ITH Poker Forum

[Bren_Osoro]

What exactly does it mean to balance your play? If you defend your blind against a button raise, then check/raise the flop, should you try to have the same amount of drawing combos as value combos? Slightly more value combos? Does how much equity you have on your draws affect the desired ratio between value combos and draw combos? The topic of balance is often refered to, and I think most people have a general idea of what it is but I havn't seen it thoroughly explained. On dry boards, something like K82 rainbow theres probably not enough draws you can check/raise to achieve balance. What do you do in that situation. Probably c/r some of the air hands at the bottom of your distribution but how do you know how much to add?

The above is a post I made about seven months ago on the short handed and heads up limit holdem board but in those seven months I recieved no replys. I decided to repost it here because ultimately it's a math question. I'm trying to get as precise in defining the term "balance" from a game theory perspective as possible.

[nsidestrate]

First of all, read The Mathematics of Poker by Chen and Ankenmen. This will go a long way towards building a mathematical model of balance and it explains the concepts in good detail.

It is difficult to build a precise model of a game theory optimal (GTO) balance to a complex game like poker. The notion of GTO is critical to understanding balance mathematically. It is best defined in poker by short stack pushbot situations in SNGs. A GTO optimal solution to a poker situation is one in which neither player can change his range without making his results worse against the other player's range. In poker it is best defined in short stack all-in "pushbot" situations. There are numerous charts that lay out the optimal range to push with and the optimal range to call with. Any variance from the optimal range by the pusher or the caller is -EV. The range for both players playing the GTO range is said to be balanced.

In your specific situation, the point of balance is to avoid letting the other player exploit your play. If you check raise only strong made hands, he can easily fold most everything. It is therefore important to mix in draws and bluffs to force him to pay you off. There were some posts a long time ago by Willem (and someone else whose name escapes me) where they did a ton of mathematical analysis on some subset of situations that would interest you. I can't find it at the moment and I'm too hung over to try to replicate it in detail now. Even if I did, it would be worse that their analysis. I'll PM Willem and see if he can find it.

Until then, I strongly suggest you pursue the Chen/Ankenmen book.

[Willem]

Digging us some threads:
http://www.internettexasholdem.com/poke ... 55052.html
http://www.internettexasholdem.com/poke ... 54582.html
http://www.internettexasholdem.com/poke ... 56964.html

But the best thing you can do is read the Chen/Ankenman book. It's a complicated book but this GTO stuff is also complicated, no easy way to the dark side here . One thing I do need to mention is that most of this book is theory, and not (directly) applicable in practice. Still the only book giving enough detail to actually do something with balance and game theory.

Nside does a good job at describing in a nutshell what balance means. Balance means any bet you make can be either bluff or a valuebet in all possible situation, with the valeubet/bluff ratio appropriate to the size of the pot. As to exactly how much you should bluff, the Chen/Ankenman does a very good job at giving you the tools to do that yourself, including multi-street stuff.

Equity of your draws can be ignored in practice. Your draws have equity, but your made hands (against which your opponents are drawing) don't have 100% equity. You draws will have like 30% on average, while your made hands have around 75-80%. These two things cancel each other out enough that allows us to simply ignore this complication.

[Bren_Osoro]

Thanks for the quick responses. I recently started reading the Mathematics of Poker. It's a tough read in spots but it's very interesting. Those threads you dug up are helpful aswell. I havn't had the time yet to read them fully and contemplate everything, I just sort of skimmed them real quick. But I look forward to analyzing them. Have any of you guys ever played around in stox ev and tried to come up with balances strategies? I recently bought stox ev and it's something I want to try to do, but I still havn't fully learned how to use the program so I don't know how difficult something like that would be.

Equity of your draws can be ignored in practice. Your draws have equity, but your made hands (against which your opponents are drawing) don't have 100% equity. You draws will have like 30% on average, while your made hands have around 75-80%. These two things cancel each other out enough that allows us to simply ignore this complication.

That's a really good point. I always thought that how much equity on average you had on your draws would influence balance from a gto perspective. After reading that quote it seems so obvious and I can't believe I didn't figure that out myself awhile ago.

[Willem]

Equity of your draws can be ignored in practice. Your draws have equity, but your made hands (against which your opponents are drawing) don't have 100% equity. You draws will have like 30% on average, while your made hands have around 75-80%. These two things cancel each other out enough that allows us to simply ignore this complication.

That's a really good point. I always thought that how much equity on average you had on your draws would influence balance from a gto perspective. After reading that quote it seems so obvious and I can't believe I didn't figure that out myself awhile ago.

It's not that obvious, and it took me and Fenris some time to realize this.

The most correct way to look at it is to view both made hands and draws as drawing hand. With a draw, you are drawing to a card that completes your draw, with a made hand, you are drawing to cards that don't give someone a better hand. These things get even more fun in PLO, where the made hands and draws are equal in strength, as opposed to Hold'em where made hands are stronger.

The most easy way in Hold'em is to simply ignore this all.

[Willem]

Thanks for the quick responses. I recently started reading the Mathematics of Poker. It's a tough read in spots but it's very interesting. Those threads you dug up are helpful aswell. I havn't had the time yet to read them fully and contemplate everything, I just sort of skimmed them real quick. But I look forward to analyzing them. Have any of you guys ever played around in stox ev and tried to come up with balances strategies? I recently bought stox ev and it's something I want to try to do, but I still havn't fully learned how to use the program so I don't know how difficult something like that would be.

I think that people that can actually do this stuff in StoxEV are not going give away their secrets. I'm not sure if it's even practically possible at all.