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how do I calculate the equity needed to push preflop? how do I calculate the equity needed to push preflop?
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01-22-2017 , 06:13 AM
#1
hello world
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Lets say game is 1/2. and we are in the small blind in a heads up match. We have 12 bb left($24) and decide it is a push or fold situation. We know opponent will call with top 40% of his hands and fold the rest.

What is the mathematic formula to know how much equity do I need to make this push at least break even?
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 09:53 AM
#2
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For the situation you outlined it would be:

(.6 * 13) + (.4 * ( 24 * (Equity of your current hand against a 40% calling range)))

i.e.,

EV(current hand) = (Percent Villain folds) * (Hero Stack Size after fold) + (Percent Villain Calls) * (Equity of heros hand vs Villains Calling Range)
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 02:20 PM
#3
hello world
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Quote:
Originally Posted by 4bet20x
For the situation you outlined it would be:

(.6 * 13) + (.4 * ( 24 * (Equity of your current hand against a 40% calling range)))

i.e.,

EV(current hand) = (Percent Villain folds) * (Hero Stack Size after fold) + (Percent Villain Calls) * (Equity of heros hand vs Villains Calling Range)

I believe you outlined the standard formula to know the ev of a play. However, what I am looking for is the Equity I Need to Have given a certain pot odds, folding frequency, and desired EV (>0).
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 03:39 PM
#4
Kelvis
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Quote:
Originally Posted by hello world
I believe you outlined the standard formula to know the ev of a play. However, what I am looking for is the Equity I Need to Have given a certain pot odds, folding frequency, and desired EV (>0).
Set the EV to 0 and solve for equity.
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 03:55 PM
#5
browni3141
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Say 'f' is villain's folding frequency. 'q' is equity when called.

EV = 1.5f+(1-f)(24q-11.5)

EV must be >= 0.

0 <= 1.5f+(1-f)(24q-11.5)
(-1.5f/(1-f)+11.5)/24 <= q

q >= 38.5%

If a 40% range is {44+,A2s+,K2s+,Q4s+,J7s+,T7s+,97s+,87s,A3o+,K7o+,Q 8o+,J8o+,T8o+}, you shove {22+,A2s+,K2s+,Q2s+,J7s+,T8s+,98s,87s,76s,A2o+,K2o +,Q8o+,J9o+,T9o}

It should be noted that at 12BB a push/fold strategy is not so good HU.
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 08:50 PM
#6
hello world
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Quote:
Originally Posted by browni3141
Say 'f' is villain's folding frequency. 'q' is equity when called.

EV = 1.5f+(1-f)(24q-11.5)

EV must be >= 0.

0 <= 1.5f+(1-f)(24q-11.5)
(-1.5f/(1-f)+11.5)/24 <= q

q >= 38.5%

If a 40% range is {44+,A2s+,K2s+,Q4s+,J7s+,T7s+,97s+,87s,A3o+,K7o+,Q 8o+,J8o+,T8o+}, you shove {22+,A2s+,K2s+,Q2s+,J7s+,T8s+,98s,87s,76s,A2o+,K2o +,Q8o+,J9o+,T9o}

It should be noted that at 12BB a push/fold strategy is not so good HU.
Thank you.

I was thinking, what is the reason we must aim for EV=O ant +5, +20 or a an abitrary number? After all we want to maximize ev, don't we?
how do I calculate the equity needed to push preflop? Quote
01-22-2017 , 10:52 PM
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statmanhal
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The scenario you set up offered only two options – push or fold. The fold option has EV of 0. Therefore you maximize your EV by finding the minimum equity that a push requires and that would be the equity that has EVpush = 0.

For the more general case, you first estimate your equity. Then you hypothesize various bet sizes (including a check) and villain’s corresponding fold probability and choose that bet size that maximizes EV. Not very easy to do in a detailed way. Solver programs is a lot easier way to choose good actions in such cases.
how do I calculate the equity needed to push preflop? Quote
01-23-2017 , 02:52 AM
#8
hello world
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Quote:
Originally Posted by statmanhal
The scenario you set up offered only two options – push or fold. The fold option has EV of 0. Therefore you maximize your EV by finding the minimum equity that a push requires and that would be the equity that has EVpush = 0.

.
Interesting. What would happen if i set up EV >4, for instance ?
how do I calculate the equity needed to push preflop? Quote
01-23-2017 , 01:12 PM
#9
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Quote:
Originally Posted by hello world
Interesting. What would happen if i set up EV >4, for instance ?
Don't know why you would do that but if you do, set the EV equation given above to 4 and solve for q. You'll find the needed equity is quite high.
how do I calculate the equity needed to push preflop? Quote
01-23-2017 , 02:01 PM
#10
browni3141
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Quote:
Originally Posted by hello world
Thank you.

I was thinking, what is the reason we must aim for EV=O ant +5, +20 or a an abitrary number? After all we want to maximize ev, don't we?
We set EV >= 0 because we are looking for all profitable hands. When you are restricted to push/fold EV is maximized by shoving all hands which are profitable shoves and folding all hands which are unprofitable shoves. If we set EV >= 5 then you'd be folding profitable hands.
how do I calculate the equity needed to push preflop? Quote
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