Hey, this is not specific to PLO but I'm giving a PLO example so I'm posting it here.


MP: 136.2 BB
CO: 528.6 BB
Hero (BTN): 100 BB
SB: 100 BB
BB: 99.6 BB
UTG: 158.2 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has J A A T

UTG raises to 3 BB, MP raises to 10.4 BB, fold, Hero raises to 35.6 BB, fold, fold, UTG calls 32.6 BB, MP calls 25.2 BB

Flop: (108.2 BB, 3 players) 8 2 4
UTG checks, MP checks, Hero bets 64.4 BB and is all-in, fold, MP calls 64.4 BB

Turn: (237 BB, 2 players) J

River: (237 BB, 2 players) 3

MP shows 6 9 7 T (High Card, Jack)
(Pre 32%, Flop 27%, Turn 40%)
Hero shows J A A T (One Pair, Aces)
(Pre 68%, Flop 73%, Turn 60%)
Hero wins 225.2 BB
Rake paid 11.8 BB

MP is faced with my allin CB on the flop with UTG folded. He has 27% equity against my hand and in this case lets assume he knows what I have exactly.

In the same time to make this a breakeven call MP only needs 27% equity as well(pt4 calculates it and we can do it ourselves like risking 64bb to win 237bb = 64/237 = 27%). So without rake this would be a breakeven call.

This means EV of folding = EV of calling I assume?

And here's what I don't understand. If MP folds on the flop he will lose his intial preflop investment of 35.6bb. If he calls he will:
win 237bb 27% of the tim 0.27*237
lose 100bb 73% of the time 0.73*-100
(0.27*237)+(0.73*(-100))=-9bb
So when he calls his EV is -9bb and this looks a lot better than -35.6bb when it should be the same? What am I missing?

Sunk cost

The loss from calling with odds mitigates folding our equity share. It is 'less losing' to call than it is to fold. In that sense, it is 'relatively profitable' to folding.

have no idea what either of you is saying

I haven't checked the math but for the sake of demonstration, the only calculation you need to make is this one: (0.27*237)+(0.73*(-100))=-9bb

The 35.6bb is a sunk cost; neither calling nor folding will change that. So its relative nature has no bearing on your decision. Assuming your math is correct, calling on the flop is a 9bb mistake. It has no relation to the 35.6bb already committed on a previous street. If you wanted to assess whether it's profitable for villain to call pre, you would run a different calculation.

I haven't checked the math but for the sake of demonstration, the only calculation you need to make is this one: (0.27*237)+(0.73*(-100))=-9bb

The 35.6bb is a sunk cost; neither calling nor folding will change that. So its relative nature has no bearing on your decision. Assuming your math is correct, calling on the flop is a 9bb mistake. It has no relation to the 35.6bb already committed on a previous street. If you wanted to assess whether it's profitable for villain to call pre, you would run a different calculation.

tl;dr don't compare the 35bb to the 9bb

I ****ed up my equation:
win 237bb 27% of the tim 0.27*237 ->here it should be win 137bb not 237 because our 100bb investment is not a prize
lose 100bb 73% of the time 0.73*-100
(0.27*237)+(0.73*(-100))=-9bb->so (0.27*137)+(0.73*(-100))=-36bb which is the same as folding
everything makes sense now! thanks aveemaria for explaining the sunk cost term in detail and all

The mistake you are making is not factoring UTG dead money. If we have 27% equity, folding loses 27% of the current pot + 27% of villain's bet = 0.27*172.6= 46.6bb

If we call the bet we now win 27% of a bigger pot = 0.27*237 = 64bb so the ev diff between calling and folding makes a call the correct play. The pot is inflated because of UTG dead money.

ev fold=0

mp call 64.4bb to win 160.8bb = 108.2bb (the pot) + 64.4bb (your bet) - 11.8bb (the rake)
or to loose his 64.4bb

ev call= 27% x 160.8bb- 73% x 64.4bb= 43.4- 47= -3.7bb.

Even without rake it is slighty ev- to call.

I totally agree with pay4ruin

doordonot I used to think the same way but it's just insane to think of that situation that way what you're saying is that calling is +17bb better than folding which is terribly wrong. I suggest you look into that and try to understand it .. it's all explained here

I ****ed up my math.

You have invested 35.6bb into the pot. If you fold, you lose it.

EVfold=-35.6bb

If you call you win 137bbs 27% of the time and lose 100bbs 73% of the time

0.27(137) - 0.73(100) = 36.99-73 = -36.01bb

EVcall=-36.01bb

Since EVfold > EVcall, it's more +ev to fold

The reasons for this are interesting. The first one is that you need 27.1729957% equity to breakeven, not 27%. The second one is there is money in the pot you have not invested.

The point at which a call is 'breakeven' is when EVfold=EVcall. In other words, there is no expectation difference between calling and folding. Rake makes this a fold even more.

dorodonot: you clearly sucks at maths lol

The money you invested preflop is not your money on the flop anymore. On the flop you left 64.4bb to invest to win the pot. if you get sufficiant odds then call.

ev fold is always zero because you decided to not invest more money into the pot.

Open your mind and check the math yourself and you will see its precisely the same. Who knows maybe you'll learn something you haven't seen in a video.

DoOrDoNot's most recent calculations are correct. Treating prior investments as dead money (where folding = 0 EV) is also correct. They are two different ways of saying the same thing.

In a practical sense I'd prefer setting folding at 0 EV, because it simplifies calculation. But what's wrong is insisting that only one of the two approaches is correct.

yeah I agree with rei, now we're all saying the same thing, tho folding is actually better here due to rake which everyone pointed out already in the first place.

I find practically the way I do it is better because it reinforces for me the fact that a call still carries a negative absolute expectation. It also shows up in PT4 as a loss when you fold. Pot odds are (always?) concerning the relative expectation between calling and folding but getting it in as an underdog will rarely show anything but a negative absolute expectation. Sometimes of course calling as an underdog can show the opposite if what your opponent has invested is large enough.