Quantifying the value of position in limit HE

[soko]

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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?

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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%

[lotus776]

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

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

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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.

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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
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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.

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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.?

[stigmata]

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.

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


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

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


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

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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.

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


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

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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.

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