Spoony Exercise 8: Semi-Bluffing
In Exercise 7 we took a look at how to analyze pure bluffing scenarios in a vacuum. We noted that a pure bluff has no equity in the pot when called, and that we'll rarely be pure bluffing at the tables before the river because it's fairly rare to be drawing dead. Additionally, you'll often have plenty of hands with some equity that you could bluff with on early streets, so it doesn't make sense to bluff with hands that have little or not equity at all. Here we're going to think about analyzing semi-bluffing situations.
Suppose we have 7s6s on a board of Ac8s5d heads-up out of position against one opponent and the pot is 9bb. If we bet 7bb, analyzed as a pure bluff our opponent would need to fold more than 7/16 = 43.75% of the time for our bet to be profitable. However, suppose that when our opponent calls, we have 8 outs to make a better hand on the turn. There are 47 cards left in the deck, so our chance of hitting is 8/47 or about 17%. So about 17% of the time our opponent calls, we win the pot PLUS the amount he called on the flop anyway. (Note that to keep this simple, we're going to ignore any future betting and redraws and all of that).
Now a cool thing about this is if he's folding more than 7/16 of the time, we know we're +EV anyway as a pure bluff, so adding our equity the times he calls can only make us more +EV. If your bet is +EV as a pure bluff, you don't need to analyze any further. If your bet is about even as a pure bluff, and you have equity when he calls, then you know your bet is +EV then too.
But let's look at an example of the power of having this extra equity. What if we put our opponent on a range, and decide that from that range he's going to fold 30% of the time on the flop, call 60% of the time on the flop, and raise 10% of the time on the flop (to which we have to fold). Then look at each of the possible outcomes:
1. 30% of the time he folds and we pick up a 9bb profit
2. 10% of the time he raises and we have a profit of -7bb
3. 60% of the time he calls, and 83% of that time we miss and have a profit of -7bb
4. 60% of the time he calls, and 17% of that time we profit the 9bb on the flop plus his 7bb call that we win too for a total profit of 16bb
Even if there's no more future betting, we're +EV in this scenario (our EV will be 0.146bb). And he's only folding 30% of the time!
For this exercise, go back to your hands from Exercise 7 and take a look at how much equity you think you will have when you are called. This is a short exercise that's fairly easy to do with the help of PokerStove. Just check your equity against his calling range and post your findings.
