Fundamental GTO theory from a newbie's point of view
01-05-2015
, 11:12 AM
I'm no GTO expert. So this is all I know so far from talking to people, starting to read Will Tipton's books along with stuff by Matt Juanda, Ed Millers and mathematics of poker, not to mention my research with gambit and pokersnowie.
I hope that people can contribute to this thread and support the growing understanding on GTO, so everyone can improve faster as opposed to everyone being in the dark.
I'm a 6m NL grinder myself (former live semi-pro), and I believe GTO would be especially useful for multitabling, when its hard to keep track of exploitable tendencies.
Hopefully, this thread will be more than philosophical understanding but actually discussing practical uses of GTO to real situation. Lets start!
Feel free to correct me as I'm still a newbie
And feel free to post ideas, and ask questions!
What is GTO (Game theory optimal)?
So GTO basically is a mathematical way of playing perfectly. Its both unexploitable and optimal. As per Nash equilibrium "both players at equilbrium cant unilaterally increase their EV by changing strategy". You can think of it as two players adjusting to each other, and changing their strategy, swinging back and forth and maybe they'll settle at equilibrium.
In order to understand GTO better, people like to use "toy games", or simplified sub games to understand concepts.
The main elements of GTO include playing unexploitably. What that means, in my understanding, is to play balanced (more on that later). Balancing your range, means playing different hands same way (and same hands differently), a form of information hiding, so that your opponent cannot work out what you have.
But just playing balanced is not enough, you also have to play optimally and ultilise your range effectively, trying to make the most EV out of your range. That is a harder concept to understand in my opinion. That would include using good bet sizing (so triple barrel my stack rather than just shoving flop, would ultilise my range more effectively, even if i do it with a balanced range). more on this later.
Unexploitable play: Balancing/Combinatrix
I think balancing is definitely related to playing unexploitable, at least in the same ball park. It means having a good amount of bluffs to "balance" the number of value hands. This should match the pot odds given (2:1 bluff/value ratio to match the 2-1 pots odds in a pot size bet). This is more complicated given the fact that we should use combinatrix to get an accurate picture of how many combinations of bluffs and combinations of value hands they have.
E.g. If AA is in their value range, It's not just one hand, its actually 6 hands, because there are 6 combinations of the pocket pairs: AsAh, AsAd, AsAc, AhAd, AhAc, AdAc. So we are looking at the total number of hands in terms of combinations.
Remember that card removal effects (blockers) thus would have a significant change on the number of combinations in their range. Having A of spade in our hand could halve the number of AA in their range, and could be the difference in a key decision.
The Indifference principle
Its the core idea to balancing. In Layman's term, having a balanced range in spots, makes our opponent indifferent to calling or folding (in a PvBC model at least.)
Same applies for calling and folding against bets. Calling with correct frequencies make the villain indifferent to bluff more or value betting more. If we call too often, they can exploitatively value bet more, if we dont call enough they can exploitatively bluff more.
Models
We use models to analyse spots to understand ideas easier. For example a PvBC (polarised range vs Bluff catcher model) is useful for analysing river spots where i have medium strength hands and my opponent have nuts or bluffs. Of course in multistreets model, its obviously harder since, equity is not defined like it is on the river. Solving GTO solutions on turn would be harder than river since there is still one more card to come, so the game tree is bigger.
How my range interacts with the board
Obviously difference ranges from preflop (such as a 3b pot compared to a single raise pot) interact differently with the flop texture and later streets
A 3 bet pot would create different distributions with a A87 two hears then a single raise pot. Different % of gutshots, % flush draws, %top pairs etc. etc would be created (use flopzilla or something like it to analyse). This would obviously be a factor in balancing our ranges as we need to be aware of our distributions on flop textures.
Other ideas relating to exploitability: autoprofit
Alot of maths comes into being unexploitable. One such is to understand how much of our range we need to defend based on the pot odds and ranges. Obviously this is an overall thing, and vary depending on the texture. More on this later.
Maximising our gains
Other than playing unexploitably, we want to maximise our EV of our range. This is the "optimal" part of game theory optimal (not sure). To do so we must understand how the stack sizes work, and use bet sizing effectively, based on our ranges, and their ranges etc. More on this later as we discuss some examples
Tools use to analyse GTO ideas
To visualise how the EV of strategies work, we use game trees (use tools like card runners EV or gambit) to create trees and work out the EV of different strategies ranging from equilibrium strategy to maximally exploitative strategies. Some tools like pokersnowie (AI program) are also good to demonstrate ideas of GTO along with GTO range builder.
That's it for tonight!
Anyone wanna add some more general concepts? Would be nice to hear some ideas on the symmetry of distributions and general range topics.
I hope that people can contribute to this thread and support the growing understanding on GTO, so everyone can improve faster as opposed to everyone being in the dark.
I'm a 6m NL grinder myself (former live semi-pro), and I believe GTO would be especially useful for multitabling, when its hard to keep track of exploitable tendencies.
Hopefully, this thread will be more than philosophical understanding but actually discussing practical uses of GTO to real situation. Lets start!
Feel free to correct me as I'm still a newbie
And feel free to post ideas, and ask questions!What is GTO (Game theory optimal)?
So GTO basically is a mathematical way of playing perfectly. Its both unexploitable and optimal. As per Nash equilibrium "both players at equilbrium cant unilaterally increase their EV by changing strategy". You can think of it as two players adjusting to each other, and changing their strategy, swinging back and forth and maybe they'll settle at equilibrium.
In order to understand GTO better, people like to use "toy games", or simplified sub games to understand concepts.
The main elements of GTO include playing unexploitably. What that means, in my understanding, is to play balanced (more on that later). Balancing your range, means playing different hands same way (and same hands differently), a form of information hiding, so that your opponent cannot work out what you have.
But just playing balanced is not enough, you also have to play optimally and ultilise your range effectively, trying to make the most EV out of your range. That is a harder concept to understand in my opinion. That would include using good bet sizing (so triple barrel my stack rather than just shoving flop, would ultilise my range more effectively, even if i do it with a balanced range). more on this later.
Unexploitable play: Balancing/Combinatrix
I think balancing is definitely related to playing unexploitable, at least in the same ball park. It means having a good amount of bluffs to "balance" the number of value hands. This should match the pot odds given (2:1 bluff/value ratio to match the 2-1 pots odds in a pot size bet). This is more complicated given the fact that we should use combinatrix to get an accurate picture of how many combinations of bluffs and combinations of value hands they have.
E.g. If AA is in their value range, It's not just one hand, its actually 6 hands, because there are 6 combinations of the pocket pairs: AsAh, AsAd, AsAc, AhAd, AhAc, AdAc. So we are looking at the total number of hands in terms of combinations.
Remember that card removal effects (blockers) thus would have a significant change on the number of combinations in their range. Having A of spade in our hand could halve the number of AA in their range, and could be the difference in a key decision.
The Indifference principle
Its the core idea to balancing. In Layman's term, having a balanced range in spots, makes our opponent indifferent to calling or folding (in a PvBC model at least.)
Same applies for calling and folding against bets. Calling with correct frequencies make the villain indifferent to bluff more or value betting more. If we call too often, they can exploitatively value bet more, if we dont call enough they can exploitatively bluff more.
Models
We use models to analyse spots to understand ideas easier. For example a PvBC (polarised range vs Bluff catcher model) is useful for analysing river spots where i have medium strength hands and my opponent have nuts or bluffs. Of course in multistreets model, its obviously harder since, equity is not defined like it is on the river. Solving GTO solutions on turn would be harder than river since there is still one more card to come, so the game tree is bigger.
How my range interacts with the board
Obviously difference ranges from preflop (such as a 3b pot compared to a single raise pot) interact differently with the flop texture and later streets
A 3 bet pot would create different distributions with a A87 two hears then a single raise pot. Different % of gutshots, % flush draws, %top pairs etc. etc would be created (use flopzilla or something like it to analyse). This would obviously be a factor in balancing our ranges as we need to be aware of our distributions on flop textures.
Other ideas relating to exploitability: autoprofit
Alot of maths comes into being unexploitable. One such is to understand how much of our range we need to defend based on the pot odds and ranges. Obviously this is an overall thing, and vary depending on the texture. More on this later.
Maximising our gains
Other than playing unexploitably, we want to maximise our EV of our range. This is the "optimal" part of game theory optimal (not sure). To do so we must understand how the stack sizes work, and use bet sizing effectively, based on our ranges, and their ranges etc. More on this later as we discuss some examples
Tools use to analyse GTO ideas
To visualise how the EV of strategies work, we use game trees (use tools like card runners EV or gambit) to create trees and work out the EV of different strategies ranging from equilibrium strategy to maximally exploitative strategies. Some tools like pokersnowie (AI program) are also good to demonstrate ideas of GTO along with GTO range builder.
That's it for tonight!
Anyone wanna add some more general concepts? Would be nice to hear some ideas on the symmetry of distributions and general range topics.
01-06-2015
, 11:16 PM
Wouldn't gto= you play tight from every position pretty much?.
Like let's say you open X range utg in a full ring game vs all unknowns, our range needs to be un-exploitable, so a 3bet doesn't become instant profit but we also aren't making mistakes vs an opponent who 3bets tight as well, hence due to the possibility of tight 3bettors in this spot it means we have to open very tight so that we don't have that many hands to fold in the first place in this spot.
^^ You can say the same for every other position as well, so hence gto makes you play really really nitty, atleast in spots where you don't have to defend your sb/bb.
I mean what you think a gto btn open would be in a 6-9max cash game?, i feel like it could be as low as 20% of hands, hence not sure gto is really something anybody would want to aspire to play like due to the fact everyone has exploitable tendencies & is why vs randoms people find it +ev to open wide in a steal position due to a large population folding too much(this opens up to where we can't be gto though).
All in all i think playing a perfectly gto strategy wouldn't be good as too many assumptions would be made & you would never exploit anybody as your whole strategy is a defensive one in which you can't be exploited, if anything the rake exploits you for being a nit.`
p.s if im way off then let me know hehe.
Like let's say you open X range utg in a full ring game vs all unknowns, our range needs to be un-exploitable, so a 3bet doesn't become instant profit but we also aren't making mistakes vs an opponent who 3bets tight as well, hence due to the possibility of tight 3bettors in this spot it means we have to open very tight so that we don't have that many hands to fold in the first place in this spot.
^^ You can say the same for every other position as well, so hence gto makes you play really really nitty, atleast in spots where you don't have to defend your sb/bb.
I mean what you think a gto btn open would be in a 6-9max cash game?, i feel like it could be as low as 20% of hands, hence not sure gto is really something anybody would want to aspire to play like due to the fact everyone has exploitable tendencies & is why vs randoms people find it +ev to open wide in a steal position due to a large population folding too much(this opens up to where we can't be gto though).
All in all i think playing a perfectly gto strategy wouldn't be good as too many assumptions would be made & you would never exploit anybody as your whole strategy is a defensive one in which you can't be exploited, if anything the rake exploits you for being a nit
.`p.s if im way off then let me know hehe.
01-07-2015
, 09:11 PM
01-09-2015
, 12:55 AM
Quote:
Wouldn't gto= you play tight from every position pretty much?.
Like let's say you open X range utg in a full ring game vs all unknowns, our range needs to be un-exploitable, so a 3bet doesn't become instant profit but we also aren't making mistakes vs an opponent who 3bets tight as well, hence due to the possibility of tight 3bettors in this spot it means we have to open very tight so that we don't have that many hands to fold in the first place in this spot.
^^ You can say the same for every other position as well, so hence gto makes you play really really nitty, atleast in spots where you don't have to defend your sb/bb.
I mean what you think a gto btn open would be in a 6-9max cash game?, i feel like it could be as low as 20% of hands, hence not sure gto is really something anybody would want to aspire to play like due to the fact everyone has exploitable tendencies & is why vs randoms people find it +ev to open wide in a steal position due to a large population folding too much(this opens up to where we can't be gto though).
All in all i think playing a perfectly gto strategy wouldn't be good as too many assumptions would be made & you would never exploit anybody as your whole strategy is a defensive one in which you can't be exploited, if anything the rake exploits you for being a nit.`
p.s if im way off then let me know hehe.
Like let's say you open X range utg in a full ring game vs all unknowns, our range needs to be un-exploitable, so a 3bet doesn't become instant profit but we also aren't making mistakes vs an opponent who 3bets tight as well, hence due to the possibility of tight 3bettors in this spot it means we have to open very tight so that we don't have that many hands to fold in the first place in this spot.
^^ You can say the same for every other position as well, so hence gto makes you play really really nitty, atleast in spots where you don't have to defend your sb/bb.
I mean what you think a gto btn open would be in a 6-9max cash game?, i feel like it could be as low as 20% of hands, hence not sure gto is really something anybody would want to aspire to play like due to the fact everyone has exploitable tendencies & is why vs randoms people find it +ev to open wide in a steal position due to a large population folding too much(this opens up to where we can't be gto though).
All in all i think playing a perfectly gto strategy wouldn't be good as too many assumptions would be made & you would never exploit anybody as your whole strategy is a defensive one in which you can't be exploited, if anything the rake exploits you for being a nit
.`p.s if im way off then let me know hehe.
Um this is an interesting question. You have to remember GTO is a framework to think about poker, its a tool to help us play better, especially postflop. Just because we don't want to be exploited, doesn't mean we stop playing hands that are +EV.
1. Remember when i said GTO is NOT just about being unexploitable. It is also maximising our EV in the game trees that will come after.
2. You have to balance our range preflop too, we cant just have AA, KK etc, we need to balance with some weak hands to make sure we MAXIMISE our potential with our value hands as part of playing optimal.
3. Playing a wide range in position forces our opponents to defend with a range, instead of giving them walks. This can lead to pre or postflop spots like autoprofiting where our villains are losing money from an theoretical point of view.
4. I think this is especially important (could be wrong tho). Playing with a decently wide range in some spots, allows as us more options. When the flop comes, an equity distribution is created based on the hands we play preflop. Playing with only top like 10% means its hard to have hands like 2 pairs, good flush and straights. Thats why other than to balance, we keep our range wide, especially if we can play hands with good postflop playability. I need to study more on flop equity distributions.
In fact, this is the pre BTN opening range that snowie uses:
If anyone have more to add, or can make corrections to my points, please do so.
01-09-2015
, 10:59 AM
Quote:
Um this is an interesting question. You have to remember GTO is a framework to think about poker, its a tool to help us play better, especially postflop. Just because we don't want to be exploited, doesn't mean we stop playing hands that are +EV.
1. Remember when i said GTO is NOT just about being unexploitable. It is also maximising our EV in the game trees that will come after.
2. You have to balance our range preflop too, we cant just have AA, KK etc, we need to balance with some weak hands to make sure we MAXIMISE our potential with our value hands as part of playing optimal.
3. Playing a wide range in position forces our opponents to defend with a range, instead of giving them walks. This can lead to pre or postflop spots like autoprofiting where our villains are losing money from an theoretical point of view.
4. I think this is especially important (could be wrong tho). Playing with a decently wide range in some spots, allows as us more options. When the flop comes, an equity distribution is created based on the hands we play preflop. Playing with only top like 10% means its hard to have hands like 2 pairs, good flush and straights. Thats why other than to balance, we keep our range wide, especially if we can play hands with good postflop playability. I need to study more on flop equity distributions.
In fact, this is the pre BTN opening range that snowie uses:
If anyone have more to add, or can make corrections to my points, please do so.
1. Remember when i said GTO is NOT just about being unexploitable. It is also maximising our EV in the game trees that will come after.
2. You have to balance our range preflop too, we cant just have AA, KK etc, we need to balance with some weak hands to make sure we MAXIMISE our potential with our value hands as part of playing optimal.
3. Playing a wide range in position forces our opponents to defend with a range, instead of giving them walks. This can lead to pre or postflop spots like autoprofiting where our villains are losing money from an theoretical point of view.
4. I think this is especially important (could be wrong tho). Playing with a decently wide range in some spots, allows as us more options. When the flop comes, an equity distribution is created based on the hands we play preflop. Playing with only top like 10% means its hard to have hands like 2 pairs, good flush and straights. Thats why other than to balance, we keep our range wide, especially if we can play hands with good postflop playability. I need to study more on flop equity distributions.
In fact, this is the pre BTN opening range that snowie uses:
If anyone have more to add, or can make corrections to my points, please do so.
What is the % for that buttton open?.
