Just how much of an equity advantage is it to have to be IP? Perhaps it gives a ~ 10% edge? It wouldn't be a static number, since playing 57s IP gains a higher percentage equity value than AA would.

I would love to pool data on this subject...
PM sent...
I think we should start a skype group of people willing to look at some empirical data.

It depends on too many factors. I think there was just a huge thread on the topic recently. I'm too lazy to search for it but maybe you can find it.

I think it would be much more interesting to examine the mechanism by which positional advantage gains its EV. There's an interesting statement made in the Mathematics of Poker along the idea that the more streets there are the less meaningful position is. I haven't verified it myself, so I don't have a strong understanding of why that's the case, but I think it's more interesting than the other. Or the other might be more interesting if it told us a little more of the nature of position.

Kinda hard when I have no idea what to enter in the search bar; I'm q[uite interested in this, so some clues would help

Position gains advantage by gaining and retaining more information. The more streets there is, the more information that has been released. The first 5 units of information will supply much more information than the next 5 units, because we go from having no idea whatsoever, to a more specific range. I'll try to rewrite if that doesn't make sense.

http://forumserver.twoplustwo.com/15...ative-1142583/

This. And another important factor in how much advantage position has is stack size, because of the leverage you get from it.

I think the "amount of streets" thing is probably a bell-curve, and idk about stack-size but I'd guess that it's dependent on the amount of streets because there is only so much money you can put into a pot.

If there are for example 4 streets with blinds 1/2 and you have stacksize of 1000bb, most situations will be between 3.5bb - 3x pot (pre pot=~8.5bb*3*3*3=229.5bb )

So anything over ~229.5bb for normal pot (no 3bet pre) will increasingly add less leverage advantage.
But if you have only 3 streets leverage advantage will become less relevant at 76.5bb(8.5*3*3) for normal pot.
(i do *3 to represent betting what's in the pot and getting called)
So that is to say, with 4 streets, as long as most pots are not 3bet pots preflop, whether you have 500bb or 1000bb effective stacksize doesn't matter nearly as much as the difference between 200bb and 500bb effective.

cheers, quite an uninformative thread but

Well that'd depend on how the graph for the bell-curve is mapped; if it's done for total value gained from being IP, than it'd flatten out rather than decline, whereas if it's made for the value of seeing the next street, it would gradually decline to 0, although it wouldn't look like a bell as it'd shoot up and come floating down.

Note that position is not just about % to win. It's about making more when you do win and losing less when you lose.

This is obvious in hindsight. Consider a game which is identical to texas holdem with 100BB stacks, except that all five board cards are dealt on the flop, and then there are 200 more streets of pure betting, without any cards being added to the board. It should be obvious that in such a game position is meaningless post-flop, simply because the post-flop game proceeds in a sort of "auction": fashion, and the only bet anyone should ever make postflop is 1BB each time (I don't have a game-theoretic proof that making only 1BB bets is best, i.e. it's a dominating strategy, but I think this shouldn't be hard to prove). So, as we can see, when there are 200 streets, then position is meaningless.

Now, what happens if we cut the number of betting streets to one? I think in this case, position is the most important it can ever be, since the OOP player would have to "fire into the void", and for the IP player, calling or folding would be an easy numbers game. In fact, I doubt such a game can be played no-limit, simply because the IP player has such an amazing advantage.

Notice that in the one-street case there is no "leveraging stacks" or "threatening stacks". In fact, the above analysis seems to suggest that "leveraging" or "threatening" are the weapons of the OOP player, that he uses to nullify his positional disadvantage. He's saying to the IP player "listen, my range is narrower than yours, so on average my cards are better, and if I keep betting you'll have to fold, so you might as well fold now". This seems to conflict with the popular belief that deep stacks help the IP player, so either I'm getting something wrong, or there is something else going on. This relates to AdrienD's comments, in a way that I don't fully understand.

I don't think that's true. Either player can cut the number of streets down whenever they want by simply going all-in. Therefore, if more streets cuts down on the IP player's advantage, he could just use larger bet sizes to cut down on the number of streets to maintain his advantage.

Semantically, you're right. the IP player is indeed able to make bigger bets in order to cut down on the number of streets. But I'm pretty sure that's always a bad thing to do (in technical terms, it's a "dominated strategy"). I claim that no matter what, betting more than 1BB in such a game is always a mistake, game-theoretically. So if the IP player tries to eliminate betting rounds this way, he'll just end up costing himself money, compared to his optimal strategy.

This makes absolutely no sense to me...

Are you referring to my post, or to something else?

For the benefit of the readers in the thread, here is a sketch for a proof for why no one should ever make a bet of more than 1BB when there are, say, 200 betting rounds (the proof sketch below is far from air-tight, and more work is needed to make it into a real proof).

Suppose at some point a player was considering making a bet of, say, 2BB. Compare this to just making a bet of 1BB and then another 1BB in the following betting round. When he bets 2BB, it's just as if he was betting 1BB, and committing to betting another 1BB in the following round. So, he gave his opponent information for free: he told him what he's going to do next; on the other hand, he didn't get any benefit from giving this information for free. So, we see that betting 2BB at once makes no sense: whenever we contemplate betting 2BB, we'd be better off betting 1BB and then another 1BB in the following betting round.

The thing that makes it really difficult to quantify is that everyone knows each other's position and presumably uses that information accordingly. The betting of a player with positional advantage means less because everyone knows he has positional advantage. But then you get into the level thing (I'm last to bet so I know what everyone in front of me did but everyone in front of me knows that I will know what they did...).

Or am I missing something?