So I'm trying to figure out fold equity on my lonesome and I'm having some confusion due to my general inability to math.

The Formula I have is:
0 =XP + (1-X-)(-LV+WH)
Where:
X = Breakeven Folding Frequency
L = Maximum Loss
V = Villain's Equity
P = Current Pot Size
W = Maximum Gain
H = Hero's equity

Now if we take a hand - Full Ring Table, we 3x open the CO (on 100BB) with T8o, it folds to the BB who has 110BB and he 3bets to 10BB total. From previous hands we know that he can light 3bet, and we're giving him a range of (22+,A2s+,KJs+,QJs,A8o+,KQo). Now if we 4bet to 25BB we're expecting him to fold everything but (TT+,ATs+,KQs,AJo+). Also we have no intention of putting any more money in if he raises us again.

So here's where I'm getting a bit confused. Would this mean our values are:
X = 0.56 (Being that he folds 56% of his range - this is one of the main points of confusion for me)
L = 25 (this is the maximum amount we plan to put in in Big Blinds - and we're assuming in this example that it's only preflop play)
V = 0.65 (This is [22+,A2s+,KJs+,QJs,A8o+,KQo] vs our T8o but I'm thinking this too could be very wrong
P = 13.5 (pot Size in Big Blinds - I'm thinking this is possibly the only bit I got right fingers crossed haha)
W = 13.5 (Again in BB - since I'm assuming this is only a preflop model - the maximum we can gain is the pot right?)
H = 0.35 (H should equal 1-V in any case I'd imagine?)

And that gives us an answer of 2.489 which leaves me clueless as to whether or not I've done it right.

Anyway would love to get some help on this because writing it out has just left me more confused than before (in fact reading it back makes me think that we're meant to solve for X - eurghhh)

I've never really seen it calculated in this way. Out of curiousitu, where did you get this formula? The part of your formula that begins (1-x) is a stand in for all action that happens if your raise does not succeed in getting villain to fold so this would be approximating a lot of play left in the hand

Reading the rest of your post it's like you're trying to approximate 4bet bluffing equity?

The bluffing formula I'm familiar with looks like this:

EV = X*P - (1-X)*B

Where:

X = Frequency with which opponent folds
P = Pot size before our raise
B = Bet or raise size

Note you can use this for any raise preflop, not just the first. The assumption is we lose 100% of our raise/bet when we are bluffing, which is not true as no hand has 0% equity preflop.


Yes this seems correct if that is the amount of combinations villain folds from the 3bet range you provided.

This doesn't really seem right. Like I said this part of the equation seems to be standing in for all scenarios where villain doesn't fold. If that's the case there are scenarios where we fold immediately and lose that maximum but there maybe other scenarios where we see a flop and have equity to continue and lose our stack.

According to your equation/assumptions that seems correct

It would be the size of the pot before your 4 bet so assuming villain is not one of the blinds and the blind structure is .5bb/1bb then it would be 1.5+3(your raise)+9(villain's 3bet) = 13.5 BB

My comment about maximum loss applies here as well. It could be pot or it could be remaining stacks.

Yes it should. In fact you could eliminate a variable and just write (1-V). Also I don't know if the subtraction operator after the X in your equation was a typo or not. I also think that the (-L*V + W*H) has other issues for what you're trying to use it for. Maube its just what you've called your variables.

Yes typically you use this type of equation to figure out how often villain needs to fold to make your bluffs breakeven (i.e. set EV = 0 and solve for X).

Yup apologies, L should be 22(given that we've already put in 3 big blinds) so then we've got:
X = 0.56
P = 13.5
L = 22
V = 0.65
W = 13.5
H = 0.35

And so the EV = +3.347

Now if we do it your way:
EV = X*P - (1-X)*B
I'm getting EV = -2.12

That right?

I'm assuming you plugged numbers into the formula correctly but I still don't think your equation is correct. I'm going to rewrite it here for clarity:

X*P + (1-X)*(H*W-(1-H)*L)

Where:

X = Villain's folding frequency
H = Equity of our hand vs villain's range
W = Maximum gain
L = Maximum loss

So now let's isolate these terms:

X*P is simply the amount of money we gain from the pot P when villain folds with frequency X.

(1-X) stands in for the frequency of ALL villain actions besides folding.

(H*W-(1-H)*L) is an estimation of the EV we have SEEING ALL 5 BOARD cards in the event villain calls. This is where your equation breaks down for anything but an all in.

If you're 4bet/folding to a raise with a hand then the (H*W-(1-H)*L) does not matter and we can use the equation I provided as you quite literally are always losing your investment by folding.

If you have to play postflop because villain calls a lot then there are issues with (H*W-(1-H)*L) because you will not be able to capture all of your equity in the pot with future betting, so H and 1-H aren't accurate and there's really no way to approximate maximum gain and loss in that scenario (since a portion your remaining stack is still at risk or a portion of villain's stack can still be won).

So like I said I think there are issues with your original equation that would prevent you from using it for anything in a preflop situation. You could use your original equation to evaluate turn and River betting situations but I think you'd have to look at the variables differently than you are now.

Oops yeah apologies there was a random "-" in the first equation that I forgot to get rid of (as well as just general confusion from my end).

Firstly, thanks for breaking down the terms and explaining them for me.

Secondly, given that I am 4bet folding AND only trying to apply this to an isolated preflop 4 bet I'm going to go with the first formula you provided:

Thirdly, if I can make sure my working is ok(?); (as long as I can do teh High Schoolz Math for the initial scenario)

EV = X*P - (1-X)*B

EV = (0.56*13.5) - ((1-0.56)*(22))
EV = (7.56) - (9.68)
EV = -2.12

Which means that every time we make this play preflop we're losing 2.12 BB (which seems odd to me I thought for sure it was going to be closer or even plus EV but hey - live and learn)