The second topic I had wanted to discuss was raising OOP, and how the stacks getting deeper affects OOP play in general. From this first thread we can summarize the points about GTO play neatly into three points:

1) As the quality of your range increases you should raise a larger amount with a wider range of hands
2) As the stacks become deeper the effective quality of the range of the player in position increases, on a diminishing curve
3) As stacks become deeper, then, the player in position should scale his or her bet size upwards, to some unknown degree

Optimal exploitive strategy may deviate wildly from this, of course, depending on the tenancies of the opponent in question.

Now, if the above is true, let's take a look at the converse:

1) As the quality of your range decreases you should raise a smaller amount with a narrower range of hands
2) As the stacks become deeper the effective quality of the range of the player out of position decreases, on a diminishing curve
3) As stacks become deeper, then, the player out of position should scale his or her raise size downwards, to some unknown degree

Now here are some interesting points that go along with that:

It is likely possible to play with deep enough stacks that playing any hand but AA (which will have to push) OOP is unprofitable in GTO strategy (either for a call or for a raise). With infinite betting streets this would certainly be the case.

Because most players do not scale their bet-sizing in position according to the stacks, however, there is a soft cap on how deep the stacks can effectively be, regardless of actual stack size. If we look at a mini-game where we are check-calling down with TP, and can make no other actions, for example, we won't really care whether our opponent has 100BB or 500BB if he open-raises to 3x and bets only in proportion to the pot post-flop.

Typically it seems that players OOP tend to re-raise either larger or same amounts as the stacks get deeper with a narrower range of hands, which is an exploitive strategy based on the assumption that our opponents will play poorly against these re-raises. To look at a case of extremes, however, you might often be very happy to make one re-raise size with AK with 100BB stacks, but would not feel comfortable making that same re-raise size, or larger, with 1000BB stacks.

That's what I have for now. Feel free to chime in with additional input on the GTO side of things (or corrections if I've mucked anything up) and I'd like to hear any comments on exploitive strategies as well.

This confuses me: isn't the quality of your distribution just the strength of your range of hands? Are you saying that as your range gets stronger you should widen it? I think I must be misunderstanding what you mean by "quality of distribution"

Whoops, that's a misnomer (range is all the hands you could possibly hold, distribution is what you actually make an action with). Edited to reflect that.

Bryce what is your GTO argument for positional advantage? Is there a way to prove that positional advantage is somehow built into the game and isn't just a reflection of the vast majority of players having exploitive tendancies?

because I agree it would seem that if it is in fact built in then KK at some point would be unprofitable to play oop to any size raise, but if its not built in it would mean that the BB and SB would be equivalent in value HU. Both seem very intuitively incorrect.

I can vaguely remember a sklansky thread or something proving positional advantage but im not sure if i even agreed with it at the time.

I think this is incorrect. From a GT perspective, you can simply always call the exact range that villain is betting on every street in every situation. Although I suppose this means there is no inherent value in position. However, this assumes perfect information... poker is a game inherently of imperfect information and this is how we attempt to play exploitative poker.

SB can beat this strategy by simply always betting a proportion of BB's range which is slightly less than the odds SB is laying the BB to call.

bryce,

please reword your post using standard terminology. typically you cannot expand the width of your range without vitiating the 'quality' of it. if you're using position and stack depth or any other criteria to determine 'range quality' (as you defined range in your follow-up), please say so. without lucid and agreed upon definitions a meaningful discussion cannot take place.

I'm saying BB can always match SB's every action with the same distribution, using your terminology. If I bet (AA, flush draw) you call with (AA, flush draw).

This strategy presupposes knowing SB's betting range, or perfect information, as you said yourself earlier. Since poker is a game of imperfect information, this is not a valid strategy. However, GT could be just as easily applied to games of imperfect information (you seem to suggest it can't?).

You guys are using the terms "perfect information" and "imperfect information" too loosely for a discussion on game theory. Poker is a game of perfect information.

I'm not suggesting it at all.

If you like, I can say that poker is a repeated game with imperfect information about opponent's past strategies.

I think "almost perfect" is best!

This is way off topic, but isn't poker a game of imperfect information because you don't know the game state? You have perfect information of your opponent's past decisions, but imperfect information regarding what nodes your opponent was at when making those decisions.

It's not 100% perfect, but it's probably a pretty big stretch to call it imperfect given the fact each player observes the actions of his opponent.

vanveen for mod (of this thread)

i really hope this thread goes no where

I can't tell what you're saying here but it sounds like you're saying that the stronger your distribution the larger you should raise?

If so this is false. (On the authority of Bill Chen anyway.)

The stronger your distribution the more you want action and the less you need to raise to make your opponent indifferent to calling with whatever hand he should be indifferent to calling with.

As a practical matter if someone raises to 4x utg 10-handed and 2x on the button they should be a lot easier to play against than someone who does the reverse. (Fold to the utg unless you're getting odds to crack a big pair, reraise the 2x button raise liberally and also call with hand like T9o that you would have been forced to fold for a 3x raise.)

I didn't read your other thread but if you haven't you should really read Bill Chen's book if you're interested in this stuff.

You're wrong and I can't imagine Chen saying this. With your strong EP range you're generally commiting a higher % of your stack postflop than with your weak LP range. Therefore you need to raise bigger to cut down on opponent's implied odds.

Care to bet?

It's exactly what he said, and I even think it's available several places online as well as in MOP.

Micturation Man: Bryce is refering to "quality" as the value of a range, rather than showdown equity. That is, the starting hand range's quality is higher for the button when playing a stack of 200bb than when playing a 20bb stack, even though it's the exact same range of cards.

There are two things.

One the smaller you raise the wider you can make your range, which improves the EV of the hands that were originally in the range.

Two, considering the above it doesn't follow that because your range is stronger UTG than OTB that you will commit more money on average postflop. You can for example fold some overpairs to a flop c-rz if you had raised UTG that you would have to stack off with if you had open-raised on the button.

Say as a thought experiment that you are forced to choose one of two strategies in a 100 BB NL ten-handed game - either (a) you have to open for 6x UTG and 2x on the button, or (b) you have to open to 2x UTG and 6x on the button.

Which would you preferr? Seems to me that (b) is a lot more viable for various reasons.

I think part of the reason people feel like the opposite is true is because they are used to getting more action than they should when they make a big UTG raise without realizing that they are exploiting calling station opponents who could just fold everything but their best hands and possibly their best implied odds hands.

I could be wrong though, this is just what a got from a correspondence with Jerrod a long time ago. I actually have rejected in practice all of the preflop bet sizing stuff I got from them and just do 3x to 4x from all positions depending on stack size.

There hasn't been too much discussion in this thread but I think it is generally an interesting concept. I often scale my raise up as stacks get deeper but its usually because I am playing a very passive opponent who doesn't 3b much and likes to call down...so I can easier manipulate the size of the pot as I wish.

Against more active opponents who 3b regularly pf and are active postflop i dont find as much need to increase raise size as the pots seem to grow themselves.

I guess I would ask how do you think optimal strategy should change if you are BB and your opponent is opening to 5-6xbb as the normal opening size and how this should affect your calling/3betting range. How does this change as stacks vary from 100-300bb? 500? etc

This won't get anywhere near the point of AA-or-fold in the BB if the SB's raises are intended to produce a constant stack-to-pot ratio.

Once the SB gets to 100% open-raise, if he ups his raise size in order to keep a constant ratio of stack-to-pot, then the BB's always going to have the same pot odds to push or fold preflop, and can always push the same hands, setting a lower bound on his loss no matter how big the stacks get.

Even at 50:1 stack:raise, the BB can push ~20% of his hands, with an overall result of ~-.67 BB/hand.

what about a billions bb's deep?

You don't need to be a billion bb's deep. I'd bet 1000 or 1200 would be sufficient.