I'm looking for spots to do this but I have no idea how a soft pool would react. For example the Q44 A board...my concern is that I have no idea how population reacts. Do they massively over fold river and then I'm just value owning myself? Or do they simply over fold turn by folding too much top pair and then I'm REALLY value owning myself on rivers? I pretty much never see a 250% overbet in my pool so I'm sure no one knows how to react to it and the natural tendency is to fold.
I pretend to.. I bet big on turns leaving the geometric size remaining and then bet small on rivers. My reasoning? In small stakes people end up at the river with very inelastic holdings (busted draws and strong made hands)
There is a mathematical proof of this concept in "The Mathematics of Poker" by Bill Chen. The theorem states that a polarized range vs a range of bluff catchers, maximizes its ev by betting geometrically.
Yes in the Book, authors using the inequality of arithmetic and geometric to demonstrate that chapter 19 at the end of the Book ( the famous AM and GM inequality)
Ive done my own proof of this as well. I made a function which is the sum of the pot odds you offer the opponent on multiple streets of betting, and uses calculus to find the maximum point of that function. For three streets I made a two-variable function, for two bet sizes (flop bet size and turn bet size. The river bet size is equal to your starting stack - the sum of the bets you've made so far. Therefore you only need two variables. I designated the stack size by some constant number. I made the final bet be a constant - the two bets you've made so far) I took two partial differentials and set them both to zero, and setting the differentials to zero directly gave equations which shows that ratio between successive pot sizes after a round of betting and calling was the same, i.e. the pot was growing at a fixed rate, which means its geometric betting. So on a two-street version of the AKQ toy game for example, the only way the bluff catcher can be indifferent to a turn bet is if the polarised person checks the river with enough bluffs which corresponds to the turn pot odds. Thats why I made a function which is equal to the sum of the pot odds you offer your opponent across all streets, and find the maximum point, given the constraints of a finite and fixed amount of money you'll be betting in total across all streets. If the pot is "p" and the bet you make into that pot is "b", pot odds is how much you can bluff with a polarised range, and pot odds is given by b/(2b+p) in this scenario. This function is an asymptote, and it gets harder and harder to make this number bigger with larger and larger bets. And it never reaches the limit of 0.5. So intuitively at least, thats why its superior to spread your bets across multiple streets with a polarised range, rather than one street. Exploitatively however, I've found that big shoves on one street work better sometimes : D
Love the spread sheet. Used it to make a rough table for 2 and 3 bets to go with spr 1-4 going up by .5 increments. Cool patterns emerged and it’s easy to remember.
I feel like this entire concept doesnt work because its based on opponent MDF, and MDF only applies to raises. The concept behind MDF is if you bet and your range fails to reach the MDF, your opponent can raise with their entire range profitably, making your bet unprofitable. You dont need to have a MDF to a single bet because certain flops/turns/rivers are worse or better for your range, so your opponent is already in a profitable position because they have >50% equity in the pot. Not needing an MDF is especially true when youre defending the BB because you had odds to call preflop, so its ok if the flop cbet (or a combination of flop/turn/river bets) is instantly profitable for your opponent because you only need 32% equity to continue preflop vs a raise to 2.75 BB.
The MDF approximation becomes much stronger when ranges become more polarized (which is when you'd want to implement a geometric betting strategy). Which is why I stress that point in the video. MDF still applies on earlier streets, it's just offset by some constant when "bluffs" have equity as a check. In this article, we explore MDF vs GTO frequencies and graph the result against different flop c-bet sizes: blog.gtowizard.com/mdf-alpha/
I don't get the BB calling range against the turn 175% overbet @14:56. Why does A10 fold more than the other aces? And why does K3 and K4 call more than the higher one pair kings?
Why would you want to maximize the amount of money villain puts into the pot when you are bluffing? For the sake of balance, I assume you use geometric sizings when bluffing too, but what's the benefit of it when you are perfectly balanced?
Easiest way is to just ballpark it by thinking about the stack/pot and how that will change next street. You can also memorize a few key geometric SPRs, e.g. an SPR of 13 has a geo sizing of pot over 3 streets. The full formula is too complex to memorize and calculate in game. blog.gtowizard.com/pot-geometry/
Does it therefore make sense to bet geometric with every nut-draw on the flop that doesnt have a lot of equity when the draw misses? You are polarized from the start and want to get all the money in when your draw hits.
These are naturally polarized hands do well to bet geometrically. However, they must be protected by some nutted hands to ensure they can realize their equity.
Immensely informative video, as always. I have a question, In the formula given for Geometric Sizing in the artice "Pot Geometry" what does 2stack variable stand for ? TIA
How do you take into account that flop is often overfolded relative to MDF when you calculate the compound MDF when betting geometric vs non-geometric ?
No, but these strategies aren't usually implemented on the flop in most cases anyway. Trying to keep it simple! We've covered GTO defence compared to MDF in this article: blog.gtowizard.com/mdf-alpha/
it's covered in that link he gave you, but the short answer is that we overfold according to mdf when our opponent's "bluffs" have more than 0% equity as a checkback. We're trying to make them indifferent, so we're meant to "overfold" until our opponent's ev for betting the lowest ev hand in their checking range (when they're playing a nash equilibria strat) becomes identical to the ev for checking the lowest ev checking hand.
MDF is the core principle to look at if we're looking at toy spots like at the beginning of the video. Perfectly polar with enough bluffs to choose from. The problem is when people make the mistake of assuming that the toy games map to the real game 1:1, or that the principles illustrated by toy games apply in the same way to a large number of different spots. That mistake isn't made here, and some places where the concepts found in the toy games are more or less applicable (and why) are explored later in the video.
@@walmart120 As poker players we want to simplify when possible. If we are rounding here, we can say mdf is liferally never useful theoretical concept to consider.
@@YOU2pressDELETE yes that is true. simplify to apply. But u need to consider new ideas and concepts to evolve. which lead to better strategy. f.e. PIO solver, u cant ever apply it 1:1. which is not the goal. the goal is to get statistical clue of what is the superior strategy. it is about guidelines. which always came from new ideas...
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Do you bet geometrically in your games? Why or why not? Let us know down below!
Absolutely yes, it'd be stupid to not keep this in mind while playing
I try to but my math isnt good enough
@@MrMagicMarleyMarl do shrooms your math skills will ⏫⏫📈📈
I'm looking for spots to do this but I have no idea how a soft pool would react. For example the Q44 A board...my concern is that I have no idea how population reacts. Do they massively over fold river and then I'm just value owning myself? Or do they simply over fold turn by folding too much top pair and then I'm REALLY value owning myself on rivers? I pretty much never see a 250% overbet in my pool so I'm sure no one knows how to react to it and the natural tendency is to fold.
I pretend to.. I bet big on turns leaving the geometric size remaining and then bet small on rivers. My reasoning? In small stakes people end up at the river with very inelastic holdings (busted draws and strong made hands)
There is a mathematical proof of this concept in "The Mathematics of Poker" by Bill Chen. The theorem states that a polarized range vs a range of bluff catchers, maximizes its ev by betting geometrically.
Yes in the Book, authors using the inequality of arithmetic and geometric to demonstrate that chapter 19 at the end of the Book ( the famous AM and GM inequality)
Ive done my own proof of this as well. I made a function which is the sum of the pot odds you offer the opponent on multiple streets of betting, and uses calculus to find the maximum point of that function. For three streets I made a two-variable function, for two bet sizes (flop bet size and turn bet size. The river bet size is equal to your starting stack - the sum of the bets you've made so far. Therefore you only need two variables. I designated the stack size by some constant number. I made the final bet be a constant - the two bets you've made so far)
I took two partial differentials and set them both to zero, and setting the differentials to zero directly gave equations which shows that ratio between successive pot sizes after a round of betting and calling was the same, i.e. the pot was growing at a fixed rate, which means its geometric betting.
So on a two-street version of the AKQ toy game for example, the only way the bluff catcher can be indifferent to a turn bet is if the polarised person checks the river with enough bluffs which corresponds to the turn pot odds. Thats why I made a function which is equal to the sum of the pot odds you offer your opponent across all streets, and find the maximum point, given the constraints of a finite and fixed amount of money you'll be betting in total across all streets.
If the pot is "p" and the bet you make into that pot is "b", pot odds is how much you can bluff with a polarised range, and pot odds is given by b/(2b+p) in this scenario. This function is an asymptote, and it gets harder and harder to make this number bigger with larger and larger bets. And it never reaches the limit of 0.5. So intuitively at least, thats why its superior to spread your bets across multiple streets with a polarised range, rather than one street.
Exploitatively however, I've found that big shoves on one street work better sometimes : D
Love the spread sheet. Used it to make a rough table for 2 and 3 bets to go with spr 1-4 going up by .5 increments. Cool patterns emerged and it’s easy to remember.
Great work as always! Love these lessons
Maybe the best poker content video I ever see! Thanks!
Good stuff!
The line is yellow:)
Interesting what you said a the end on J66 spot "when he calls flop our small bet we become clairvoyant "
I feel like this entire concept doesnt work because its based on opponent MDF, and MDF only applies to raises. The concept behind MDF is if you bet and your range fails to reach the MDF, your opponent can raise with their entire range profitably, making your bet unprofitable. You dont need to have a MDF to a single bet because certain flops/turns/rivers are worse or better for your range, so your opponent is already in a profitable position because they have >50% equity in the pot. Not needing an MDF is especially true when youre defending the BB because you had odds to call preflop, so its ok if the flop cbet (or a combination of flop/turn/river bets) is instantly profitable for your opponent because you only need 32% equity to continue preflop vs a raise to 2.75 BB.
The MDF approximation becomes much stronger when ranges become more polarized (which is when you'd want to implement a geometric betting strategy). Which is why I stress that point in the video.
MDF still applies on earlier streets, it's just offset by some constant when "bluffs" have equity as a check.
In this article, we explore MDF vs GTO frequencies and graph the result against different flop c-bet sizes: blog.gtowizard.com/mdf-alpha/
@@GTOWizard great thank you, ill look into it
I don't get the BB calling range against the turn 175% overbet @14:56. Why does A10 fold more than the other aces? And why does K3 and K4 call more than the higher one pair kings?
A10 is blocking the gutshot i guess, but so are AJ and AQ. And K3 and K4 are even blocking some of the COs 33 & 44 bluffs.
Why would you want to maximize the amount of money villain puts into the pot when you are bluffing? For the sake of balance, I assume you use geometric sizings when bluffing too, but what's the benefit of it when you are perfectly balanced?
Your bluffs are zero EV when balanced so it doesn't matter the size of the pot, but your value hands win more.
This is #1 BS. You either win 50% of the times or you Kose 50% of the times. Poker is all about BALLS!
@@hanzohanzo1639 found the fish
@@hanzohanzo1639
Even I know better to claim that, and I'm a micro fish
@@granjerojose Why do the value hands have more than 0 EV when the bluffs have 0 EV in a perfectly balanced strategy?
Good video but then why weren’t geo sizes included in GTOWizard’s sims?
Really enjoyed the video. WHen playing, how do I know/calculate the perfectly geometric betting size?
Easiest way is to just ballpark it by thinking about the stack/pot and how that will change next street. You can also memorize a few key geometric SPRs, e.g. an SPR of 13 has a geo sizing of pot over 3 streets.
The full formula is too complex to memorize and calculate in game. blog.gtowizard.com/pot-geometry/
for turn to river you can use : Effective Stack - Current Pot / 3
Does it therefore make sense to bet geometric with every nut-draw on the flop that doesnt have a lot of equity when the draw misses? You are polarized from the start and want to get all the money in when your draw hits.
These are naturally polarized hands do well to bet geometrically. However, they must be protected by some nutted hands to ensure they can realize their equity.
Immensely informative video, as always. I have a question,
In the formula given for Geometric Sizing in the artice "Pot Geometry" what does 2stack variable stand for ? TIA
That just means 2 times the stack
good stuffffffff
thx for the effort as always
Really deep stuff, thanks for the great content 🔥🙂
I mean is this guy the most clever person on the planet? He certainly looks the part
@16:30 that explanation of bi-modal distribution is incorrect. That’s not why you have that phenomenon. It’s a lot more nuanced than that.
Care to elaborate?
How do you take into account that flop is often overfolded relative to MDF when you calculate the compound MDF when betting geometric vs non-geometric ?
No, but these strategies aren't usually implemented on the flop in most cases anyway. Trying to keep it simple!
We've covered GTO defence compared to MDF in this article: blog.gtowizard.com/mdf-alpha/
it's covered in that link he gave you, but the short answer is that we overfold according to mdf when our opponent's "bluffs" have more than 0% equity as a checkback. We're trying to make them indifferent, so we're meant to "overfold" until our opponent's ev for betting the lowest ev hand in their checking range (when they're playing a nash equilibria strat) becomes identical to the ev for checking the lowest ev checking hand.
Ooooooo, graphs
🥰
Usually decent content, but this is pure garbage. Whenever someone starts talking mdf as the core priciple for defending, RUN!
MDF is the core principle to look at if we're looking at toy spots like at the beginning of the video. Perfectly polar with enough bluffs to choose from. The problem is when people make the mistake of assuming that the toy games map to the real game 1:1, or that the principles illustrated by toy games apply in the same way to a large number of different spots. That mistake isn't made here, and some places where the concepts found in the toy games are more or less applicable (and why) are explored later in the video.
u got no clue about theoretic stuff and why its useful right?
@@walmart120 As poker players we want to simplify when possible. If we are rounding here, we can say mdf is liferally never useful theoretical concept to consider.
@@YOU2pressDELETE yes that is true. simplify to apply. But u need to consider new ideas and concepts to evolve. which lead to better strategy.
f.e. PIO solver, u cant ever apply it 1:1. which is not the goal. the goal is to get statistical clue of what is the superior strategy.
it is about guidelines. which always came from new ideas...