Advanced Strategy: How often does your opponent need to 3bet, so that you can 4bet/call TT?

Written by: Hoodlincs
· Date Added: 28 Mar, 2011 · Number of views: 2101

**Introduction**

This was inspired by a friend of mine who plays nl50 and wanted to work out whether he should 4bet/call in a spot vs a reg. So here is an example of mine to explain it.

$1 NL (6max) 4 handed.

**Hero CO ($100}**

BTN ($100)

SB ($100)

BB ($100)

**Preflop:**Hero is the CO and is dealt

Hero raises to $3

, BTN folds, SB re-raises $11

, BB folds, Hero... We are considering whether we can 4bet/call TT.
The basic maths (I will try to keep it is as algebra free as I can).

Expected value (EV) can be broken down into 2 parts: our EV when we get all in, and our EV when we get him to fold. To calculate the EV of getting all in, you simply need to do the following equations:

EV when all in

= (The total pot – what we risk * our equity in the hand) – (What we risk * his equity in the hand)
EV when he folds

= we win whatever is in the pot.
Total EV of the play

= (EV when all in

* how often we get it in) + (EV when he folds

* how often he folds)
Let's think about his range, and assume that he is going to be shoving over our 4bet with JJ+ and AK. Pokerstove tells us that our equity in the hand is 33.6%. from the hand so far, we also know that if we commit to 4bet/calling we will be risking 97bb (we put in 3bb already) to win a total pot of 201bb (both of our stacks + the 1 big blind).

Therefore, the EV of getting the stacks in is: (201-97 * 0.336) – (97 * 0.634) = 34.9 – 61.5 = -26.6bb, and therefore in this example,

EV when all in

= -26.6bb
So clearly we have negative expectation when we get all the money in, and that is because we are getting the money in with 33.6% equity vs his range. However, “EV when all in” is only part of the equation – we have to consider how much we win when our opponent folds too. When our opponent folds after we 4bet, we win 15bb (his 11 + the 1bb + our 3bb initial raise). Therefore,

EV when he folds

= +15bb
At some point, there must be a cutoff where the small blind folds so often to our 4bet that it doesn't matter if we lose money when we get all in because we more than make up for it the times he folds. This is called 'fold equity' and to find out whether we have any 'fold equity' we can make a simple equation. All we need to do is replace how often we need him to fold with 'x', and set the answer of the equation to zero. Then we can solve the equation for 'x' and it will tell us how often our opponent must fold in order to break even, whilst also showing us that if our opponent folds anymore than is required, then we make a profit. It is basically a re-arrangement of the formula for

Total EV of the Play

.
Fold equity equation: 0 = [what we win when he folds*x] – [what we lose when he doesn't fold*(1-x)]

From the figures we already calculated earlier in the article, we know that when he folds we win +15bb, whilst when he doesn't fold we lose 26.6bb (because we get all the money in). Therefore we can substitute the numbers into the equation, solve it, and get a figure for 'x'.

0 = [15*x] – [26.6*(1-x)]

0 = 15x – 26.6 + 26.6x

0 = 41.6x – 26.6

26.6= 41.6x

x= 26.6/41.6

x = 0.64, or 64%.

So, if we expect out opponent to fold 64% more than 64% of the time, we show a profit by 4bet/calling. To put this into more useful terms:

If he is 3betting 9% of hands in this spot and he is shoving JJ+ and AK (the top 3% of hands), we show a profit by 4bet/calling TT here. If he is 3betting 8% or less, then we make a loss and if he is 3betting 10% or more then we are just printing money by 4betting.

It is impossible to model whether 4betting is better than calling but these type of spots you don't want to spend a ton of time focusing on – once you know whether 4betting is +ev or not, you can just go from there. You should spend a decent amount of time going back over this article and re-entering numbers based on different shoving ranges and different starting hands for yourself (what happens when he is 5bet bluffing sometimes, or if he is only shoving QQ+, or if we have AQ to start the hand instead of TT etc).

I hope that you found this article interesting, please put any questions in the comments section and I will get back to you.

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