Quantifying the value of position in limit HE
 

I am curious if anyone has ever tried to quantify the value of position in limit HE.

For instance, here is a problem whose solution would interest me very much. Players A and B both put two small bets into the pot. They are both dealt a hand in the top 40% of possible hands. A flop is now dealt, and they play limit HE through to the river, with player B having position.

What is player B's advantage in this game, in small bets per hand?

Re: Quantifying the value of position in limit HE
 

In HOH 2 there is a heads up situation where he quotes Howard Lederer on how since they both had the same hands the one in position is 2-1 to win it.

Re: Quantifying the value of position in limit HE
 

this is in NL, though. in ciaffone's middle limit book, he says that the button is worth a half a bet. king yao has done some attempts to quantify it more, i think...

Re: Quantifying the value of position in limit HE
 

Restricting the hands to the top 40% will make no difference since both players know this is happening. In this game, having a 60th-percentile hand is like having the worst possible hand in regular play, while having an 80th-percentile hand is like having a median hand in regular play. The relative values of some hands change, but the advantage of acting last should be constant.

I don't think B has an advantage as big as half a small bet. If A checks he puts B in the position of acting first, only B has the option of checking without allowing A to bet. That's not a huge advantage, especially if A mixes things up a bit and sometimes checks, then raises B's bet.

B would have the best of it, but it's nothing like the difference between acting first versus acting last in a full table; or being on the button preflop when everyone else has to put money in the pot or fold before you decide what to do.

Re: Quantifying the value of position in limit HE
 

I set up a 10 seat $1/2 game in Turbo Texas with the 'Bret Maverick' advisor profile at each seat, froze the button and ran it for 1,000,000 hands. Each player's strategy and skill is exactly the same, each player should get about the same cards over that number of hands, the only the thing that should vary is value of position. The results (sorry but the message entry form doesn't format columns at all):

Position SB/Hand
-------- -------
SB -.71
BB -1.54
UTG .107
4 .154
5 .140
6 .155
7 .198
8 .229
9 .207
Button .36

I think the win rates/position should be considered in relation to each other rather than as absolutes. I.e., the button will win about (.36 - .106) = .254 sb/hand more than UTG. Also, the fact that some later positions won less than the preceding one suggests the long run is much longer than supposed for luck to even out.

Re: Quantifying the value of position in limit HE
 

This is a great empirical way to determine the answer.

Note that better players probably gain a little more value in later position than weak ones. You could try a table of all weakies, and one of all TAG players. Also, a million hand sample is not nearly large enough, do you have time to try a larger run?

Re: Quantifying the value of position in limit HE
 

I like your method a LOT.

Unfortunately the fact that the BB was losing more than 1SB per hand suggests there is something wrong with the TTH programming. Because they could hold their loss to 1SB per hand by just folding everything.

Re: Quantifying the value of position in limit HE
 

Also looking at your results, they add to a lot less than zero. I assume this is due to the rake, which has a big impact at those stakes.

What happens if you set it to higher stakes -- say 100/200?

Re: Quantifying the value of position in limit HE
 

I too, am very interested in a process for defining this, or at least narrowing it down.

On a given hand, I would estimate that one person with position over another in a HU pot would have a .25BB/hand advantage, but that is only an estimate and I'm not sure how to begin to think about it for multiway pots.

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
I like your method a LOT.

Unfortunately the fact that the BB was losing more than 1SB per hand suggests there is something wrong with the TTH programming. Because they could hold their loss to 1SB per hand by just folding everything.

[/ QUOTE ]

Actually, the Big Blind posts 2 SB/hand, so he did improve a bit by playing some of his hands.

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
Also looking at your results, they add to a lot less than zero. I assume this is due to the rake, which has a big impact at those stakes.

What happens if you set it to higher stakes -- say 100/200?

[/ QUOTE ]

The rake distributes equally to all players over the long run so the ratios would be the same regardless of the rake. Using algebra you could easily find the coefficient of rake by multiplying every stack by x then solving for x so that the sum of all numbers equal zero. that would tell you the SB/hand if there were no rake.

Edit: However I am not convinced that a million hands is a long enough run to make the orignial numbers accurate enough, cause using the method I stated x should equal 1.05 if the rake is 5%

Re: Quantifying the value of position in limit HE
 

if both are dealt the same hands, Lederer said once that the person in last position has a 2-1 advantage

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
if both are dealt the same hands, Lederer said once that the person in last position has a 2-1 advantage

[/ QUOTE ]

Well, if Lederer said 2-1 advantage, it must be. Why do famous players feel they are allowed to pull numbers out of their ass with no data? That is for people like me. We better calculate exactly 2-1 edges.

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
I set up a 10 seat $1/2 game in Turbo Texas with the 'Bret Maverick' advisor profile at each seat, froze the button and ran it for 1,000,000 hands. Each player's strategy and skill is exactly the same, each player should get about the same cards over that number of hands, the only the thing that should vary is value of position. The results (sorry but the message entry form doesn't format columns at all):

Position SB/Hand
-------- -------
SB -.71
BB -1.54
UTG .107
4 .154
5 .140
6 .155
7 .198
8 .229
9 .207
Button .36

I think the win rates/position should be considered in relation to each other rather than as absolutes. I.e., the button will win about (.36 - .106) = .254 sb/hand more than UTG. Also, the fact that some later positions won less than the preceding one suggests the long run is much longer than supposed for luck to even out.

[/ QUOTE ]

Thank you for quantifying the value of position. I graphed your numbers in excel, which illustrates the severe disadvantage of BB, the sizable disadvantage of SB, the simular small advantage of UTG through 9 positions, and the significant advantage of the button. No surprise to most readers here, but nice to see it quantified.

What are your thoughts on the timing of entering and leaving games?

What changes are appropriate with hand selection, raising, etc.?

Re: Quantifying the value of position in limit HE
 

This is an interesting problem that I have also been thinking about recently. It also appears to be an incredibly difficult problem, and I rapidly become unstuck whichever direction I approach it from. Iv'e been thinking about it recently so I thought I would post my random thoughts so far:

Whilst the analysis of TruckeeSlick is interesting, I'm not sure how useful the results are for helping us at the table. Standard starting hand charts are already decently adjusted for position, and these are reflected in the results of simulation studies themselves. It doesn't help us in specific situations.

In particular, perhaps more interesting as I move up stakes is the problem which stox alluded to: The value of position when HU after the flop. The most common example being blind stealing/defense, blind wars, or the situation where player A raises, and player B reraises.

To simplify things, I have been thinking about the following problem; A raises in the CO, B re-raises on the button. Both players play equally well. If we can define that player A is stealing from the CO with the top 30% of hands, then from a pre-flop equity point-of-view, then we can simply 3-bet with top 15% of hands. This would have to be adjusted according to 1)the juice from the blinds 2)rake 3)chance of the blinds holding a decent hand 4)chance of being capped by the CO when he holds top 7.5%, etc.

However, we now have position and initiative (which is related to fold equity) and these concepts become somewhat entagled. If we can quantify the value of this then we could possibly lower our 3-betting requirements accordingly. From this we could know the exact 3-betting hands against a similar TAG player when we have good knowledge of their raising standards.

We can already see that an apparantly simple example rapidly becomes over-complicated. And we haven't even begun to think about how the player plays post-flop. However, once this problem is tackled, it might be easier to extrapolate to more complex examples of how we adjust starting hands according to position and/or initiave.

But how do we tackle even this simple problem?

1) Simulation studies: I'm don't have either TTH or Poki, but can we simulate something this specific?

2) SQL query on PT: It's a really diffuclt question, I have no Idea where to start.

Apologies for rambling, hope this makes sense, any thoughts/criticisms welcome.

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]

Position SB/Hand
-------- -------
SB -.71
BB -1.54
UTG .107
4 .154
5 .140
6 .155
7 .198
8 .229
9 .207
Button .36


[/ QUOTE ]
Did you work in some rake? It looks like there is -0.7 left on the table.

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
[ QUOTE ]

Position SB/Hand
-------- -------
SB -.71
BB -1.54
UTG .107
4 .154
5 .140
6 .155
7 .198
8 .229
9 .207
Button .36


[/ QUOTE ]
Did you work in some rake? It looks like there is -0.7 left on the table.

[/ QUOTE ]

[ QUOTE ]
The rake distributes equally to all players over the long run so the ratios would be the same regardless of the rake. Using algebra you could easily find the coefficient of rake by multiplying every stack by x then solving for x so that the sum of all numbers equal zero. that would tell you the SB/hand if there were no rake.

[/ QUOTE ]

Re: Quantifying the value of position in limit HE
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Position SB/Hand
-------- -------
SB -.71
BB -1.54
UTG .107
4 .154
5 .140
6 .155
7 .198
8 .229
9 .207
Button .36


[/ QUOTE ]
Did you work in some rake? It looks like there is -0.7 left on the table.

[/ QUOTE ]

[ QUOTE ]
The rake distributes equally to all players over the long run so the ratios would be the same regardless of the rake. Using algebra you could easily find the coefficient of rake by multiplying every stack by x then solving for x so that the sum of all numbers equal zero. that would tell you the SB/hand if there were no rake.

[/ QUOTE ]

[/ QUOTE ]
I read TruckeeSlick's post and didn't see that anywhere. Sorry if I missed in another part of this thread.