How EV relates to position

[Edg3]

New to this, so bear with me, trying to figure out the maths behind poker and these forums seemed like a good place to start.

I understand in principle why having position over your opponents is useful as there is an advantage to acting last, but how can this be expressed mathimatically?

It just seems strange to me that EV varies with position, when surely at any position a set of cards stands the same chance of winning a hand?

Cheers

[pzhon]

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I understand in principle why having position over your opponents is useful as there is an advantage to acting last, but how can this be expressed mathimatically?

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There isn't any clean method since poker is messy. Similarly, you can't determine a priori what the largest advantage is of one hand over another, as this varies from poker variant to poker variant.

You may want to look up [0,1] games, studied by Jerrod Ankenman, BillC, et al. These are abstract versions of poker where the players are dealt numbers between 0 and 1 instead of cards. This may help you to isolate the effects of position.

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It just seems strange to me that EV varies with position, when surely at any position a set of cards stands the same chance of winning a hand?


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If you were all-in, yes. However, the hands are not all-in. More importantly, you have to consider the size of the pots when you win/lose. Some hands are more profitable than their winning chances suggest because they tend to have an information advantage, allowing them to make more profitable value bets or bluffs. Similarly, having a good position tends to give you an information advantage, which means you can value bet or bluff more effectively, and you less frequently call and then face a raise behind you.

Here is another way to see that the probability of winning is not everything: Suppose there were only one round of betting. The difference between the best possible hand and a hand at the 99th percentile would be significant, particularly in NL. When the difference affects whether you win the pot, the pot will be huge, and having the nuts allows you to value bet much more effectively. The difference between a hand at the 20th percentile and a hand at the 21st percentile is negligible. When it affects whether you win the hand, the pot will be tiny. However, the difference between the probabilities of winning were the same.

[dardo]

Just think about it a little more and you'll see it. You have mroe control over the hand. Specially last bet when the pot is larger.

regards,

dardo

[Edg3]

Yea, I get it from a common sense point of view, but I was wondering about it more from a purely mathematical standpoint. Will chase up that [0..1] thing some more.