Winnings by position: a smooth slope?

[Pirc Defense]

I noticed in my PokerTracker stats that without fail I play more hands from the button than the cutoff, less still in the cutoff +1, and so on. However, money won from each position does not follow such a smooth transition.

Should it? Theoretically, I mean.

One is probably playing more premium hands from UTG than when on the button, which might explain any difference, even taking into consideration the benefits of having position.

Any thoughts on this?

[Pirc Defense]

No takers?

I thought this would be an interesting issue.

Please validate me!

[Nottom]

Well your hands played % is going to converge pretty quickly to a relatively accurate number over not too many hands, so it makes sence that this follows the expected patern.

Money won however is going to have a lot of varience. Just like it takes many many many hands to figure out an accurate esitamate of your winrate, so to does it take many many hands to figure out what your winrate is at each position.

So for example, if you play 250K hands at a full 10-handed table, you will have a pretty accurate read on your total winrate. However you will have only played 25K hands at each spot, which is not enough to get an accurate number. Compound that with the fact that you play a much lower % of hands from EP (say 10% for easy math) and you may only have 2500 hands to actually provide you with any data, thus providing quite inaccurate position data even over a quite large number of total hands.

This help explain anything?

[Pirc Defense]

I appreciate your reply, Nottom, but it doesn't speak to the theoretical aspects of the question.

If we had a googol of hands at each position, then what should the money won distribution look like? Would it be deriveable from the number of hands played at that position?

This seems to be an interesting question...surprised it's not getting more play. And in the Poker Theory forum, no less!

[Nottom]

Theoretically, I would expect to see a nice slope.

In an ideal world you would play a hand if and only if was +EV from that position and the EV of the position is simply the weighted sum of all the +EV hands. As you get closer to the button, each hand should gain a small amount of EV and as a result you can add a few more hands and the positional EV should go up.

[Pirc Defense]

[ QUOTE ]
In an ideal world you would play a hand if and only if was +EV from that position and the EV of the position is simply the weighted sum of all the +EV hands. As you get closer to the button, each hand should gain a small amount of EV and as a result you can add a few more hands and the positional EV should go up.

[/ QUOTE ]

In other words, your theory might conclude that KQo on the button has the same EV as 99 UTG, though you'd pick 99 over KQo at the same position?

[Nottom]

[ QUOTE ]
In other words, your theory might conclude that KQo on the button has the same EV as 99 UTG, though you'd pick 99 over KQo at the same position?

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I'm not sure I follow what you are saying here.

[Phat Mack]

Interesting question. It seems that if you are playing the most hands from the button, and had the best position on the button, you would win the most money on the button. One thing that might offset this is if you are playing too loose as your position improves.

Is there any way you could post or link graphs of winnings as a function of position, and hands played as a function of position?

[Pirc Defense]

[ QUOTE ]
Interesting question. It seems that if you are playing the most hands from the button, and had the best position on the button, you would win the most money on the button. One thing that might offset this is if you are playing too loose as your position improves.

[/ QUOTE ]

Exactly. It is an interesting question because we're not sure what the relationship between the two is, or even if a significant relationship does exist.

[ QUOTE ]
Is there any way you could post or link graphs of winnings as a function of position...?


[/ QUOTE ]

I would but I don't have near enough hands for my data to mean anything (100,000+ hands lost when computer fizzled, back to ~8300 hands).

Nottom:

For any given position, 99 is a better hand than KQo; that is, it would win more money in a simulation. For any given hand, being on the button (or otherwise acting last) presumably has a higher EV than the same hand played UTG.

The question then becomes, at what mix of hand and position does 99 and KQo have roughly the same EV? Is KQo on the button as strong as 99 UTG? I read your theory to say that they would approach the same EV.

Knowing the answer to this would explain why a theoretically correct slope of money won by position, given that hands played by position differs for logical reasons, would either follow the same slope, or not.

Like Phat Mack pointed out, you loosen up on the button. You do this because you're compensated with better position. Should you then win more money from the button than UTG? And then are you winning more/less money in an absolute sense, or more/less on a BB/hand sense.

Glad someone else sees this as interesting!

[Nottom]

[ QUOTE ]
The question then becomes, at what mix of hand and position does 99 and KQo have roughly the same EV? Is KQo on the button as strong as 99 UTG? I read your theory to say that they would approach the same EV.

[/ QUOTE ]

I would agree with this analysis.

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Should you then win more money from the button than UTG? And then are you winning more/less money in an absolute sense, or more/less on a BB/hand sense.

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Exactly, my stats don't show a smooth slope, but they certainly show a much better winrate in LP than EP even if thete are some bumps along the way.

(My 6-max stats actually show a quite nice little trend as I approach the button as my BB/hand goes 0.07, 0.10, 0.14, 0.16 as I move from UTG to the button)