Quantifying the value of position in limit HE

[catlover]

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?

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.

[SunOfBeach]

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...

[AaronBrown]

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.

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.

[tessarji]

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?

[catlover]

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.

[catlover]

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?

[stoxtrader]

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.

[Toonces]

[ 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.