This was just a random question popping up in my mind lately. For example, you have a very LAGGY opponent who 3bets you from the BU and you sit with AK in the CO in a 6max cashgame 100 bb effective stacks. His 3bet-range vs you is say 30 percent, so your hand is ofc an easy defend. Lets assume he only 5bets AK, QQ+ and he has a HUGEEE fold to 4bet meaning you might consider flatting oop as a viable option ( Im just trying to get an example in which flatting a 3bet oop is the best option ev-wise).

Now, when you miss the flop and your opponent shows a lot of aggresion youre in a ****ty spot. And the number of situations in which you are oop in poker are ofc. endless. So my question:

How much would playing out of position be worth in terms of absolute equity?

Is there any way to calculate this at all lol? Would be damn useful I think

There's no widely known answer to this question. If you come up with a "formula" that works with reasonable stack sizes you would be one of the strongest player on the planet.
It's definitely worth more the deeper you are and most people believe it's probably worth more on boards where hand strength is more likely to change on further streets. Beyond that, who knows.

Maybe there's some definite answer for some toy games that only deal with river play. But this wouldn't generalize to actual gameplay.

Anyway, in your example, if he truly 3bets 30% then he won't get many folds post-flop. AK is not a hit or fold type of hand, especially with these stack sizes. AK either flops a pair _or_ two overcards. And against a 30% starting range most boards should be open for attack.

How much are apples worth in blue of shapes?

Position adds nothing to your card equity, it only adds to your fold equity, in other words your chance of winning without a showdown. And the amount of that boost is very opponent-dependent.

It also tends to increase the amount you win with your strong hands.

I think your question seems to be a bit jumbled up of at least 2 parts.

(i) How much is a position worth in terms of equity?
(ii) A specific 3bet 4bet question

Part (ii) can be generally answered by an ev calculation however it is a pretty difficult one but there are calculators that can make this quite easy. You could try "CardrunnersEv". With this you can supply the pre/post ranges to see which hands are profitable and by how much.

I think you could calculate some sort of an answer for (i), here is one way (In practice stack depth and player types etc. will greater alter any valuation).

You could approximate how much you gain in some position and compare this to the mean you make when playing complete orbits to see how much this position is worth to you.

Say, in your db, you make 3bb/100 hands at bb=$1.00, so anything that gives you greater than 3bb per 100 hands is a benefit.
In your db your position stats are (I've just made these up so they may not 'add-up' to 3bb/100.)

BB: -0.6 bb/100
SB: -0.2 bb/100
UTG: 0.5
MP: 1.5
CO: 3.5
BTN: 4.0 bb/100

If a pixie asked if you wanted stay on the Btn for all hands and due to some pixie-magic nobody would notice anything, and keep playing the same way, you would say yes.
Ah, but then the pixie says for this service it will cost you 2bb or $2.00 per 100 hands. At first look this sounds good as you make $4.00 per 100 from this position but then you remember you earn $3.00 per 100 without the magic, rather than the $4-$2 with, so it isn't worth it.

Perhaps we could say that you would be willing to pay up to $1.00 per 100 games to keep the button as this is the break even point for you. So this is some sort of estimate of this position's worth to you.

This is simply the value gained at this spot minus the average made per 100 when played in rotation. You lose $0.60/100 from the BB so if the pixie actually paid you $3.60 per 100 hands then it again is break even to you to stay always in the BB.

The Btn position worth 1.00 bb/100, CO: 0.5 bb/100, ... BB: -3.60 bb/100

This may be a wrong or a bit too simplistic for any real use but at least I had some sort of a go at a valuation. Maybe you could extend this type of approach and compare the 'value' of hands where you raise and get re-raised by the Btn with hands when you raise and get re-raised by an oop player like the SB.

It's a good post but OP asked for equity (a probability), not EV. Perhaps EV is what he really wanted.

Yes, I guess I started musing on how to find the value of position by trying a bit of a thought experiment.

Is 'absolute equity' meant to be value you gain from being in position here?
So for another dodgy thought experiment...

For the raise/3bet/4bet ... etc there wouldn't be enough data in the average db but using cardrunnersEv you could perhaps find out how much position is worth by doing 2 trees.

In tree 1, hero raises, 3 bet by Btn .. Hero ...
In tree 2, early player limps, hero raises, 3 bet by BB, limper folds, Hero ...

The extra limper fold is to take out the effect of the dead BB in the hand. I couldn't think of a way of getting roughly the same game in with the Hero in position and then out of position.

Find the mean ev of these two trees and then compare the value of 1 to 2 to this mean. It's complex but it should return a value for how much the position is worth in these cases.

Ok, now I've done a bit more thinking and using this approach it wouldn't be much use as the Hero in position has much more flexibility in adjusting the pot size (a lot of the position benefit) but there will be too many choices in trying to simulate this and the Villain's choices to get a sensible result. I'll keep on musing ... perhaps it is possible to use the cardrunners 'solver' to fill in values and a result ... or perhaps snowie.. ah, I think I'm losing the plot.

I think I remember yaqh* saying that in heads up no limit holdem range vs range ev, he found that position was worth ~10% of the preflop pot.

*sup where you been dude?

6

As others have mentioned/alluded to you can't really "calculate" an EV against a human opponent because you would have to know what they'll do in every situation. Your best bet is to try and solve the game assuming some conditions are fixed. For example, if both have players have a fixed 30% range, 20bb is already in the pot (with 90bb left for each player), players are restricted to certain bet sizes (1/2 pot, 3/4 pot, 1/3 pot, etc..), and preflop is already completed then I believe the game is small enough that its computationally solvable. Once the game is solved you just compare EVs to both players which will tell you the value of position.

All that said, that doesn't tell you the "value of position" in a more general sense which has to do with a couple major factors:

1. Much of a the value of position is merely just the value of not posting blinds when your opponents have to.

2. Much of the value of position is just gaining information on predictable opponents. Against opponents who mix up of their game correctly any info gained isn't nearly as valuable.

How good are you at poker?

If you're awful, position is almost irrelevant. If you're the best player the world has ever known, you could possibly play winningly from position without cards.

Even in simple toy games, one street, two bet games, the value of position is around 1/8 for the player acting second. I would imagine in real life poker, position has even more value than in toy games. The ability to act last on each street, particularly the river, allows you to control the size of the pot. Thus, position has a lot of value when you are playing in larger pots, where you need to control the size of the pot, and you can't afford to make mistakes. So position has a lot of value, and allows you to play a looser range pre flop with positive expectation.

Eh no.

Interesting. In bb/100, what is a good out OOP bb/100 in opposite to IP, what do you see in your own numbers? Is there a ratio?