seem unlikely compared to the other possible hands. Your call should make it clear that you have a legitimate hand, either made or drawing. There are still two players and 7 big bets in the pot.

The River is a Q♥

If your opponent was on a straight draw, he has either hit a pair of Queens on the River or caught his straight draw. With straight draws of Q9 and KQ, he now has the top pair. With 98, K9, he has now caught his straight. This Q is a very dangerous card for you. Since the opponent is a good player, you should know that he knows the Q is a dangerous card for him too. If all he had was a J or a T, he would be afraid that the Q filled your straight or made you a higher pair. If your opponent still bets on the River, you have to readjust your previous thoughts that he may have been semi-bluffing and has now likely hit a higher pair than yours or filled a straight, or had you beat to begin with. Even with 8-1 odds, your chances look very dim based on the way this hand has developed. The only hand you can beat now are an unlikely worse Ten still betting into you (you must realize he should be afraid of the Q even more than you if he just had a T) or a stone cold bluff on the River with a hand like A3. You should fold.

Another situation that comes up often, especially in shorthanded games where players will semi-bluff often, is when a Turn or River card comes that is right in the middle of a possible straight draw. For example, with a Flop of J73, a T, 9 or 8 are all very dangerous cards especially if you have a pair of 7s or lower. This is because any straight draw has either made their straight or now has a higher pair than you. You may be comfortable calling down an opponent that you think may be semi-bluffing when you have middle pair, but when one of these danger cards come, it may be time to bail on the hand.