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 Post subject: Fold Equity Math
PostPosted: Wed Jan 09, 2013 7:20 pm 
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Hello,

I am working on figuring out fold equity for my HU bot and was hoping somebody could check that my logic/math is correct.

Lets assume the bot raises $45 with 8c6c and BB calls so there is $95 in the pot. Lets also assume we both have even stacks at 1000. The villains calling range is 30% of hands minus typical raising hands (99+, AK). The flop comes 7h3c5d giving the bot an overcard, OESD and backdoor flush draw. The villain donk bets $75 into $95.

So given his range we can assume that he can only be value betting top pair+ or 10+ out draws and anything else is a bluff. That is only 13% of his range. So our fold equity is 87% (I think?). So we run our equity vs that 13% range and we get roughly 39%. Now the decision is whether to call, shove or fold. so we do the math:

We shove and he folds = .87 * 170 = 147.9
We shove and win = .13 * 1095 * .39 = 55.51
We shove and lose = .13 * -1000 * .61 = -79.3

EV in Shoving = +124.1

Something seems amiss however. Am I calculating the fold equity correctly or ? Any help would be appreciated.


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 Post subject: Re: Fold Equity Math
PostPosted: Wed Jan 09, 2013 8:34 pm 
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After pondering this for awhile I think the missing component is how often the villain would actually be bluffing in this spot which would of course greatly affect the fold equity and in turn all of the math to a large degree. So now it really comes down to the type of player he is. Against a polarized postflop range we would have to assume 50%. Against a passive nit it could be less then 10% or even 0.

Tight Guy with UnPolarized Range:

We shove and he folds = .10 * 170 = 17
We shove and win = .90 * 1095 * .39 = 384.3
We shove and lose = .90 * -1000 * .61 = -549

EV in Shoving = -147.7

Loose Guy with Polarized Range:

We shove and he folds = .43 * 170 = 73.1
We shove and win = .56 * 1095 * .39 = 239.14
We shove and lose = .56 * -1000 * .61 = -341.6

EV in Shoving: -29.3

So even if the guy is bluffing 50% of the time this is a bad shove. We still have equity so a call is definitely the right play here against all player types. Technically we do not have the pot odds to call but we still have outs to improve and get paid off so the implied odds are pretty good here. If either player type checks the turn we also have a good bluffing opportunity. That would be a way better spot to shove on.


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 Post subject: Re: Fold Equity Math
PostPosted: Fri Jan 11, 2013 1:14 am 
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Well as always there is another formula to determine fold equity that changes the above calculations by a huge amount. The other one I have seen is this:

Fold equity = (chance our opponent will fold) * (opponent's equity in the hand).
Fold equity = (0.5) * (61) = 30.5%.

Then compute it this way:

Total equity = our current equity + fold equity.
Total equity = 39+ 30.5 = 69.5%.

That radically changes the math and is clearly a possible shove (or leveraged raise depending on the stacks) vs a loose guy with a balanced range. Lets assume a 10% chance for the nit and our equity becomes 45.1%. To break even with the nit he would have to fold around 20% of the time. Considering he may have just one pair he may easily fold that amount of time if he is not short stacked. I think a 20% chance the he will fold is not out of line for a tight opponent. In fact he may even be more likely to fold against a big raise/shove as he will not likely want to stack off with less then two pair. The only difference between him and the loose guy is the % of air in his range when he bets (especially OOP)

So what is the best way to determine this?


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 Post subject: Re: Fold Equity Math
PostPosted: Sun Jan 13, 2013 7:40 pm 
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Yet another way to do it:

http://www.fpppro.com/fold-equity-calculator.php

if we input: $925/39%/$95/$75 we get 67% or 33% fold equity. So the above equation does make more sense and correlates. I think that will be the best equation to use but add in -5% for errors. One thing that is apparent from that calculator is that it is assuming the villain folds 50% of the time which may or not be true.


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