Right, so it's just an EV calculation where there is only 1 possible outcome. There's nothing wrong with that.

Yes, the EV would be $10.

The EV of each poker hand varies. So are you therefore against totally against the EV calculated by Holdem Manager and PokerTracker? They show different EV values from hand to hand - they actually vary depending on which cards are dealt. According to your logic, that would entirely defeat the purpose of EV.

Karganeth, I'm not sure you have acknowledged the difference between the two types of EV Sherman mentioned. It seems clear to me that you're interested in #1 but can you at least see the difference between it and #2, and why your method is no good for #2?

Suppose John has 22 and Sandy has AA. Sandy open-shoves all-in preflop and shows her cards because she just wants to take the blinds. But John wants to protect his blind, so he calls. Flop is blank, John turns a set, then Sandy rivers a higher set.
John then whines, "Damn 2-outer...on the Turn I was a 96% favorite. I made a great play, my EV was +$92. Sandy is a donkey!"
Sandy retorts, "I was 100% to win on the river, my EV was +$100 and yours was -$100. You're the donkey!"
Which of their EV calculations is right?

Answer: neither! For each player, the moment of their DECISION is what matters. John's EV of calling the all-in was < -$60, because before the board came, he was <20% to win. When deciding to put his chips in preflop, he didn't consult a crystal ball, he didn't know he'd be 96% to win once the Turn came.

Have you never heard the term, "results-oriented thinking"? Or "Sklansky dollars"?

The situations vary, but the EV of a particular decision in a particular situation NEVER varies. The EV of you betting on Tails is ALWAYS 0. The EV of John calling an all-in with 22 against AA is always -60.

Perhaps only Rusty is allowed to read my posts in this thread. I too feel that my comment, which seems to completely resolve this issue, has gone unattended. Thus, subsequent posts which ignore it make me smack my head.

I'm not allowed to put people on ignore or you'd probably just be talking to yourself entirely

Looks like #2 to me.

I took the time to write a fairly simple hand to show how my EV calculations match up with actual results. The hand is as follows:

JsTs BTN $200
AdAc SB $400
Qh6h BB $400

Preflop: BTN raises to 40, SB calls, BB calls.

Flop: Jh Th 2c

SB Checks, BB Checks, BTN Bet 160 (all in), SB calls, BB calls
Now this is where we can see different results. If the turn is not a heart the SB will bet all in and the BTN will fold. If the turn is a heart, the SB will check, the BB will bet all in then the SB folds.

I will now input this hand into CardRunnersEV which uses a monte carlo method to determine EV. It ran the hand 5,000,000 times to get an average for the EV amount.



So let's see if the EV method I'm proposing would arrive at that same value $168.41.

The EV calculted would depend on the card we saw on the turn. The following list is of the equity JsTs against the remaining hand (there is no situation where JsTs is not all in against a single hand on the turn).

As: 0% (1 card)
Ks, Kd, Kc, Qs, Qd, Qc: 73.81% (6 cards)
9s, 9d, 9c, 8s, 8d, 8c, 7s, 7d, 7c, 5s, 5d, 5c, 4s, 4d, 4c, 3s, 3d, 3c: 80.952% (21 cards)
Jc, Jd, Tc, Td: 95.238% (4 cards)
2s, 2d: 9.524% (2 cards)
6s 6d 6c: 83.333% (3 cards)

Ah, Kh, 9h, 8h, 7h, 5h, 4h, 3h: 9.524% (8 cards)
2h: 14.386% (1 card)

So if the turn was a As, our EV would be -$200 because we invested $200 to have a 0% chance of winning $600.

As - EV would be -$200
Ks, Kd, Kc, Qs, Qd or Qc - EV would be $242.86
9s, 9d, 9c, 8s, 8d, 8c, 7s, 7d, 7c, 6s, 6d, 6c, 5s, 5d, 5c, 4s, 4d, 4c, 3s, 3d, 3c- EV would be $285.71
Jc, Jd, Tc, Td: - EV would be $371.428571
2s, 2d - EV would be -$142.857143
6s 6d 6c - EV would be $300.00

Ah, Kh, 9h, 8h, 7h, 5h, 4h, 3h - EV would be -$142.857143
2h - EV would be -$113.685714

In our EV calcualtions we would never see the value $168.41. But what happens when we take the weighted average of these values?

1/43*-$200+
6/43*$242.86+
18/43*$285.71+
4/43*$371.43+
2/43*-$142.86+
3/43*$300.00+
8/43*-$142.86+
1/43*-$113.69=
$168.45

There is a small difference of $0.04 but this is due to not running enough simulations and rounding errors. I can run more simulations if you request or I could send you the CardRunnersEV file so you can see it for yourself.

The EV method I propose would work perfectly because its average matches with the actual results. There is no bias caused by calculating EV. In the current PT4 program, no EV would be calculated at all because they mistakenly believe it would be biased somehow. Holdem Manager correctly calculates EV in these situations. The EV calculation would not match the EV we knew, but its average would. It converges faster than actual results, which is what we want.

But why should the EV calculation assume that if one person when all in on the turn the other person would have went all in otherwise? That is what your calculation assumes (if I am following it correctly, to be honest it is somewhat difficult to follow each step). When you made your decision to go all in you had no way of knowing that one of the players would eventually fold. What if they checked it down the rest of they way? Then should your EV be calculated against both hands? Of course not because the fact that they checked it down means something. Just like the fact that one person bet means something.

Those two cannot be combined to determine if you are playing well. They can be used of course to determine if the game is being dealt fairly. But I think most people use the EV calculations to determine if they are playing well.

That's just because I happened to create a hand where that happened. I could do the same analysis where sometimes both players would check down. It would make analysis more complicated though. If both players checked down then the EV of the JsTs would match his actual winnings (as I explained to heehaww earlier) so it would all work out perfectly.

The EV calculation method I used did uses no knowledge about any of the player's strategy.

The calculation at the end to determine the average of the EV calculation values does use knowledge about the players' strategies. But this is just to confirm that it does match up with the simulated EV (from CardRunnersEV). We would never see this weighted calculation done in Holdem Manager because it does not have access to any player's strategy.

Edit: I just ran the CardRunnersEV simulation from my previous post with 100,000,000 trials and it matched exactly with $168.45.

Is there any chance of someone backing me up and trying to explain this to the PokerTracker developers? I feel quite hopeless at the moment. I have tried to explain it to them in every way possible but nothing seems to work. If anyone is good at explaining probability to others then it'd be a big help. This mistake is going to be in PT4 for years if nobody tells them it's wrong.

There is 0 chance I will tell them. But that should be obvious.

The bottom line is that if there is any remaining option for any player in the hand to make a subsequent decision before showdown, then you can't calculate "equity" for any player because obviously decisions are not random. EV on the other hand, can be calculated using whatever assumptions you want to make about the distribution of the open decisions. But I don't think that is the question here at all.

I agree with you. No EV calculation should be made when there are still decisions to be made. My argument is to do EV calculations when there are no more decisions to be made by any player.

The cards are random no matter what decisions are made. The players cannot influence the probability of the cards being dealt on the flop, turn or river and that is key.

If you went all in against 32o with AA in a $200 pot (87.214% equity), your hand would be worth 0.87214*$200=$174.428. Imagine if you could sell your seat - once sold, the buyer would win the pot just as you would had you not sold it. If you could sell your seat at the moment there were no more decisions to be made (which in this case coincides with the point you went all in but does not always), it would sell for $174.428.

Here's the scenario that people mistakenly disagree with me on. The scenario: you went all in for $100 with AA on a flop of K J 2 against two players (who both had $200 stacks) who had JT and 98. They both call. The turn is 5 and the player with J:Club:T bets $100 and the other player folds his cards face up. Now both your cards are turned face up and the only thing left to do is deal the river card. If you could sell your seat, how much would it sell for, keeping in mind your equity in this situation is 88.095%?

The PokerTracker developers are saying "There's no way to know how much it would sell for. There were decisions made after you went all in - the seat cannot be sold!".

Yet if we put it on the market, the seat would sell for 0.88095*$300=$264.28500. It is worth that much because it factors in our chances of winning multiplied by the pot size. Since we know the exact probability of each card coming out, it's a simple calculation to see how much it's worth.

I think that perhaps if I phrased it this way, the PokerTracker developers might understand it more. I might first start by asking "would you buy his seat for $10? What about $30? Can you come up with a formula to work out how much his seat is worth" and then once they give me the correct formula I'll say "AHA! That! That is what I've been trying to tell you all along!"

But that isn't your "all-in equity" which is probably what they disagree about. It is your "all-in-plus-turn-plus-fold" equity. So including this figure in a pool of all-in hands to get an aggregate +/- EV figure for your results is wrong. So then my question is, yes that's the correct equity at that point but what is it useful for? You could go ahead and deal the next card and say your equity is either 0% or 100%. Not useful there either.

It seems to me to be similar to when people calculate the flop and turn equities for a preflop all-in hand. Those are meaningless because the board cards are really dealt all at one time and we are just exposing them one at a time for fun. Similarly I think your equity calculation there, while correct, is meaningless. It was not a decision point for YOU, and an equity calculation for your hand only has usefulness at your decision point (when you go all in).

I have not looked at the PT thread where you discuss this, but if those guys are saying they can't include this calculation in the normal +/-EV results for all-ins, they are correct.

Yeah, I don't understand how Karganeth doesn't get that the two different calculations are for two separate things. The calculation he is talking about might be useful if you wanted to see if your "EV" (calculated his way) matched with what cards were dealt out. Or in other words, is the deck being dealt out fairly? The other calculation (the one PT currently uses) is useful if you want to see if your all-in decisions are +EV or -EV (i.e., if you are playing well).

The question is, do you want to know if the deck is being dealt fairly or if you are playing well? I think most PT users would want a calculator that lets them know if they are playing well. At least, I would never purchase PT to see if the cards are being dealt fairly. Most people can find someone who has a program (that is much simpler than PT) to do that for them.