• Bronze
Joined: 01.06.2014
I'm trying to come up with an approximation formula to estimate positional advantage.

I am assuming that we are heads up and on the flop, the stack to pot ratio or SPR is X and the equity edge for the player who is OOP is Y

So far I have come up with the following

The OOP player can execute (1-0.0125*X+Y*0.25) of his equity

eg. BTN vs SB heads up to the flop and the SPR is 20. Equity for SB is 45% and so the equity disadvantage is 10%

Then SB can execute (1-0.0125*20-0.1*0.25) = 72.5% of his equity.

This assumes that SPR and Equity advantage are the only two factors effecting positional advantage in a gto sense.

Does anyone know if there has been any theoretical work in trying to estimate positional advantage anywhere online? I would like to learn a method for approximating this better as I feel it is extremely useful. My current approximation may be very inaccurate and I would like to at least improve it somehow with more data.
• 7 replies
• Bronze
Joined: 01.06.2014
Just to show another example of why I think this might be an okay approximation, if you take a SB 3bet vs BTN range, BTN calls and we see a flop, we expect the positional disadvantage for the SB to disintegrate for two reasons. Firstly, SB most likely has a range advantage, and so cannot get blown off his hand so easily. Secondly, the SPR will be something like 4 as opposed to 20 in a single raised pot. Assuming now that SB has 55% equity on a given flop, SB can execute

(1-0.0125*4+0.1*0.25) = 97.5% of his equity

Obviously it is not so easy as only using these two factors in order calculate a formula for positional advantage - many other factors like hand playability and other qualitative factors will have their place. However what has become clear to me is that the extra accuracy in adding in other factors besides these two will be so small it won't be of concern. Overall the playability of one particular hand over another will balance out range-wise and the information will be simply contained for the most part in the Y constant for the factor of equity advantage.
• Bronze
Joined: 01.06.2014
Okay so I've ran one or two more simulations in CREV and it seems that this formula seems to work to within about 5-10% of a big blind or so, so I'm hopeful that this is a good approximation.

Once again I would love any input if you know something about this kind of positional advantage gto stuff and hopefully we can come up with a very useful formula for practical use. I looked up some stuff on 2+2 but nobody seems to be very sure of anything and the one formula I did find didn't seem to work so far as I could tell. It used HotvsCold equity and I have no idea what that is. Maybe it's something in Power Equilab.
• Bronze
Joined: 01.06.2014
Update:

The initial estimate appears to be actually nowhere close to a correct approximation. Far more statistical analysis will have to be done in order to get a good approximation. Also the analysis may be more limited than I thought at first. Will do some more work unless it gets too crazy.
• Bronze
Joined: 10.02.2009
Interesting modelling, but there are too many variables at play with individual hero and villain bluff and calldown frequencies to easily say "this is the disadvantage".

For certain player types (not talking skill levels, just play styles) the disadvantage is going to be dramatically higher or lower depending on these bluffing and calling freqs.
• Bronze
Joined: 01.06.2014
Perhaps but I'm actually interested in it from a GTO perspective. I recently realised that in most situations, GTO strategy is not actually that far away in EV from a more basic strategy which might be much simpler to learn off for practical play. And then I realised that all I would need is to estimate what the GTO EV in a given situation is. Once I have this, the plan would be to construct a more basic strategy that isn't GTO but still gives roughly the same EV. So I'm not worried about what players are IP and OOP.

I am still doing some tests and the possible values for the SPR and EV factors are everywhere right now. It may be the case that such an approximation formula wouldn't be accurate over all the possible ranges and SPRs in No Limit, and even if there did exist something maybe I should replace SPR with Sqrt(SPR) or Number of Bets/Raises Possible before All in jam.

Overall playing around with different scenarios in CREV at least gives me a sense of what spots have what levels of positional disadvantage for the OOP player.
• Coach
Coach
Joined: 07.02.2009
The thing is the R varies greatly for specific hand groups also vs different ranges. And vs different players but that's not an issue as you can simply come up with up values off-tables against good unkown ones, set up your ranges and then adjust ingame once you know rough baseline values where you see exploits on people's games.

I'll mention my reverse engineering wild guesstimate for ingame EV method tonight quickly.

Also imo you trying to arrive at GTO EV First is and then what is +EV in practice is a waste of time unless you're a programmer on one of the solvers already and have massive computational power available to you
• Bronze
Joined: 01.06.2014
Yeah I thought it would be easier to come up with an approximation formula than it actually is. Will try to watch the recording, thanks.