[Math] FE Calc Clarification

This is such an old article, and I was going to bump but the text got so long it might be worthwhile just to start a new thread.

I thought I knew this shit in and out a few months ago but tried to figure out a way to calculate this on the fly. (ie, without using an online calculator or speadsheet with stuff set up)...figured out I was way off with a lot of stuff. (which might explain why I'm such a monkey sometimes thinking something is +EV when it's pure spew. (Fwiw, if anyone knows a good way if calculating this mentally, do tell. I've been trying to isolate the FE algebraically and shit. Not fun.)


Referring back to the thread (full hand there), I'm confused about this part:

The CO leads into you for $20. That makes the pot $49.50 and you have $86 behind. You have 9 flush outs (for right now we'll discount that he might have a higher flush draw or be bluffing , and the fact that you have backdoor draws), which is good for about 35% pot equity. What is the EV of moving all in right now? EV = FE(49.50) + (1-FE)[(0.35*137.50) + (0.65*-86)]

Where does this number come from, and how do you calculate it?

Also, if anyone has the time, it would be great it I could get some clarification on what exactly these terms mean.

As I understand fold equity in relation to the hand example:

FE = % of the time villain will fold, thus yielding us the pot
49.5 = current pot that you stand to steal by betting
1-FE = % of the time villain will calls
.35 = Equity in the pot, only relevant if he calls
137.5 = Final Pot - effective shove?? 200-86 /=/ 137 though... ( for future reference, I want to think of this as the "to win" value)
.65 = obviously his equity; 1 - our equity
86 = effective shove (I'd like to call this the risk value)


I remember that WoT from DC in a very old Duel video did a similar calc, found here:
http://www.deucescracked.com/forums/13-Videos/topics/7849-Duel-WiltOnTilt-1-?page=3&per_page=15#posts-54909

..which goes like this (scroll halfway down):

So say he c/c the 115 on the flop, the pot is now 440 and we got 625 left. Now if we bet 200 into 440 it only has to work: 0 = 440x - (1-x)[880 * .04 - 220] 0 = 440x + (1-x)[880 * .04 - 220] 0 = 440x + (1-x)[-184.8] 0 = 440x + 184.8x - 184.8 0 = 624.8x - 184.8 184.8 = 624.8x x = 184.8 / 624.8 = 29.6%

Here, I'm guessing there are a few typos/gross approximations, but note that his "risk" value is normal but his "to win" value is the entire pot, including his risk. I'm pretty sure this is right, but it feels to me like it is in conflict with the original post. I can't really explain it too well but it's possible that he is counting his "to win" twice since with the "440x" and "880*.04" terms.

Thoughts LP?

137.50 should be the size of the final pot total with all the money in. I'm going to assume villain didn't have you covered for the full $86 left.

edit: oh I just read the article. Huh, that's weird. It looks a little more complicated than it should be, but I'm not sure.

from the article maybe it is a typo, the 137.50 i mean?
cause that middle part of the equation looks like the value of if you stick your money in and win, which would be 86+49.50 = 135.5, only 2 off from 137.50
i don't think the 137.50 is the final pot value, but rather a total of if villain calls and what is currently in the pot, since maybe you do not calculate the total pot since some money you already have with you and it's silly to stick money in and say you can win your own money back?
that's one thing that has always confused me on pot odds, if you should consider what the pot would be with your own money, if you have a choice to put it in or not.

usually this is used to work out the required FE for breakeven with a semi-bluff

from a spreadsheet i made a while back:
=-(B4*B1/100-B3)/ (B2+B3-B4*B1/100)*100

B4=total pot size after call
B3=size of the bet/raise
B2=pot size before bet/raise
B1=equity% when called
gives FE as a percentage

the first equation looks correct except 137.50 should be 135.50

thats def a typo

EV = FE(49.50) + (1-FE)[(0.35*137.50) + (0.65*-86)]

he folds and u win FE% time 49.50
+ he calls and u wine 35% of the time 135.50
- he calls and he wins the other 65% of the time ur stacks 86

clear typo

I was going to say it has to be 135.5 but that's not true either.

Assumptions:
1. Pot before he leads = 29.5
2. Effective stacks = 86

Therefore, when called we risk 86 to win the current pot plus the reminder of his stack which is 86+29.5 = 66+49.5 = 115.5

EV(raise) = FEQ*(pot)+(1-FEQ)*(EQ*(winAmt)-(1-EQ)*(loseAmt))

EV(raise) = FEQ*(49.5)+(1-FEQ)*(0.35*(115.5)-0.65*(86))

Your original question was concerning the winAmt. Before we make our play our stack is 86.

winAmt - the amount we will add to our stack after we play
loseAmt - the amount we will lose from our stack after we play

Also, an easy way to estimate the required FEQ is to assume that we have zero EQ in the pot when called. This will give us the percentage of time a bet has to work to win the pot immediately. This will be an overestimate of the required fold equity:

No_EQ = bet/(bet+pot)

Example: CO opens for 3xbb and we decide to 3bet to 10.5bb (pot). How often should our 3bet work assuming we can never win the pot if called/shoved on?

No_EQ = 10.5bb/(10.5bb + 4.5bb) = 70%

115.5 looks right to me. thanks.

ugh, turns out I'm still a little confused.

Basically, if you look at the WoT hand, he is using EQ*"EndPot" instead of EQ*"winAMT".

winAmt, as I see it, is "EndPot - Risk".




Intuitively, I would think winAmt would be the correct thing to use, so why does he use:
0 = 440x - (1-x)[880 * .04 - 220]

880 instead of (880-220)? It has something to do with the equity he has I would guess, but then shouldn't we do that too in our example hand?

nvm I'm good.

He did some manipulation in the parentheses:

EV(raise) = FEQ*(pot)+(1-FEQ)*(EQ*(winAmt)-(1-EQ)*(loseAmt))

EV(raise) = FEQ*(pot)+(1-FEQ)*(EQ*(winAmt) - loseAmt + EQ*(loseAmt))

EV(raise) = FEQ*(pot)+(1-FEQ)*(EQ*(winAmt + loseAmt) - loseAmt)

EV(raise) = FEQ*(pot)+(1-FEQ)*(EQ*(effective_pot) - loseAmt)

He bets 220 into 440 on turn with EQ = 0.04:

pot = 440
effective pot = 440 + 2*220 = 880
loseAmt = 220

I see a page of numbers and give up.