How to calculate profit

[chief444]

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No. You're ignoring the fact that when he wins, he gets his SB back, so he only loses his flop call 91% of the time.


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Oh yeah...my mistake.

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KQ is calling correctly. This is just a function of your missed math above though.


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Yeah, I guess when you round the equity up to 9% and neglect the redraw it is actually.

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No. Here's an obvious counter-argument. If you bet and are called and you have only a 50% chance of winning, you don't make any money. The thing you are ignoring here is that, while the AK wins .91 SB of his opponent's bet, he loses .09 of the bet he put in himself.


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OK fine. I usually keep these terms seperate when I do the EV calc and you made it sound as if this were just the one term and not both combined.

The second half is confusing because I have no idea what you're calculating or where your numbers come from. It's certainly not how I would do the calculation here so I'm not sure why you think it's any sort of standard way. Also as for comparing it to checking...I really doubt if anyone would do that for AK vs. KQ on a ATx board. I'm not sure why you think this very specific HU example relates to AK against a bunch of unknown hands. But I really doubt if anyone would feel the need to estimate the EV of checking in this example. Your first part (other than the rounding up of EV) is how I've always done it and how I've seen it done for an example like this. So I'm not sure what you feel is new here. It's a completely different situation when you're 5-6 handed. Then I'd be looking at it from an equity point of view because I don't know the opponent's hands so I pretty much have to assign ranges and run a simulation for any analysis, basing my decision off of the equity resulting from the simulation against a wide range of hands for my opponents. This is especially true with a bunch of loose limpers and the raise coming from the BB since no one had to cold-call.

AK_EV + KQ_EV = Existing_Pot is not a new formula. It's what I've always used for an example like this and what I've always seen used for an example like this. I'm not sure why you feel it's some new method.

[colgin]

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The EV of the KQ draw is:

91% of the time: -1 SB
9% of the time: 11 SB (4 initially in the pot, plus 11 put in by AK post flop)

EV KQ draw = .91(-1) + .09 (11) = .08 SB (note that there is no a priori reason this number had to be positive)

Hence, EV (AK) = pot - EV (draw) = 4 - .08 = 3.92 SB

I claim that, under the assumptions for this problem, this is the EXACT EV for AK, not an estimate, and that any system of calculating profit which wants to be taken seriously must produce exactly this number.


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Eric,

I might take issues with your assumptions here, but under those assumptions the math seems to be right. I calculated the same 3.92 EV under these assumptions looking at pot equity on a street-by-street basis:

AK's Pot Equity of Pot on Flop = 91% x 4 = 3.64
AK's PE of Flop Bets = (91% x 1) - (9% x 1) = .82
AK's PE of Post-Flop Bets = (91% x 0) - (9% x 6) = -0.54

Total = 3.92

Mind you, I think your method, or any other similar one (such as what I did), becomes much more difficult (if not impossible) in multiway pots, particularly if you factor in what happens when players make other non-nut hands with which they might choose to continue. I would point out that neither of our EV calculations factor in the possibility of a split pot when a Jack comes on a turn and a Quenn comes on the rvier, but for simplicity sake I think that is fine.

All the best.

Colgin

[pudley4]

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EV (turn) = 91% * 9% * 6SB <-- EV gained by betting when KQ misses, instead of checking, that is, the equity of the draw that will fold, compared to checking +


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What is this term for? It's a duplicate term - this has already been calculated in your initial EV (the 91% win rate already counts the times your opponent folds the turn.)

[CallMeIshmael]

Nice post... before I post how I would do it, I think this was a mistake right?:

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you will bet the flop and KQ will call (incorrectly).

EV KQ draw = .91(-1) + .09 (11) = .08 SB

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(Also, I havent read any of the replies yet, so sorry if this is a total repeat).

Anyways... here is how I would do it:
(this will make the same assumptions as you: ie. we lose 9% of the time, and ignore redraws.)

91% of the time: AK bets the flop, then the turn, and take it down. We win 5 SBs this way.

9% of the time: We bet the flop, then the turn, get raised, and call down. And lose. We lose (1+4+2) = 7 sb.

5*0.91 - 7*0.09 = 3.92


If you want to do a method of street by street, it should look like this:

Ev (initial) = 0.91 * 4sb

Ev (flop) = 1sb * 0.91 - 1sb 0.09

(91% of the time we win a SB, 9% of the time we lose)

Ev (turn) = 0.09 * -4sb

(this is where the method posted was going wrong. You never make money on the turn. If he is putting money in the pot, it is with a hand that will beat you (again, disregarding the Q on the river))

Ev (river) = -2 * .09

0.91*4 + 0.91*1 - 0.09*1 - 0.09*4 - 0.09*2 = 3.92SB

[elindauer]

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Nice post... before I post how I would do it, I think this was a mistake right?:

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you will bet the flop and KQ will call (incorrectly).

EV KQ draw = .91(-1) + .09 (11) = .08 SB

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Yes. I wrote out the assumptions before I did the math. I just assumed calling with a gutshot in a 4SB pot was wrong.

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If you want to do a method of street by street, it should look like this:

Ev (turn) = 0.09 * -4sb

(this is where the method posted was going wrong. You never make money on the turn. If he is putting money in the pot, it is with a hand that will beat you (again, disregarding the Q on the river))


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Absolutely right. I hope that this error will help illuminate why calculating EVs street by street when you want to find a true EV for a hand is confusing. Let's look more closely at the turn:

First, I hope you see that the logic of betting being profitable when your opponent misses is quite reasonable and hard to disprove. After all, if we assign a betting in this spot to be 0 EV, it implies that we have to assign a turn that goes check-check a NEGATIVE EV, which is counter-intuitive. How do we lose money if we don't put anything in the pot? Why is it that on the flop, a check-check flop should be assigned EV zero, but on the turn when he misses, it should have a negative value? This is quite hard to explain and leads to lots of mistakes when the calculations are done this way.

It seems that we first have to know what the correct action is, then we have to go back and assign the correct action to be zero, and calculate deviations from there. Of course, this assumes that we have correctly calculated the EV initial based on everyone playing perfectly for the rest of the hand. So, to do a street-by-street calculation, we have to do the following:

1. figure out what the proper action should be for the various possible cards that are dealt
2. for each situation, calculate the EV gained on whatever bets go into the pot correctly, and add these up.

I think it should be pretty clear that this method is highly error-prone for all but the most careful mathematician.


In real-world calculations, the method of estimating the value of the draw(s) and subtracting them from the pot is going to be much more feasible and simple. If you hold top pair and suspect you are up against a flush draw, you just make an educated guess at the true odds the flush faces, the EV of the call from the pot, and you have the rest. Doing it street by street from the top pair's point of view can be done, but it can easily lead to subtle mistakes that cause major errors in the answer. When you use the draw EV method, you are always going to be in the right ballpark.


So the point is, when we're arguing about the best action, PARTICULARLY when the debate is based on the idea of passing up a small edge to get a bigger edge later, we should abandon any arguments that are based on "making more on this street", and how these sum to a bigger number, since these arguments are so easily confused and misleading, and focus on arguments stating that hero's true EV is greater. This debate, I believe, will more often lead us to the correct conclussion, which is what this forum is all about.

If there are no objections to this, I'm now going to reopen a thread on the value of raising AK vs 3 limpers, with the goal of having a discussion of this, I think, interesting topic that doesn't get bogged down with the mechanics of EV calculations.


edit: by the way, there's one more reason the street-by-street arguments are misleading at times, and that is that in these calculations, it is not unusual under reasonable assumptions for the hero to lose money on the later streets. That is, the current street calculations rarely take into account the implied odds for the draw. When you look at things from the point of view of the current EV of the draw, you naturally think about implied odds and, having played these so many times, we've gotten pretty good at estimating them. You'd almost never forget to add in a couple big bets when looking at the value of a flush draw, while this is very easy to do when looking at top pair on a street-by-street calculation.

[elindauer]

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EV (turn) = 91% * 9% * 6SB <-- EV gained by betting when KQ misses, instead of checking, that is, the equity of the draw that will fold, compared to checking +


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What is this term for? It's a duplicate term - this has already been calculated in your initial EV (the 91% win rate already counts the times your opponent folds the turn.)

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Hi Jeff,

Good job, you found it. See my other post on this topic for a discussion.

Thanks,
Eric

[SeaEagle]

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So the point is, when we're arguing about the best action, PARTICULARLY when the debate is based on the idea of passing up a small edge to get a bigger edge later, we should abandon any arguments that are based on "making more on this street", and how these sum to a bigger number, since these arguments are so easily confused and misleading, and focus on arguments stating that hero's true EV is greater. This debate, I believe, will more often lead us to the correct conclussion, which is what this forum is all about.


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Maybe you'll cover this in the new AK thread, but I'm really interested to see how you calculate the "bigger number".

I'm pretty sure most of us calculate the immediate EV and then kinda guess at the implied EV, a method that would have had virtually all of us folding KQ on the turn in this thread. I would love to see some examples of this at work in a more complicated hand.

[MaxPower]

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EV (turn) = 91% * 9% * 6SB <-- EV gained by betting when KQ misses, instead of checking, that is, the equity of the draw that will fold, compared to checking +

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This is the problem and if you change 6SB to zero SB, then you get the same answer. I'm not sure what your point is except that you did the 2nd one wrong.

This just shows how you make money in the early betting rounds with hands like these.