You get AA and go all in preflop. Two callers.

Flop K Q 3. The other two players get all in and show KK and QQ.

In your poker database would you expect it to calculate your EV based on the preflop matchup, or the flop matchup? Why?

I'd want it based on preflop, because that's where our actions ended ... but I wouldn't be shocked for the software to do it when all cards are revealed (because all software is crap, and that's the simplest thing to do ... and isn't wrong much).

I'd probably put this in the same category as the times we get 98%+ of our stack in on the turn, and are calling/shoving all rivers ... sometimes our 80% turn EV is actually 100% sometimes it's 0%.

The least wrong of the two choices is to calculate the preflop equity as if all 3 players were all-in preflop. The equity after the flop cards are known is entirely irrelevant to your all-in decision.

That said, the correct answer is that your all-in EV cannot be calculated at all for this hand, because the decisions of the other players were unknown when you went all in. Either player still had all options available to them and we cannot just weight their eventual choice to go all-in at 100% and ignore the other choices they could have made. Change the scenario to say that one of the other players folded to the bet post flop. Now what is your EV and at what point? Calculating it as if the 3rd (folded) player were not involved at the point of your decision (even if we knew his folded cards) would be total nonsense. This is no different.

To rephrase what NewOldGuy said, the flop is the earliest point where we can calculate our all-in EV in a way that is completely unbiased. I would not want to use a program that calculates AIEV based on the preflop odds when there is non-trivial postflop action. Yes, that means it will be off from your "true EV", but AIEV is only a partial measure of variance anyway, so I wouldn't worry too much about it.

What would you have your program do for this hand then (and why)?

It has to put something in the EV column in its database, since there is something in the Winnings column, otherwise it wouldn't be possible to draw the EV line on the graph.

What information should the EV line encode , in your opinion?

You weren't asking me, but the answer is exactly the same as the program does for non-all-in hands, which is just make the EV offset 0 for this hand. If you won $1 then your EV was $1 (for this purpose). Both PT and HM do this. That's the only thing you can do when equity at the all-in decision point was unknown and unknowable.

I would always use the equity from the street where the last action occured. So in this hand, use whatever your flop equity was. That provides a measurement of the difference between your winnings, and your expected value from the point of the last action. Which is exactly what HEM puts into that column. That is the only calculation that can be done unbiased.

Why the point of the last action? If your action was done preflop, what difference should it make to your graph display what the other players did on the flop?

I think most players use the EV difference to judge whether they're getting lucky or unlucky -- at least, I do, and I don't see any other use for it. People post graphs on BBV where the winnings line falls far below the EV line, and interpret it as them getting unlucky.

We've done everything we can at the point we went all in preflop, shouldn't it be considered unlucky that someone hit a set to crack the aces?

In non-all-in hands the EV matches the winnings (i.e. EV Difference = 0) because you made a choice on the river ; your last action occurred after the river was dealt so there's no more deck luck factor to consider.

By setting EV Difference = 0 you are actually making the statement EV = Winnings, i.e. we expected to win the amount we actually did win.

That's right, but other than excluding the hand from your history I believe that's the only good option you have. Your all-in luck graph (we agree that's all it is) should not be skewed by including hands like the one described in this thread where the outcome includes non-luck factors. I think you have to treat it just like the non-all-in hands, i.e. EV = winnings, so that the all-in luck graph remains accurate.

That said, the utility of the all-in graph is pretty limited and a good argument can be made that it's just an interesting novelty and most players shouldn't even refer to it at all, ever, as it just becomes a useless distraction for them. I would bet that well over half of the posters on this forum don't understand what their EV graph really means, and that's obvious in many many threads. They treat luck as something to be analysed and managed. And so fine points like this discussion are only meaningful for a very small subset.

Because like we've already said multiple times in this thread, it's impossible to calculate your preflop AIEV. You can calculate your equity with AA against KK and QQ, but your real equity is somewhat higher, since sometimes one of those players will fold what would have been the winning hand. There is no possible way for HEM to calculate how often that happens.

Yes it is unlucky, that doesn't mean we can calculate it and put it into a graph. There are many other components to variance, like coolers, how often fancy plays work, misclicks, etc and most of them can't be calculated, only estimated.


No, you're just saying there is no AIEV component to this hand.

Exactly this... it's possible to be way over EV on your all-ins, but still have an overall unlucky session. And vice-versa. It's a stat that's accurate for what it shows, but it just doesn't show the whole picture.

This is true of course. But your equity after the turn card is even less realistic than the flop calculation I was suggesting.

The fact that you can do an exact calculation after the turn card, doesn't mean that the result of the calculation accurately represents what information you are trying to encode in the "EV" field.

If you view graph of Winnings and EV though, then the EV line will change even for non-all in hands. The EV graph is not just all-in EV, it has to take a data point for every single hand.

Yes, there are a huge number of factors that can't be encoded in the EV line. This is why I'm making the point of "what is the purpose of the line", and if we accept that it is to try and represent your luck as best as the software possibly can (do you accept that?) then it doesn't seem to make sense to include a figure based on what the turn card was, in the scenario I gave in the original post here. (right?)

In other words, the flop calculation and turn calculation are both inaccurate, but I am saying the flop one is more realistic, in this scenario at least.

What program does that? HEM sure doesn't.

In HEM there are two things that show AI luck. The $EV diff column, which shows your gain/loss in equity due to AI luck (and $0 for non-AI hands). This column only shows equity changes, not your actual EV for each hand. The other thing is the "Display AI EV" option on the graph window, which just shows your winnings minus the $EV diff column. For non-AI hands, both lines stay constant relative to each other.

Take your AA/KK/QQ hand in op and assume the board bricked out. Let's also pretend the pot (that you're eligible to win) is $100. Let's also pretend it was all-in preflop. Your equities are:

Pre: $67
Flop: $11
Turn: $5
River: $0

The equity lost from all-in luck is $67. You can break it up into equities lost between streets:

Equity diff (pre to flop) = -$56
Equity diff (flop to turn) = -$6
Equity diff (turn to river) = -$5

For a PFAI, it is legitimate to sum all of these equities towards your $EV diff. But in the real hand it was not all-in until the flop. Therefore your pre-flop equity is not $67 but something slightly higher because someone will occasionally fold. Another way to say this is that you weren't 67% to win preflop, you were maybe 70% or something. Only after the flop, once the action is concluded and you know exactly what your probability to win is, can you start counting equity change accurately. The -$6 and -$5 are the results of an independent random variable. So HEM will only put the -$11 into your EV diff column, not -$67.

Here's another way to look at it: if you get AIPF with AA against 9 people, and then 8 people fold after the flop and you end up losing to A6o that flopped trips, your suggestion would be that HEM should say you lost 93% equity on that hand since that's what you had pre-flop. Obviously this is wrong. Your real pre-flop equity was (slightly higher than) the 30% or so that AA has against 9 hands. It should only count equity lost after all action was concluded.

Uh - yeah it does

If you play some hands and never get all in before the river, the EV line will mirror the winnings line.

"EV diff" means "difference between winnings and EV". "EV" means how much profit you expect to make on the hand. You seem to think I'm mixing these up but I'm not, if I didn't say "diff" I mean EV, not EV diff.

"EV" is what is shown on the graph. "EV diff" is the gap between the two lines on the graph.

Also, in HEM , "EV Diff" is negative when you won the hand and positive when you lost it, it is actually (EV - winnings), and EV is therefore (Winnings + EV Diff)

Even though my equity was 67% in a $100 pot, "EV" records my expected profit for the hand as a whole (not the profit for the final decision); so here , if we were all in preflop, EV would be $67 minus the amount I wagered (let's call it $33), or expected profit of about $34.

If I lose the hand, I lose $33 where I should have won $34, so EV diff is +$67. If I win the hand, I win $67 where I should have won $34, so EV diff is -$33. In both cases the EV line on the graph goes up by $34, but the winnings line is either $67 below it or $34 above it.

But, math error aside, you seem to be in agreement that at the point my money is committed, I expect to get about $67 - $70 back from the pot.

So you would agree that the recorded EV diff of +$11 when I lose (same sign error here) doesn't actually reflect how my luck unfolded after I'd gone all in. This is my whole point on this thread. The graph will look like I went all in nearly drawing dead.

This example is substantially different to the earlier example because we cannot see the folded hands (so you can't actually compute that 30%), let's hold off on discussing this until we have resolved the earlier case, to avoid further confusion!

Yes. But there's no better way to do it. The AIEV line only reflects luck that is independent of the action.

Only if you misinterpret it. What it actually says is that you were drawing nearly dead at the point of the last action in the hand.

Yes but my point is that you can't just calculate your EV diff the times everyone went to showdown, and throw it away if someone folded. You'll just end up with a value biased towards whichever boards people are more likely to get to showdown on. The only truly independent way (ignoring card removal of course) is to use only your EV diffs from the point of last action.

That is precisely what must be done for the EV offset to reflect only the luck of the cards and have any usefulness, for that is the entire purpose. Kittens has explained it correctly to my reading.

Absolutely not, because you can only calculate the AIEV at the point when showdown is guaranteed for all players still in the hand.