One of the first things that poker players learn after they’ve got the basic rules of the game down is the value of semi-bluffing. Semi-bluffing as it is typically taught means betting without a made hand, but doing so with a holding that has the potential to make a very strong hand on a variety of turn or river cards. The most common example of this would be if you raise to $6 pre-flop in a $1/$2 cash game on the button with 7h8h, get one caller in the small blind, and the flop comes down AhTd5h. If you bet here, you’re generally only ever going to be called by a better hand so you’re certainly not betting for value. At the same time, if you do get called there is still some hope for your hand. If your opponent holds an Ace you can overtake him if a heart comes on the turn or river giving you a flush and even via the less likely route of running sevens, eights or seven-eight on the turn and river.
Calculating the Value of Semi-Bluff
When deciding whether or not a semi-bluff is in order, there are a number of things to consider, and some mathematical knowhow is required. The first thing you need to estimate is how much equity you have in the hand, or to put it another way, how often you’ll win the hand. Typically on the flop, every card that gives you a strong hand is worth a bit more than 4% equity and on the turn, each card gives you a bit more than 2%. If we take the example from above where we flop a flush draw, we figure that we have 9 outs (all of the hearts) which will give us the winning hand. Occasionally we’ll win with runner-runner cards, and occasionally the board will come a 4-flush and our opponent will have a higher heart than us. These two events are about equally likely so we’ll discount them. Our 9 clean outs give us about a 20% chance of hitting on the turn. With this information and the amount that’s in the pot, we can calculate how often we need our opponent to fold to the flop bet to make it immediately profitable in a vacuum using the fold equity formula which is as follows:
EV = (P. Fold)(amount in current pot) + (1 – P.Fold){[equity when called x amount you win] – [(1 – equity when called) x amount you lose]}
Where P.Fold is the likelihood that your opponent will fold. We set EV = 0 to find the breakeven point.
The pot on the flop in our hand above is $14, so if we plug in that information and assume that we bet $10 on the flop:
0 = (P. Fold)($10) + (1-P.Fold){[0.2 x $14] – [(1-0.2) x $10]}
= (P.Fold)($10) + (1 – P.Fold){$2.8-$8}
=(P.Fold)($10) + (1 – P.Fold){-$5.2}
= (P. Fold)($10) – $5.2 + (P.Fold)($-5.2)
(P.Fold)($10+$5.2) = $5.2
P.Fold = $5.2/$15.2
P.Fold = .342 = 34%
So in this example you can see that if our opponent folds just 34% of the time on the flop, we have a profitable bet in isolation, and this doesn’t even take into account the expected value due to our implied odds when we hit the flush. This fold equity equation comes in extremely useful for tournament players who need to rely on fold equity very often when they are shoving all in with non-premium hands during the latter stages of tournaments.
Are you Bluffing or Value-Betting?
This is a question that is commonly asked when people are looking for a reason to bet, but the truth is that the reasons for betting aren’t always black and white. People often get criticised for making bets where ‘no worse hand will call, and no better hand will fold’ but this thinking is slightly flawed. Imagine a hand where you had raised pre-flop on the button with TJ and the flop came down A63 rainbow. Obviously if you bet here there aren’t any worse hands that are going to fold. Even the tightest opponent is going to call at least one bet here with all of his pocket pairs in a button vs. blinds situation, and the only possible ‘worse’ hand that would call you is the very unlikely 45.
Nonetheless a bet here is still a very good idea. If you get your opponent to fold a hand like KQ, KJ or JQ, you’ve made him fold a hand that has about 75% equity against you and if he calls your bet with 88 or 99 you’ve still got 25% equity against those hands. As you can see, there are situations where you can make hands with a significant amount of equity against you fold, while still semi-bluffing against weak one pair type hands.
Always Try to Have Some Equity
One mistake that less experienced poker players make is bluffing with hands that have no hope. For example they might call a pre-flop raise with 22 and then check-raise a K95 rainbow board. If your flop check-raise is called in this case, you have absolutely no hope for your hand and it’s highly likely that you have 2 outs at the most and sometimes are drawing close to dead. While it’s true that good players are aggressive and check-raise the flop a lot, they usually do so with hands that have some hope; hands that have the potential to overtake their opponents and potentially make very strong hands if the board runs out well for them.
Hands like backdoor flush draws with an overcard or gutshots with an overcard, or simply just two overcards are very good in this situation. If you’re in the late stages of a tournament and you call a raise with AhQh from the small blind and then check-raise all-in on a Th8c5s board, depending on stack sizes you could get your opponent to fold a hand as strong as T9, and he will almost certainly fold hands like 89 and even if called you have two overcards, a backdoor flush draw and a backdoor straight draw. Your overcards give you about 25% equity and, a backdoor flush draw is worth about 3% in equity with the straight draw adding another 1-2%, giving you close to 30% overall to go along with your fold equity.
