The Semi Bluff in Poker

What Is a Semi-Bluff

A semi-bluff is, and I'm taking the liberty of defining it slightly different compared to what David Sklansky did in Theory of Poker, when you bet with a hand where you hope that your opponents will fold but if they don't, you have outs to improve to the best hand. The difference in definition, for those of you who have read ToP, is almost only semantic, but I have my reasons:

What It Is Not

Raising with poor equity when there is virtually no chance your opponents will fold is not a semi-bluff. There are maniacs that do this and think that they're playing "aggressively" but what they're really doing is just spewing chips. There is a time, however, when you're actually raising with a non-made hand and hope that all your opponents will call you: when you have a flush draw on the flop and two or more opponents. This is the reason I went ahead and re-defined it somewhat, because this situation does not constitute a semi-bluff - you're raising for value. You don't want your opponents to fold in this situation, you want all of them to come along with you.

Now that we've covered the definitions, let's go ahead and look at two examples and see what this is all about.

Example 1: This Board Couldn't Have Helped You, Could It?

Limit hold 'em, 9 players. You are in the big blind, holding

J♣ T♣

and it is folded to the third player, who's only a little bit loose, but very aggressive when he enters pots, who raises. Your put him on a range of 9-9+, KQs+ (includes AJs) and AQo+. The button, a loose and passive players who thinks folding before the flop is boring, calls, and so do you. There are 6 small bets in the pot. The flop comes

7♣ 8♦ 2♥

You check, and the preflop raiser bets. The button calls. You have an inside straight draw and two overcards, so getting 8-1 it's not a bad situation to call. It's pretty close, but you most likely have some implied odds making up it even if your overcards are no good - that is, if one of the other two are holding a pair of queens or higher. There are 4 big bets in the pot, when the turn shows

2♠

You check again, and again the middle position player bets. The button folds. Now, let's consider his range again. He will not fold any of his pocket pairs here, but could he fold an ace-high hand? If he can, a checkraise isn't a bad play here. The reason this tactic may be profitable is because of the combined chances of him folding and the chance that, when he doesn't, you still make the best hand. Now, for stringency, I want to include calculations. They are somewhat cumbersome, but if you want, you may skip ahead to the conclusion and take my word for the conclusion I reach.

Assumptions: Given the range we put him on preflop, there are 54 ways he can have a pocket pair. There are 16 ways for each of the non-paired hands, AK and AQ, and then there are four ways each to make AJs and KQs. If all of them are as likely - i.e. he'll be as likely to bet KQs here as AA - there are 54 hands he will not fold when we checkraise, and there are 40 hands he's likely to fold. To be a bit more conservative, let's say we give him a 25% chance to fold and a 75% chance to call or raise. If he raises, we must fold, as the pot doesn't really grant us the odds we need. But if he just calls - after all, another 2 just fell, and even pocket aces may be afraid of trips - we still have a small chance of hitting our straight. Let's say that the distribution of the 75% of hands he will not fold is that he'll call with 50% and raise with the remaining 25%. Let's work out the expected value of our checkraise. Remember, there are five big bets in the pot when the action comes to us.

Let's look through the possible outcomes:

• 25% of the time, he will fold and we will take down the pot: 0.25 * 5 = 1.25 - the pot is 5 big bets

• 25% of the time, he will re-raise and we must fold: 0.25 * (-2) = -0.5 - we invest two bets, and we lose them immediately

• 50% of the time, he will call, and we will need to hit our straight on the river to win: This is trickier. There are 4 cards that will give us the straight, so we have a 4/46 = 8.7% of improving. We do still have overcards, and some small percentage of the time, spiking a pair will be enough to win. But for the sake of simplicity, let's just say that when we hit our straight we will win an extra bet on the river, as our implied odds and when we miss, we will always fold. I'm now cancelling out the times where he will fold when we bet our straight and the times we hit our pairs and they hold up. The assumption may not be entirely fair, but we have to draw the line somewhere. Our profit for when we win is 7 big bets (the pot will be 10, but we have invested 3 of those ourselves), and we are risking 2 big bets. Math: 0.5 * (0.087 * 7 + 0.913  * (-2)) = 0.5 * (0.609 - 1.826) = -0.61. (0.087 is the chance we hit our straight, and 0.913 is the times we do not. Everything times 0.5, since he will only call our checkraise half of the times; the remaining 50% he will either fold or raise.

The sum of the expected value of the checkraise: 1.25 - 0.5 - 0.61 = 0.14 big bets.

Conclusion

Given the circumstances stipulated, we should attempt to semi-bluff this player on the turn. Now, as you can see, the decision is pretty close, only 0.14BB.  Of course, doing these calculations at the table is not plausible, but getting a rough idea what it takes, may be. The key to success is that he will lay down the best hand some portion of the time. It would be really nice if we had some sort of easily calculated mnemonic trick that we could use at the table, but sadly, this is not really achievable. There are things to look for, though, namely these:

1. The pot must be somewhat big. Don't risk a semi-bluff with a small pot. Like we saw above, we're close to breaking even if the pot is five and we checkraise.
2. Your opponent can't be a calling station. If he can't fold, we can't semi-bluff. Hitting our outs when he calls is nice, but is actually only about a quarter of the amount we made from the "bluffing" part. So keep in mind that the largest part of the profit comes from making him fold.

Example 2: Semi-bluffs Don't Have To Be Straight Or Flush Draws

I've seen people go nuts with straight (including inside straight) and flush draws on the turn, raising and even 3-betting. A couple of times, I've seen someone cap the betting in limit hold 'em on the turn with a flush draw. This is not good poker, and you shouldn't do it. However, as happy as these people are about raising an inside straight draw on the turn, I very rarely see players bet or raise with two weak overcards, which is a bit odd given that two overcards to the board has 6 outs, whereas an inside straight draw has only 4 (the comparison is a bit unfair, since overcard outs are often "tainted", meaning that some portion of the time when we do hit our overcard, our hand still hasn't improved to the best hand, but read on). Here is the situation:

You're on the button in a 9-handed limit hold 'em game, holding

Q♠ J♠

two players in middle position limp, and you raise (whether or not you should raise here is debatable, but not a part of this exercise). The small blind folds and the big blind and both limpers call. The flop comes

T♥ 7♦3♣

Everyone checks to you. Now, before we discuss whether or not betting as a semi-bluff is profitable, we need to make a few things clear:

• You do not have the best hand right now. Okay, we can't know that for certain, but it's very unlikely that none of the limpers or the big blind have a king or an ace in their hands or, failing that, that none of them connected with one of the cards on the board. And K-4 is a better hand than yours at this point, so you either need to improve by the turn or river, or you need to drive everyone out before showdown to win this pot.
• The pot at this point is 8 small bets. You won't be able to make anyone with an open-ended straight draw (or even inside straight draw, given the implied odds) fold. But someone with a hand like A-5 might fold, which would be very good for you.

Now, it's unlikely that you'll get everyone to fold. But let's figure out just how unlikely it has to be for you to just break even if you bet:

You are investing 1 bet to win 8. You will show immediate profit, then, if

x * 8 + (1-x) * (-1) > 0

where x is the chance of everyone folding. The 8 is the number of bets you stand to win, and -1 is the number of bets you risk. Solving for the break-even value of x (where the above equation = 0) yields

x = 1 / 9 = 0.11 = 11%

So, if there's even just about 12% chance that everyone will fold if you bet again, you will show immediate profit, and this is not even taking into account that you have ways to improve. Now, if we get a caller, we have to make a somewhat accurate estimation of how many outs we have. The starting points is 6 (pairing either our jack or our queen could be an out), but carries with it some problems. What if, for instance, our sole opponent holds J-T or Q-T? In that case we do not have 6 outs, but in fact only 3. The probability of this (or any other combination where he holds a card that has paired the board plus a jack or a queen) is 6/46 = 13%, presuming random cards. Of course, it's somewhat unlikely that someone limped in with J-3, but Q-T and J-T are certainly not impossible holdings, especially if they are suited. It's also quite possible that the caller is slowplaying two pair or even a set, so let's discount our outs accordingly, and figure that less than 87% of the time, perhaps more like 70%, our overcard outs are clean. 70% of 6 outs is 4.2, and rounded off for bad luck gives us 4 - so we can consider ourselves having five outs. Counting outs and especially discounting them is tricky business, but something that you should practise to the point of making it an unconscious habit. For a good read for counting and discounting outs, see Small Stakes Hold 'em by Ed Miller, David Sklansky and Mason Malmuth.

Back to our semi-bluff, then: we give ourselves 4 outs, which, incidentally, is the same number of outs we had in the first example. I will not take you through the calculations for the rest of the hand (which are increasingly complex, given the number of possible outcomes), but will instead jump right to the conclusion:

Conclusion

We learned in the first example that the pot had to be of some size for a semi-bluff to be worth attempting, as most of the value of it comes from getting everyone to fold. The pot is certainly big enough here for us to give it a shot; 8 bets compared to the 1 bet we risk by betting. We have shown that you need a success rate of 12% to show immediate profit from this, which, experience tells me, is quite possible if the game is somewhat tight. Again, if you know from reads that some of the players involved in the hand always "peel one off" on the flop, you should consider just checking here. If you can't make them fold, you shouldn't try, then it's better to just check for the turn and hope that you spike a pair or an open-ended straight draw.

Furthermore, we see that overcards can be as valuable outs as the inside straight draw in the first example.

Got It?

Having looked at two different examples, I want to take a moment to encourage you not to over-use semi-bluffing. It's a powerful tool in your arsenal, and it's highly profitable against the right opposition, but automatically clicking "bet" or "raise" just because you turned a flush draw isn't good, especially if you have position. Seeing a cheap river with your strong draw may actually be a lot better, even if there's a chance that your opponent will fold when you raise or bet. Specifically, it may be smarter to call because if he has a hand, he's likely to bet into you on the river again, allowing you to raise when you hit your hand. Winning two big bets on the river can make up for the times you just call and miss out on a semibluffing opportunity.

And, as always, don't semibluff calling stations. It's just not good poker.

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