The bluff 3-bet is fairly self-explanatory. It is a 3-bet that is designed to fold out hands that are better than it is. A “pure” 3-bet bluff is how I reference a hand that has little value heads-up. The hand that is most frequently used in this fashion is the ace blocker.
There are two ways to compute for whether a 3-bet bluff is profitable or not, which I will show you. The first method is what I call a “shorthand” method, and is the fastest way to compute for a 3-bet bluffs effectiveness.
This method is accurate, however imperfect. It won’t give you an equity calculation but just an idea of whether your play passed muster or not. Let’s say you have a large stack. On the button is a 25BB stack. In the big blind is a 25BB stack. You are in the small blind, and you have them both covered. The button raises to 2x. There is 2x the big blind in the middle from antes, 1BB from the big blind player, and half a big blind from the small blind player. You have A-2o. You believe that if you make it 5x here, neither the big blind or button will flat call you. They will either put their chips in or fold. This may seem like a simplified scenario, but many short stack situations are not that far off from this. There are so many big blinds you can pick up if you master this method.
You make it 5x. You are risking 4.5x here, because the small blind is dead. It is not part of your bet. There is 2x the big blind from the initial raise, 2x from the antes, 0.5BB from the small blind, and 1BB. This means there is 5.5x out there. You are risking 4.5x to win it. Your bet will need to work 4.5/10 = 45% of the time to be profitable as a complete bluff. That number assumes the second someone shoves or does anything other than fold we lose. Remember, we divide by 10 because that is the total pot we will win if everyone folds.
So, you know that your bet needs to work 45% of the time. First, look at your button player’s fold to 3-bet percentage. Say it’s 60%. What percentage of hands do you think the big blind is shoving over a raise and a re-raise? Let’s say it’s A-Qo+, A-Js+, and 7-7+. Quick, what percentage is that?
If you had no idea what number we should assign the “playing” percentage here, or what number that range represented, go play Flopzilla some more. The practice will do you good. That range is 6.5% roughly. That means he’s folding 93.5% of the time, and 0.6 x 0.935 = 0.561. Both players are folding 56.1% of the time here. The play clears.
The process I described above is what I do most often when I’m playing multiple tables and do not have time for any deeper analysis. Notice that this does not account for when big blind shoves and clips some of button’s playing range. Also note how I had to project a range onto big blind, and know the percentages of said range off the top of my head. I also needed some remedial knowledge of multiplication tables. If I had turned that equation to 6 * 9 I would have had 54, which would be close to what the answer was.
Everything I described is unused by 99.9% of regulars, and it far more exacting than their “feel” method. The turnover rate for professional poker players confirms that there is far less talent than people who think they are talented believe. This method is more accurate, and a sixth grader could learn it. All it required was some playing with ranges, a statistic-tracking program, and remedial knowledge of your multiplication tables.
Now, let’s say you have a bit more time. You can use my second shorthand method. I use this most frequently in hand history discussions with other people who value their time, and also do it when I’m trying to get through a whole hand history in a day and can’t explore fully every interesting spot I find.
In this situation you should put these ranges in Flopzilla. The first you should find is big blind’s range, since his only input is all-in or fold it is the simplest. Figure 30 shows what I came up with.
Notice how I put my hand into the “dead cards” section. It has changed what his jamming range is. Before, the range I had memorized was 6.5%. However, when I take a moment to put in the blockers I find the more accurate answer, which is he only has this range 5.88% of the time, which we’ll round up to 6% from now on. The percentage of the time he is folding now is 94%.
That settles that number. Now let’s get the button player’s opening range. We look at his HUD and see he is raising 62% of the time, and it’s over 20 some trials! This seems a little extreme. Perhaps he picked up a few hands.
It is a good practice when computing for a bluff’s effectiveness to give our opponents nightmare ranges. If we can bluff the worst they can throw at us we can make a note to bluff always. Figure 31 shows what I figured was the tightest he could be playing.
I put a black circle around the number of combinations this is. While you can do the computations just with percentages it is good practice to start counting the combinations. In many instances it can be more accurate, and it helps you make more natural decisions at the table when you’re trying to count how many hands are actually out there against you.
So, we have 504 combinations to start. Now, let’s trim this range to decide what we think he is 4-betting against us (Figure 32).
This is a pretty optimistic range for a guy who seems generally honest versus 3-bets. We have him 4-betting every single pair, and even the weak broadways 25% of the time (as evidenced by my playing with the “weight” function).
By the way, you may disagree with my ranges several times in this book. Remember always that I’m trying to make an average for the guy on his toughest day. Perhaps you think he’s folding some of these combinations. Maybe you think he’s 4-betting more of his broadways. I’m basing my opinion on having watched more hand histories than anyone I know, but I understand I can be wrong. What’s more important is you get the methodology.
You now take the number of combinations that are left. Did you look at it without the circle this time? In this case, it would be 185 combinations played out of 504 starting, and 185/504 = 0.367. He is playing 36.7% of the time, so he is folding the rest of the time, which is 63.3% of the time.
Remember, we gave him an atrociously good starting range compared with what his statistics said, and we gave him a healthy bluffing range, and our position improved. Now if we compute for 0.633 x 0.94 we get 0.595 or 59.5%. Our play seems to succeed more often than we first estimated at 56%.
When you solve in this fashion, you will find that your play succeeds more often when the position from which the raise comes is later, and succeeds less when the raise is from an earlier position. The deeper analysis also gives you further ideas of what you should be looking for, such as Raise First by position.
When you have the time you should enter all the factors into CardRunners EV and see what your actual equity was on the play. If you’re playing live you don’t even need the hand history to make a CardRunners EV calculation. You’ll need to write down the factors in a notebook and apply them to the program.
You’ll notice when we open the program we’re given the option to pick the positions of the players in the hand. The ones in yellow are the ones I have selected (Figure 33). You’ll also have noticed I edited the other sections as well, where we input how large the blinds are and what the players stacks are. I have given our opponents 25BB, and our stack doesn’t really matter. We have them covered, so we should put a larger number, but the effective stacks are 25BB.
We now hit the button on the right that says “Start new tree.” You’ll notice we now start with significantly less data then we did the last time in this book when we did a CardRunners EV calculation (Figure 34).
Don’t panic. Just hover your mouse over the first node. It will give you the playing actions. Select “Raise” and enter the bet sizings. Underneath it there will be text that says, “All hands.” Click on that to edit it, and give the opening range you want your opponent to have. Now, if you click “Fold” again above the node it will add another branch to the tree, which has button folding. We do not care about this branch. It asks us to solve for a situation that is unimportant to us, the blind versus blind battle, so we will just have ourselves folding.
We follow the same process when we come to the small blind, and make the raise of 5,000, only now when we edit hands we can just put A-2o. You don’t have to establish a folding range to account for the rest of the hands, so just enter this. You follow this process adding all the ranges we discussed in the last section, or whatever ranges you prefer (Figure 35).
This looks very daunting at first but follow the lines slowly. Look at each node. See how it lists our percentages, ranges, and bet sizings? That’s all you’re entering. If you can do basic data entry, you can do this.
I encourage you to try this at home if you have a copy of CardRunners EV to see if yours looked this way. The only branch you won’t necessarily need is the one where I showed us folding out if button folded. That is there to show you what to do if the program makes us solve something we don’t care about. Sometimes CardRunners EV requires you to finish a tree in order to run the numbers, so it’s important you see how a tree branch is written off.
Figure 36 shows what happens if we hit the “EV Calculate” button at the bottom left.
Our play is good for roughly 1.5BB. We can now see this is too significant to pass up. Sometimes you will run these numbers and find your play was good for 0.1BB or something negligible. In this case, we can write off the play, or try to find the numbers that provide for a clearly profitable play, as we can assume our margin of error will frequently spoil this small edge.
Notice how in this analysis nobody is making an unprofitable decision at any point in the hand. This is why when people say “my play was profitable” it doesn’t really mean anything. You can wait for aces and shove all-in preflop every time, and then you will never make an unprofitable play. Here, these players are making a profit off their plays, but they are folding so much that they allow a third party to come in and steal from the pot regularly.