Playing vs. 3bets – The 4bet Bluff
Our raising range in the CO and the BTN is especially wide when compared with, for example, our UTG raise range. Many players on the micro and low stakes don't even pay attention to this. None the less, 3-betting seems to be becoming more and more of a trend lately. You will often have to face 3-bets, and especially when out of position (OOP) this can put you in a difficult spot. We have an arsenal of options with which we can counter players who often 3-bet us: decrease the size of your 3-bet, 3-bet less frequently, shove more often, shove more flops, and so on. In this article we will be discussing another move, which, when used correctly, can be very profitable: the 4-bet bluff.
When to use the 4-bet bluff?
Let's first take a look at what we hope to accomplish with a 4-bet. As always, the main goal of the move is maximum EV. We can achieve this in a number of different ways, depending on the situation. First of all we have the 4-bet for value. This is what we do with hands like AA, KK, AK and similar hands. With these hands we are almost always sure to have the best hand and want to get the money in because our equity is often bigger than that of the range of our opponent. But be careful. A 4-bet for value can have positive EV, but maybe just calling a 3-bet is even more profitable. In other words: EV call > EV 4-bet. These situations can occur and it will be up to you to bear that in mind.
Secondly, we can 4-bet bluff. This happens with hands that we can almost never call for +EV, but that we can 4-bet for +EV by representing value. The +EV for these hands doesn't result from the actual strength of our hands, but from the fold equity we believe to have against the wide 3-bet range of our opponent. A 4-bet bluff, therefore, is a hand with which you re-raise your opponents' bet, but fold when your opponent moves all in.
In order to 4-bet bluff successfully, a couple of factors need to be considered:
- Fold equity: we think it is likely that our opponent will fold better hands;
- Max EV: a 4-bet bluff is the best option in the given situation, meaning that the EV of a 4-bet bluff is higher than that of a call or a fold;
- Light 3-bettor: we are up against someone who 3-bets with a wide range of hands, which means he will have to fold many of his hands against a 4-bet;
- Stacksizes: we prefer to do this against large effective stacks (>100BB), in order to put some extra pressure on our opponent, and so that neither we, nor our opponent, is pot committed too soon (opponent can no longer fold after his 3-bet or we can no longer fold after our 4-bet);
- 3bet size (relative to stack sizes): If the size of the 3-bet is small (in terms of absolute BB and relative to the stack size) a 4-bet is more likely as you are risking less money and you aren't pot committed as fast.
Different strategic options
If you never 4-bet bluff, your opponents will quickly have figured you out and automatically put you on AK and KK+ every time you 4-bet, which will make it difficult for you to get your monsters paid off. The question is whether or not this is important on the 100 NL tables and lower, where players tend to not pay too much attention. But OK, we'll just assume that we're playing against a good, attentive player. These are the kind of players we are trying to exploit. To do this, we have two options.
The first option is never to 4-bet. If you always just call their 3-bets, they have no idea whether you're doing this with good, excellent or speculative hands. The advantage of this is that you are very unpredictable and can't make the mistakes you could make with a '4-bet or fold' strategy. But there are also disadvantages with this strategy:
- We are not getting maximum value out of our premium hands before the flop
- It will be hard to get a good read on the wide range of the loose 3-bettor
- You will often end up playing big pots OOP against a loose 3-bettor
- You don't have the initiative in the hand
- You are not punishing loose 3-betting
Furthermore, it is very unprofitable to keep calling 3-bets. A study by the makers of Hold'em Manager showed the following:
The left column shows the frequency of calling 3-bets, and the right column shows the median winrate for players with a given 3-bet call frequency. The median is calculated by arranging all the winrates from lowest to highest and taking the middle value. This means that for the group of players calling < 23.7% of 3-bets, 50% of the players have a higher winrate than 3.65 and 50% of the players have a lower winrate than 3.65. As we can see from the table, the players calling < 23.7% of 3-bets have the highest winrate. Calling 3-bets very often is therefore not the optimal choice. But as we know, every situation in poker requires some adjustments. Let's say you have AA against a loose 3-bettor who likes to shove against your 4-bet…go ahead and 4-bet against this one. But if you're playing against a loose 3-bettor who will often fold against a 4-bet, but is likely to fire out another bet on the flop if you just call, a call might be the better option. Many factors come into play when making this kind of decision, but with some logical thinking and a decision tree of your opponent in front of you, you should usually make a good decision.
A second option we have, in case our constant calling of 3-bets becomes to predictable, is 4-betting for value and, every now and then, add a couple of bluffs to your range. As a result, it will become very difficult for your opponents to put you on a hand. In addition, we now have the initiative in the hand + we get more value out of our good hands.
Whether you are going to call the 3-bet or 4-bet yourself depends on what you expect your opponent to do postflop. Will he often fold on the flop? Then just call and often shove on good flops. If he doesn't give up his hand easily after the flop, you might want to consider giving up the hand before the flop. Always think logically about the probable course the hand will take and act accordingly. I myself like to call 3-bets every now and then, sometimes I 4-bet for value, and sometimes I 4-bet bluff, depending on my opponents' tendencies postflop. Since this article is about 4-bet bluffing, we are going to continue with the second option: 4-betting for value and sometimes as a bluff.
Imagine we're playing a 100NL game and the effective stacks are $120. We open to $3.50 on the CO with a hand like Qs10s. In the BB we have an opponent playing 22/20/3.5 and who has a 3-bet vs. steal percentage of 10% over a sample of 720 hands. He 3-bets to $13.50, bringing the total pot to $17.50. Our hand can't go up against a 3-bet because we can't call. In most cases we have to choose between folding or 4-betting. Folding has an EV of $0. Calling has –EV. What is the EV of a 4-bet bluff here? If it's greater than $0, this would be the optimal decision.
The 3-bet range of our opponent is 10% of all hands. Which hands these are exactly doesn't really matter to us. What is important is his fold-play combination. By that I mean: what percentage of his hands will he give up and what percentage won't he give up? Let's say he will shove with JJ+ and AK but folds the rest. Quickly calculate the number of possible combinations: we know two cards in the deck, which means that (50*49)/2 = 1225 combinations remain (divide by 2 because Qs9d is the same hand as 9dQs). From these 1225 hands he raises 10%, or 123 combinations (rounded up). We also know that he will shove JJ+ and AK, which are 37 combinations (6 JJ, 3 QQ, 6 KK, 6 AA, 16AK). This means that he will shove with 37 out of 123 combinations and will fold the remaining 86 combinations. This means he will fold 70% of the time (86/123) and shove 30% of the time.
Let's say we 4-bet to $28. This brings the total pot to $42. If he now shoves his remaining $106.50, we get pot odds of 1.6 to 1, but our hand only has about 2.3 to 1 against his range, so we would have to fold. As you can see we are not immediately pot committed after our 4-bet, and that was one of the preconditions for our 4-bet bluff. We think we have some fold equity against a loose 3-bettor and the stack sizes allow us to make a 4-bet, so all conditions are met, except from one: max EV? To be max EV, your 4-bet simply needs to be +EV, because then EV 4-bet > EV fold > EV call.
Is our 4-bet bluff +EV here? Let's do the math and find out:
EV = (chance of opponent folding)(potsize) - (chance of opponent not folding)(4bet bluff raise)
EV = (0.7)(17.5$) - (0.3)(24.5$)
EV = 4.9$
As you can see, your 4-bet bluff is a good move in this situation because it is a maximum EV decision. It's better than calling (-EV) or folding (0 EV). Bear in mind that your 4-bet is only +EV as long as he only shoves with JJ+/AK (which is a good average for most players). The more you 4-bet, the less your opponents will believe you, and therefore their shoving range will keep on getting wider and they might shove hands like AQ. Make sure to find the balance between 4-bet bluffing and folding in order to not get a loosy goosy image at the table.
Make sure never to 4-bet bluff against players who only rarely 3-bet. Players who 3-bet less than 8% of the time should usually be left alone if they do 3-bet because it will be very difficult to pull off a successful bluff against these players. That 8% is not just a random number, but sort of a turning point at which your EV of a bluff turns positive. Look at the graph below:
This graph belongs to our QsTs situation, only that now we are taking into account different 3-bet percentages of our opponent. The horizontal axis represents the 3-bet percentage of our opponent. The vertical axis represents our EV of a 4-bet bluff. As you can see, a 4-bet bluff only becomes +EV if the 3-bet percentage of our opponent is over 8% (assuming that he only continues with JJ+/AK). Always make sure your opponent 3-bets enough before you try a 4-bet bluff against him. Sometimes though, the normal 3-bet percentage is not enough to base your decision on. You can also check his 3-bet vs. steal percentage in the HUD of Hold'em Manager. These stats can more useful because they are often higher than his 3-bet statistic. Players will often make use of the 3-bet in the SB and BB because they know that the BTN and the CO will often open with a wide range. As you can see, a player needs to 3-bet quite frequently before you try a successful 4-bet bluff.
Also make sure to have a large enough sample to base your decision on. A sample should contain at least 500 hands, but preferably more than that. 3-bet stats vary a lot and can be very misleading with a small sample, which is why I recommend you just give your opponent the respect and lay down your hand if your sample on him is smaller than 500 hands. What is also very important is your opponents' ability to lay down hands, which is usually the case with a player who 3-bets frequently.
Also focus on the size of your 4-bet bluff. You have to raise just as much as you would with your premium hands, otherwise your opponents won't have a very hard time figuring out what you're doing. Something like 2 times his raise plus 2BB is often OK. However, you should also make sure not to commit yourself with your 4-bet bluff. In other words, you are getting the right odds to call his 5-bet shove. You might be thinking; if I'm getting the right odds, why not try and get myself into those situations? Well, because your 4-bet bluff then becomes –EV, as you are committing yourself with a hand with little value, and this cannot compensate for the +EV shove of your opponent.
To sum up: watch out for his 3-bet percentage, the stack sizes, the sample and fold equity.
Some more math
Now we're going to make it fun by looking at some more maths. We are making the assumption that, if we 4-bet bluff, we are not committing ourselves if he shoves. If he calls, we assume that we will always fold our hand postflop. This is a kind of worst case scenario. There will surely be moments where we can continue in the hand and still get +EV after seeing a flop (if we flop a monster for example). But to keep it simple, we will just ignore that for now. Working with the worst case scenario is actually not a bad thing: if we assume the worst case scenario and still bluff +EV, we will still be bluffing +EV in the situations where we get lucky. If he folds, we win the pot.
We know the following:
EV = win% x potsize – lose% x raisesize
The pot size is the size of the pot before we 4-bet bluff. The raise size is the money that we take out of our stack to make the 4-bet. Our initial raise is therefore not included, as this money is already on the table. Win% is the percentage of times that our opponent folds and we win the pot. Lose% is the percentage of times that our opponent calls or goes all-in and we give up the hand (worst case scenario).
We are assuming that our EV is equal to $0 here, so that we can see from which point onwards we can bluff successfully. Therefore we have:
0 = win% x potsize – lose% x raisesize
We can re-arrange this to:
win% x potsize = lose% x raisesize
win% / lose% = raisesize / potsize
We also know that win% + lose% = 1, so we can say that 1 - lose% = win%, therefore:
(1 - lose%) / lose% = raisesize / potsize
(1 / lose %) - (lose% / lose%) = raisesize / potsize
(1 / lose%) – 1 = raisesize / potsize
1 / lose% = (raisesize / potsize) + 1
lose% = 1 / ((raisesize / potsize) + 1)
This formula shows us how often we can lose our 4-bet bluff and still break even. And since 1 – lose% = win%, we end up with the following formula:
This formula counts when EV = $0. This formula can help us find the minimum win% of our 4-bet bluff that we need to break even. In our previous example with QsTs, the raise size was $24,50 and the pot size was $17,50. If we fill these numbers into our formula, we get 0.58 or 58%. This means that our bluff has to work 58% of the time (or more) to be profitable. We calculated that our opponent will fold 70%, which makes our move +EV.
If you want to calculate if your decision was the right one, just fill in the raise size and the pot size into the formula. You will then get the minimum percentage of times your bluff has to succeed. To find out how often your bluff will succeed, look at his 3-bet range and his 4-bet call/shove range. After that you can calculate how often he will fold, just as we did in our example. You don't necessarily have to calculate all the different combinations like I did, you can also just work with the percentages from PokerStove. These, however, are not always completely correct, as they don't take the card removal effects into account.
One example: a player 3-bets 12% of the time and will only shove with JJ+/AK (3% of all hands according to PokerStove). This implies that, from these 12%, he will shove 3% of the time and fold 9% of the time. We then calculate that 9%/12% = 0.75 = 75%, which is how often our opponent will fold.
To finish things off I have an example hand in which I made a successful 4-bet bluff. My opponents' stats are 30/22/2.7 over a sample of 572 hands with a 3-bet percentage of 7%. This is not enough to 4-bet bluff him in my opinion. But I also looked at his 3-bet vs. steal percentage when he was on the BB and this stood at 16%, which is ideal for a 4-bet bluff.
***** Hand History for Game 1112145128 *****
$50.00 NL Texas Hold'em - Sunday August 10 08:27:09 ET 2008
Table Bearwood (Real Money)
Seat 10 is the button
Seat 1: Zigauner ( $50.00 )
Seat 3: Fouba ( $50.70 )
Seat 6: Ebbe1904 ( $72.05 )
Seat 8: Ozymandiasz ( $53.15 )
Seat 10: RiverdalePN ( $51.35 )
Zigauner posts small blind $0.25.
Fouba posts big blind $0.50.
** Dealing Holecards **
Dealt to RiverdalePN
RiverdalePN raises to $1.75
Fouba raises to $4.50
RiverdalePN raises to $10.00
That's all for now. I hope you learned something from this article. As always, comments and questions are more than welcome on the forum. See you at the tables!