This only is true when you will balance bluffs with optimal amount of value and you have no idea if they are more likely to call or not.

If you're playing GTO, he can know your range at all times and still not be able to exploit you. (He just can't know your exact hand.) So if you're solving for the GTO play, that's what you're solving for, how to make yourself unexploitable with a face-up range.

"How should a good, balanced player vary their betsize with respect to the following conditions?


1) how should boards affect our bet sizing with our entire range?

2) How should stack sizes effect sizing from a GTO theory perspective?

--Why are we generally sizing smaller as stack sizes decrease? I'm guessing it has somethign to do with implied odds? It it even correct to do so GTO theorywise or is it an exploitation?

3) How should position affect our sizing? -- Does it make sense to size differently in and out of position? Why and how?

4) How should different player types affect sizing?

I think you just have no clue what game theory is or means. You just swallow whatever trend words people put out there.

To play GTO, you need to know every aspect of your own strategy and also every single hand and range in your opponent's strategy. So yes, it is like playing ranges face up.

Also there's not a single answer to any of your questions. The closest you can get is to play with toy games which will give you very approximate results and you will have to put more effort to know how to apply them at the table.

Aaron made an excellent post about polarized betsizing.

Yes, please. Explain.

I would love to understand aarons post about polarized ranges better. I don't think I'm fully understanding it...

And yeah still waiting for Rei to enlighten all of us

The meaning has shifted from "very strong and weak" to "strong and weak". That's it.

Consider yourself enlightened.

The GTO assumption is that the other player knows the exact probability distribution of our holdings, given the hand play to date. For example, in one situation she might know on the river that there's a 60% chance we have a flush and beat her hand, and a 40% chance we have something her hand beats.

Given this information, she can calculate what to do. We don't have to assume anything more. If your bet was B and the pot was P, her EV from calling is 0.4*P - 0.2*B. She should call if you bet less than twice the pot, fold if you bet more than twice the pot.

If you bet more than twice the pot and she plays correctly, you win P. But since there's a possibility that she might call anyway, it makes sense to bet more than twice the pot, hoping for a mistake. The more you overbet, the more you gain from a mistake, although possibly the smaller the chance she will make one. But this is exploitive play, it's not part of standard game theory.

If you bet less than twice the pot, she should call, in which case your EV is 0.6*P + 0.2*B, which is less than P because B < 2*P. That means you gave away EV. She can still make a mistake and fold, but that only gets you back to the EV of P, which you could have gotten from optimal play.

Notice that we used the same estimate of the probability of you winning for her computation and yours. This is one of the subtleties of game theory. Note that in a game, you know whether or not you have the flush, the probability is either zero or one. So you might use this information to size your bet. However, standard game theory analyses forbid this, because it would violate the assumption that she knows your strategy perfectly.

Nice anti-sexist assumption there that GTO player is a female!

Thanks, hopefully, it will end up being interesting as well. Sorry for the late reply, I've been pretty focused on another project.

Since I've been meaning to cover this topic anyway, I'll be putting some extra detail into this post over what you asked about specifically. Also because it's all linked and difficult to understand when looking at it from too narrow a point of view.

My actions which include bet sizing, ranges, aggression factors will all vary mostly based on the following factors:
Position
Number of players
Stack Size
Style
Table Layout (Stacks/Styles to my left/right)

Not necessarily in that order.

For opening action, in general I'd say the following:

• As position moves towards the button, my range increases
• As number of players go up, my range decreases and my raise size increases
• As effective stack sizes increase, my range increases and my bet sizing increases.
• As I shift styles my TAG is tighter with larger raises although, bet sizing could be an issue with needing to merge my Early street play to be more representative for all three styles for more effective post flop play in general. My SB and LAG will both be looser but with a different emphasis on the type of variance, bet sizing relative to TAG will decrease but relative to shorter stack play may still be a little larger.
• With looser play and deeper stacks on my left, I will tend to play tighter ranges with larger raises.
• With tighter player and/or shorter stacks on my left, I will tend to play looser ranges with smaller raises.

I should be discussing the various types of variance as well, but this type of discussion doesn't translate too well into online ABC play so I tend to avoid topics that will just generate a lot noise which defeats to purpose of discussing them in the first place.

Example
Action is folded to me and I hold 97o in MP.

If it's <=100 bb stacks it's an easy fold.

If I change the layout and I have loose blinds that like to defend with tighter players on my left, I'll sometimes raise my standard to get position over the blind defenders.

If I change the stacks to be much deeper. I'd come in raising more often but for a smaller standard open size.

The purpose is not to win the pot with this single bet which would be very unlikely even with a larger bet size. Instead, my intention is to balance my post flop range, improve my post flop position, *play with specific match up scenarios that can generate the largest implied odds, force other players to start defining their hands. Force other players to make mistakes.

*With 97, it's a good hand for the best monster vs monster match-ups. There are only a few of these types of hands and explains the favorite hands issue that many old school pro's talk about. Clearly they are not talking about being their favorite hands in a tournament with only 20 bbs. Contrary to many younger players beliefs, just because they've been around doesn't make them stupid.

For 97o I'm hoping for hitting a straight at some point and taking down top 2 pair or a set for a huge pot. Of course, this is a pretty rare occurrence but when playing variance with deep stacks, when I do hit my monsters, the match-ups for getting paid off are key. For example, JT8 will often face top 2 pair, T86 or 865, will often face a set. Hitting some monster on boards that will generally miss other ranges isn't worth it for the implied odds but their may be other reasons for playing them.

Notice that my straight will nearly always be the effective nuts since Q9 is the only threat and is less likely to be in a callers range where as 87o is often in a donkey scenario which both limits how much you'll get paid off and increases your reverse implied odds. If playing 97s, note that you're playing for some FD equity but you'll find the extra BDFD equity will help support playing with some more marginal situations such as a weaker combo draw that comes with the territory.

Finally my DBB draws will be much more disguised for better implied odds.

Other reasons for playing wider include, playing more hands against weaker opponents. The point here is not just to bluff because you missed. It's to create more opportunities for exploiting larger post flop mistakes made by your opponents as they happen and understanding the many scenarios in which these mistakes occur.

A wider range can represent better on boards that miss tighter ranges. For example a mid to low board, your range is still pretty well supported to hit any set, two pair, straight, etc, where as a tighter range is more polarized to op or over cards. So you can hit those hands but you can also balance on the heavy side since over-cards couldn't easily float and their own monsters of set are too small a percentage of their own range to balance effectively.

Even hitting something like second pair will often get two streets of value when facing tighter ranges such as 2 overs + a gut-shot some other kind of draw and a bet, check, bet line could be a thin value play balanced with some missed draws looking for hero calls from an under-pair or even A high.

Notice that with a wide range of variance, balancing your post-flop play becomes much more dangerous on many more boards to an opponent who is playing a tighter range that is much more transparent.

I could go on an on with scenarios but you should have a good idea of what I'm talking about.

Edit to add: Remember this is mostly for deep stack discussion. Standard play discussion is about 2 lines for most hands but deepstack discussion could go on and on for any particular hand.

You may play hands like 97o with deep stack sizes in order to flop or draw to disguised monsters, sure ... Why would opening up our range necessarily make it more optimal to lower our bet sizes, though ? Opening to a smaller amount also means a smaller pot to go into post-flop play with our monsters, make it more difficult to get all-in, and give our opponents better (implied) odds for their more speculative hands, would you not think that these are severe disadvantages, especially deep stacked, and possibly ending up OOP ?

[QUOTE=TakenItEasy;44844483]
As the stacks get deeper, your FE is greatly reduced on early streets and at 300 bbs, hands that would play against a 4 bb raise would be the same hands that play against a 5 bb raise. If your range only included value hands, than raising more is fine when this is true. However since you can only add variance to widen your range, you will be raising for value less and less often therefore the raise size should decrease, not increase.

You are not adding variance to bluff pre-flop, you are adding variance to improve your play post flop.

You use more marginal bet sizing to do this more efficiently.

While monsters may lose out on some pre-flop value, there really aren't that many monsters to begin with. JJ+ is only going to occur < 2% of the time.

Also AK is no longer a value hand but a draw. The reason being, AK needs 5 cards to be a coinflip vs the PPs so it has value when all-in but if you're too deep to shove correctly pre-flop than they are going to be a dog against 22 on 2 out of 3 flops.

Therefore you will make less for your monsters but those are few and far between.

Also they wont be your double up hands unless they hit a set. Therefore your goal with an over pair is not to get 300 bbs in, since you'll be behind when you do. Your goal is to pot control so you either get a fold or see a showdown when still ahead for the max price where you're still ahead.

You may think you're losing value for these hands by pot controlling early streets when they're ahead.

However, if you've done a good job of balancing your post flop play, you need to consider that the other variance you've played and the action you've been giving will allow you to get more streets of action for your over pairs to get paid off.

A good LAG or SB player will both earn more from over-pairs than a good TAG despite the TAG getting more value for them pre-flop.

Let me give an example instead, so that we can start somewhere reasonable.

Situation 1 ) You open UTG and get 3bet from BB, you decide to 4-bet
Situation 2 ) You open BTN and get 3bet from the BB, you decide to 4-bet

How should these sizings be different comparatively? why?
Basically which sizing should be the bigger and which should be the smaller, and why? Would this ever change at different stacksizes?

The range in Sitation 1 is definitely stronger, smaller, and more polarized than sitatuion 2.

I believe the bet size is mostly dependent on the effective stacks. The reason being you need to know how much room there is for a 2bet/call, if you are committed to a raise/fold decision, or the number of raises typical for an all-in.

Your bet size and range will both be dependent on stack size.

When raise/call situations are possible, in order to not define your range too much, you should have more of a merged range, or I believe others call it a continuation range. Note that a 4bet will cap your calling range so if you are deep, it's not a good idea to be using light 4bets in general, especially UTG, since your calling range will then become too defined.

If the next action will put you in a raise/fold decision, your range should be more polarized.

AB's posts have been amazing itt but I thought I'd add my $.02 from a more practical standpoint.

I'm assuming you're against opponents that can hand read or at least try to hand read to some extent. In general you should try to bet more on boards that favor your range given previous betting actions, stacks sizes, and especially positions and bet less or don't bet at all on those that don't. More and less are relative terms, so I apologize I can't be more exact here. Maybe larger/smaller in relation to the pot would be a better description.

I think stack size shapes range composition more than it shapes betsizing. Just realize that your goal is to maximize your EV which means getting in your stack with the best hand(s) in your range. We have 4 betting rounds to accomplish this so to get your larger stack into the middle in the same number of betting rounds you will need to use larger sizing, additional bets, or both to maximize your EV.

I wasn't aware that this was a thing, but again if you think about it as trying to get your entire stack in with the best hand with smaller stacks we can still accomplish this with smaller bets in 4 betting rounds. The other thing might be when playing against players that make more post flop than preflop mistakes we would prefer to have more money go into the pot on later betting rounds so by betting smaller and maximizing our spr we can better exploit the rounds where players make more mistakes.

I have heard several arguments for preflop bet-sizing based on position. I will lay them out here and tell you which I prefer:

1. Size everything the same. Advantages: Leaks no information about your range.

Disadvantages: May not be optimal when you vary your range by position.

2. Size your bets smaller in EP and larger in LP.
Advantages: You put less money into the pot when you're in the worst position and won't always get to realize all of your equity at the same time increasing the size of the pot when you can realize more than your share of the equity due to positional advantage.

Disadvantage: If you're adjusting your range by position you will be placing more money into the pot when your range is much much wider and you will have a much wider equity gap to overcome. At the same time by making the pot larger you actually sacrifice some of your positional advantage by lowering SPR. Another disadvantage is that by raising less in early position you are inviting more calls behind you and not making additional money for your troubles.

3. Size larger in EP and smaller in LP.
Advantages: You invite less calls behind you from EP and take maximum advantage of the equity of your tighter EP range. In LP you risk less stealing the blinds with your wider weaker range and keep SPR higher which enhances your positional advantage.

As far as postflop I think range considerations, board texture, and villain's overall tendencies dictate betsizing more than just position. Range considerations does include position though so it is factor, just not as big of one.

Not sure what you mean. As in LAG vs TAG or passive vs aggressive? Against loose passive players I think we should be betting more frequently and at a larger sizing. Against tight passive we should probably bet/check slightly more optimally but vary our betsizing based on the relative strength vs their hand.

Assuming good TAG's/LAG's I think we need to vary betting range composition and betsizings for exploitive and information hiding adjustments. We can also vary betsizing to induce certain actions that other players might not take who don't think analytically about the game (i.e. bet small to induce a raise with a nut hand, make a large bet and expect it to be interpreted as a bluff, etc.).

As far as bad LAG's/TAG's we need to be much more exploitive based on where they are bad.

Legend has it that the mythical beast of "GTO play" is blind to its enemies' tactics. It cares not what their strategies, ranges, or "styles" are.

Different player types then have no influence on sizing.