Abstract EV question

Say hypothetically you decide to take a session you played and analyze it. For the purposes of this, we'll assume that you are a perfect hand reader. Meaning you can precisely ascertain the ranges of your opponents in every situation.

How could you estimate the sum equity of your play during the session?

1. Would it be as simple as estimating the expected values of every bet/raise/call that you make and adding it up at the end?

2. Would it be more like each hand contains a set of plays that stack on each other like a russian doll, and only the last play in the hand matters?

3. Is it simply impossible to do this?


For example, say Wilhelm raises with JhTh and Klaus calls in position. The flop comes Q73 with two spades. Wilhelm bets flop, Klaus calls, turn 9. Wilhelm bets turn, Klaus calls again. River is the Ace of spades. Wilhelm shoves and Klaus folds.

For the purposes of the post session equity sum, would you add the ev's of each of his bets? Surely not. It would seem like only the last play matters. The equities of each bet overlap. The fact that its a profitable cbet on the flop is made possible in part by the fact that sometimes JT makes an oesd on the turn and can bet again profitably.


Thoughts?

I think its #1 moreso than #2 because really #2 is included in #1 in some way. You'd do your ev calcs based on the stack of plays given the probability that X card hits Y% of the time vs your opponent's Z range.

just go with your gut

Originally Posted by Renton

1. Would it be as simple as estimating the expected values of every bet/raise/call that you make and adding it up at the end? .

Yeah I think it's that one.

Your EV on the flop is based on the turn/river cards. So what I think you would need to do for a flop analysis, is evaluate your equity on the turn based upon your actions. Then for every turn card evaluate your equity for each river card.

Kind of like building a decision tree.

Obviously you could make groups so you don't have to do 1,980 equities for each flop hand you evaluate.

you say precisely ascertain ranges - how narrow a range are we talking?
regardless, i think it's more 1 than 2. It's not a vacuum though - as your line through the hand influences how the position is perceived (i.e. not the same as chess vs a robo-mind).

Originally Posted by Renton

1. Would it be as simple as estimating the expected values of every bet/raise/call that you make and adding it up at the end? .

Isn't this adding the multiple equities per hand & therefore double dipping or over-exaggerating your equity. If you have X equity on the flop and Y equity on the turn and Z equity on the river, you would not have X+Y+Z equity during the hand. Theoretically, that equity could exceed the opponents stack size.

If you were to analyze your session by simply taking the sum of expectations of all plays, then it seems your analysis would be contradictory. The reason is because at some point in a hand you would be taking a weighted average of all possible future actions, community card combinations, etc., then at any future point in the hand that information would be assumed known. (e.g., on the flop we have to determine the relative likelihoods of different turn and river combinations, but on the river we known the exact turn and river combination that fell)

Also, what does it mean to "perfectly ascertain an opponents range?" Would this not mean that you know his exact two hole cards at all times? In my opinion, the idea of a hand range is not as clear cut as most poker players assume it is.

I guess I'm not really sure what it is you're asking. If you're analyzing your session and trying to determine your expectation, are you just asking, what your expectation was knowing each hole card combination you actually had? Is it your expectation knowing each hole card combination both your and all your opponents had? You have to state explicitly what information is known and what information isn't known.

And yes, this kind of calculation is completely impossible to do analytically.

In a book called 'poker by the numbers' they figure out what you're asking using complicated tree diagrams.

And it looks like you have to look at the ev for each action that you take but you do it by looking at possible future cards, the likelihood of those cards coming & you & your opponents likely action on those cards then adding all of those to obtain a 'net ev' for a particular action.

I think just looking at the last play would be a big mistake.

For example if you found yourself on the turn with

On a board

The pot is $56

Your opponent checks to you, you think his range is most likely a draw.

A) You overbet shove 2x pot, your opponent always folds.
Looking at the final play your ev for this line is +$56

B) You bet 2/3 pot, your opponent calls the river is a club, your opponent makes a smallish bet and the pot odds justify a call in case he had a straight draw.
Looking at the final play of this hand even vs his range (flush/straight draw) it could seem close to neutral ev.

But when you add the ev from the times the river doesn't complete the flush & the times the river completes the flush but gives you a boat you would see that the net ev from betting 2/3 pot on the turn when your opponent is on some sort of draw is more +ev than overbet shoving the turn.

Yes, you would have to determine different combinations of community cards, different combinations of actions from yourself and your opponent *for each community card combination*, so it quickly becomes impossibly complex, and involves way too many probabilities that can't even be estimated. (The best way to figure this kind of thing out is surely just to use some kind of computer simulation with preprogrammed player types or something.)

In this sense, and this what was I was talking about in my other post, expectation is almost always forward-looking, so it becomes confusing when you already know the relevant information and then ask "what was my expectation in this situation?" It depends on what information is known, what information is unknown, and the likelihood of each possible state of the unknown information (quantities which are themselves almost always unknown). So, you have to state exactly what your vantage point is with respect to the unknown information.