Let’s take a look at a hand where we consider a 4-bet (Figure 38). Ask yourself while you read what you would do.
A little history: this was a $530 Shootout in the WCOOP. This player had been whipped up pretty badly by me. It wasn’t that I was playing exceptionally well, but the cards were coming my way, and my reads happened to be right that particular day. My opponent’s 3-bet had been 14%. For sure, it was at least that in this hand. I believed he was 3-betting more often than not out of frustration. For this reason I decided to put the 4-bet in.
But is it right? Let’s copy and paste it into CardRunners EV. The steps are very easy from that point. Solving for 4-bets is one of the simplest exercises you can do in CardRunners EV. Copy/pasting the hand history will set up the nodes and bet sizes for you. After that it’s up to you to input the ranges.
Figure 39 shows what your calculation should look like in CardRunners EV. I have programmed for the gentleman to be 3-betting just 14% of his hands.
As you can see we have made a profitable jam to the tune of 100 chips, as can be seen underneath the first node.
Now most players at this point would go “Sweet, we made a profitable jam. Off I go.” The more deliberate poker player will actually find the point that they have to stop 4-betting. What is the break even point? You can find this by editing down the 3-betting range to take out some bluffs.
For example, if we keep the calling range of of A-Jo+, A-9s+, 8-8+, K-Qs but keep editing out bluffing hands from the 3-betting range we can find that even versus this range (Figure 40):
We are turning a very slight profit. So we could write on an index card:
With K-Qo if we raise to 3x and our opponent makes it 8x to go we can jam 43.5x versus ____% of a threebetting range.
On the back you’d put 5%, with a note that it’s barely profitable, so you know to give yourself a cushion later.
It’s not exactly enthralling, but if you stack enough index cards like this and go through them whenever you have a free moment you will build a terrific preflop framework.
Let’s say in that hand we just discussed we decided to 4-bet to 1,500. How much did we risk? If you stared at that question for a second wondering if I just asked you to repeat the number 1,500 you are wrong. You didn’t risk 1,500. You risked an additional 1,260. Your 240 chip bet is gone. It no longer belongs to anyone. It’s not a part of what you’re risking. Like the other calculations we’ve done in this book the formula is determined by how much we’re risking divided by the total pot we stand to win. In this hypothetical case that would be 1,260/2,170. Our bet would need to succeed 58% of the time.
I generally do not 4-bet without an ace blocker. People think that a king blocker is similar, but mathematically it blocks about half the combinations an ace would. The reason for this is evident once we think about it for a moment. Many people open A-2s from any position, but wouldn’t open K-2s from the button. There are much more aces than anything in a 3-betting range. An ace blocker blocks the most 5-betting combinations.
Let’s say that a person’s 5-betting range was 8-8+, A-Js+, A-Qo+ (Figure 41).
As you can see, this range possesses 78 combinations, but in the dead cards let’s put an ace blocker combination (Figure 42).
Now the 5-better only has 66 combinations. This is more than a 15% reduction! This is wonderful news for when we are bluffing, but if we change that Ah in the dead cards to a king the range is only reduced to 71 combinations. The king blocker only provides a 9% reduction. You need almost two kings to make up for one ace blocker, even though they are so close in ranking.
Let’s look at how we would decide if a 4-bet bluff of ours was profitable. Let’s use the bet sizes we were working with. We raise to 240, our opponent makes it 640, and we make it 1,500. We assume he has many more chips than our opponent did in the last example, but he doesn’t have enough to just flat. Perhaps he has 5,500 total.
We should always be looking for someone who cannot flat us when we 4-bet bluff. If he is capable of flatting 4-bets and our bluffing range is primarily weak aces then we will be in trouble. Those hands have incredible reverse implied odds. They flop poorly and cost the player money. So he is 5-betting or folding, and our bet needs to succeed 58% of the time. How do we go about figuring out whether our play satisfied that ratio?
We start first on Flopzilla with his 3-betting range. Let’s say it was 14% like our former opponent’s was (Figure 43).
This range contains 190 combinations. Remember, our opponent defends with 66 combinations, because we’re sure to be doing this with a blocker. If he defends 66 out of 190 combinations we can figure out how often that is by calculating 66/190 = 0.347. Our opponent is defending 34.7% of his range, which means he’s folding 65.3% of the time. This 4-bet is a slam dunk! Even if you remove the ace blocker at the beginning of the process he still starts with 174 combinations. 66 of 174 means he’s defending 38% of the time, which means he’s folding 62% of the time. We’re still clearing the 58% needed. These are the kinds of bets we’re looking for.
This is generally the cutoff point for me. Technically, a 12% 3-betting range will have enough combinations to get a fold 60% of the time, but that 2% margin of error is cutting it close for me. Also, my 5-bet defending range is an average estimate. On many occasions my opponent just freaks out and ruins whatever equity I had. Accounting for the 40% of the time or whatever it is my opponent has decided he’s had enough of my crap means that my edge is pretty negligible. Look for a 13% 3-bet, preferably 14%. Also, follow my methodology to come up with your own cutoff points for if you think the person is defending wider.
I wouldn’t be doing my job if I didn’t mention here how seldom I do a 4-bet bluff. Reviewing an entire tournament series of mine I found I did the play exactly once. I do it so seldom because the players have gotten so aggressive. Notice I didn’t say they’d gotten better, but they have become more resistant to folding to (God forbid) a bet that could be a bluff. They see folding as a sign of weakness. For this reason it’s more difficult to determine when a player is going to be folding out enough to run the 4-bet bluff.
There is also less of a stigma attached to preflop bluffing. If you 5-bet and get caught, well, them’s the breaks. However, if the same guy’s backer sees him 3-bet jamming a weak hand on the flop he’ll probably hear about nothing else for weeks. For this reason I focus most of my bluffs in the postflop play, and leave the preflop 4-bet bluff to specialized situations where I am certain about my opponent’s defending ranges.
The cold 4-bet bluff spot is like a four leaf clover. They do exist, but it’s usually a waste of time looking for one. That’s not to say there aren’t times to do it. It’s just such a specialized situation that you’ll rarely find it. Many people attempt the play more frequently than they should just so they can feel like a “sick” player. They see some guy doing it deep in an EPT and assume that’s what it takes to make it there, not realizing the cameras neglect the hundreds of players who play solid games and don’t do anything overly exciting.
There are a few different ways of calculating whether a cold 4-bet is profitable or not. A great way to study is to filter for them in your database and see if they pass muster. I was amazed at how many times I was just lighting money on fire to make a “necessary” sick play.
Let’s first look at an example of a 4-bet bluff (Figure 44).
You’ll notice that the sizing is larger because we are out of position, and because our hand is easily dominated by most flatting ranges. In addition, we have chosen the ace blocker to cold 4-bet here because it blocks a number of 5- betting combinations, and we are assuming that our opponents will put a raise in or fold.
The quick way to solve whether this was a good fold or not is to use Flopzilla to calculate some ranges. The initial player’s statistics have since been wiped by my database, as they were extremely dated, but I remember that he was regularly opening 35%. I looked into my NoteCaddy notes on him and found he regularly opened UTG with hands such as J-7s; these are combinations that would suggest he had a 35%+ range. Reasonably sure that this is his range, let’s make a hand selection assortment to accompany it (Figure 45).
You may have wondered why I singled out the J-7s open as evidence that he is actually opening 35% of the hands. You can see from this hand range that J- 7% is in a range wider than 35%. When we see evidence that our opponent is possibly opening wider that counts in our play’s favor. If we only see quality holdings in the hand that he’s opened, then it’s less likely he’s a wide opener and more likely that he just got hit by the deck. Memorizing ranges and what can be done with each one and then realizing what hands are just outside of them is a great way to approximate and exploit when at the live tables.
Now, we have the initial opener’s range. Let’s design the 3-betting range now. You’ll notice our villain here 3-bets more than most players at 14%. Checking his NoteCaddy stats shows a number of odd hands that indicate he really does like to bluff from there. Figure 46 shows what his range looks like on Flopzilla.
You’ll notice I made the range much stronger than it had be. I had him defending himself more often versus further action by including hands that flopped well. He could easily flat many of these combinations and 3-bet some other gapped junk.
Our total bet preflop was 6,330, but the 400 chip big blind was already dead in the pot before we made the bet, so that doesn’t count as part of our bet. So, we’re risking 5,930 to win the whole pot, which is 10,061, and 5,930/10,061 = 0.5894. For simplicity’s sake we’ll say we need both players to fold 59% of the time in order to make a profit immediately with any two cards.
Let’s construct the opener’s 5-betting range (Figure 47).
You’ll notice I only gave him 25% of the 8-8 and A-Js combinations and half of the 9-9 and A-Q combinations. I think this is a fair estimate of how often the average player will 5-bet or fold with each of these.
After we’ve established this we should establish the re-raiser’s 5-bet jamming range. It should be a little wider than the initial raiser’s, because he has more money in the pot and he has to worry about one less person when he puts his money in. I came up with the range shown in Figure 48.
In this one you’ll notice 25% of the time I have 7-7, A-10s, and A-Jo jamming, and I have 50% of 8-8 and A-Js combinations jamming.
By now you’ll have noted that in these analyses I am circling the number of the combinations, because it is the most important part of what we’re going to do next. We had the initial raiser opening 466 combinations. We had the 3-better re- raising with 190 combinations. The initial raiser then jammed 59.5 combinations and the 3-better put the money in with 79.5 combinations. This means the UTG raiser is defending with 59.5/466 combinations, or 0.1277, which is 12.77%. The percentage of hands that are folded is 100 – 12.77 = 87.23%. That’s a pretty good start!
Now let’s look at the 3-better. He is defending with 79.5/190 = 0.4184 or 41.84% of hands, so he is folding 100 – 41.84 = 58.16% of hands. I think you can already see the problem. We’re not folding enough of the 3-better’s hands to justify the play. Worse, there’s still one more raiser! Both of them only fold 0.8723 * 0.5816 = 0.5073 or 50.73% of the time. A play that is considered oh so sexy by the poker world at large is actually fool’s gold.
It’s important to do the work because when you labor on a few of these for 10 or 20 minutes you’ll never again get the sinking feeling you get as you realize your plays don’t clear. You’re very unlikely to try and execute something so foolish again. However, if someone just tells you it’s a bad idea or if it doesn’t work out a few times in a row you will always have that nagging suspicion, which could easily manifest itself in poor play.
The “longhand” version of this is doing it with CardRunners EV, which I find to be a much better exercise when I have the time and a computer, because it is easier to adjust the hands, bet sizes, and ranges. Whereas you’d have to go back to the beginning of this process if you wanted to try a slightly different hand range, with CardRunners EV it’s just a matter of changing a few numbers. I find this very beneficial when trying to find the minimum ranges necessary to run a play.
For reference, with cold 4-bets, usually the initial raiser has to be opening 40%+ of hands and the 3-better needs to have 15% of hands or more. These need to be weak ranges, and neither player can be particularly good at defending versus the play. Then you can start considering a cold 4-bet. As you can imagine, this doesn’t come up that often.
I refer to the Flopzilla method as the shorthand version not because it’s necessarily easier, but because it can be done with any remedial hand range calculator that counts the combinations. If you’re on a break in a tournament you can even try to do one on your smart phone.
