PIO Sizing Theory - Understanding multiple bet sizing strats
Posted by tinyelvis58
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tinyelvis58
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PIO Sizing Theory - Understanding multiple bet sizing strats
Hey guys/gals. I'm trying to use PIO to conceptualize when/how to use multiple bet sizings vs a single size as part of my overall strategy. I understand there are pros/cons of each side of the coin (i.e. single sizing simpler to execute, multiple sizing harder to play against...). What I'm really trying to figure out is how much EV difference there is between strategies and how to interpret those results. Here's a quick example to demonstrate my point:
Simulation: 100bb Button Open vs BB defend on Tc9s8s (pot 700, 9700 eff stack)
Scenario 1: 4 flop sizes (30,60,90,160), IP EV 427, OOP EV 273, x56%/bet 44%
Scenario 2: 60% flop size only, IP EV 427.3, OOP EV 272.7, x 61%/bet 39%
Scenario 3: 30% flop size only, IP EV 426.9, OOP 273.1, x 46%/bet 54%
We can see that all 3 strategies have IP EVs that are extremely close (427, 427.3,426.9). Obviously the x/bet frequencies are going to be different as our sizing options change for each scenario. When looking at all of these scenarios it seems as if we should use the simplest option to execute as there is an immaterial EV difference between each.
Am I missing something here? Am I looking at this correctly?
Any help would be much appreciated.
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Multiple flop sizes are incredibly annoying to implement and doesn't add much if done perfectly, so I'd say looking for the simplest is a good idea or the one you think performs the best vs the populationon you play against. I did some practice a few months ago to see if learning to use 2 bet sizes and check would be possible to implement, and even with the best practice methods, it's a huge pain to get everything correctly. There is also a possibility that the difference you see can come from suboptimal XR size against one bet size or not having ideal turn or river bet sizes.
I'd say as long as you not play toughest lineup or regwars with extremely competent opponents, trying to implement 2 sizing's pretty useless in EV point of view.
Yeah you can go further and use 2 sizing's pre or so and it will damn complex as hell. If you use 2 sizings on the flop, likely you have 3rd option which is a check. If only 2 options 33% and 70% for example it doesn't seems as hard
Additionally you freeroll yourself for considering being a bot haha
Using 2 sizings often won't inherently increase your EV however if you want to understand the EV of it being harder to play against node lock your opponents strategy so that they play against each individual sizing like it's the only one that you use. So essentially if you're playing a strong player that can reasonably emulate a GTO response (for a human) you will gain EV from them misunderstanding the strategy that they are playing against and as a result playing differently. For example if someone assumes that you only use a 60% sizing in a certain turn spot but you also have an overbet sizing then they will assume that your 60% sizing is uncapped when in fact several of your strongest hands will actually be in the bigger sizing. As a result of this they may play back against your 60% sizing less aggressively than they should from a GTO standpoint thereby capturing more EV with your marginal hands that want to bet for value but hate facing a raise.
All good points. Thx
DNegs98 Kalupso If using multiple sizings doesn't add much EV, than what's the point of anyone implementing? Say I could implement 4 sizes perfectly (which I obv can not), why would I ever do that if there is no EV gain from one size? Clearly super elite high stakes players are trying to do this, so what is their purpose in doing so?
My original thought was you should use the strategy (in theory) that has the highest EV.
EVs are comparable in an optimal scenario. But don't forget that it's way harder for your opponent to play "optimally" when you are using multiple betsizes. In other words, the chance of driving your opponent into errors is bigger if you manage different betsizes, playing against one betsize is easier.
Thx BigFiszh So it's a matter of weighing 2 options that have same GTO EV:
a) playing a simpler strategy that is easier to play against but also easier to execute
b) playing a more complex strat that has the same optimal EV but a higher potential EV due to it being more difficult to play against (flip side being it's more difficult to execute and if played incorrectly would sacrifice a lot of EV as well).
Do strats with multiple sizes vs single size always have the same EV when played optimally? Are there scenarios where there is a significant gain in EV when executing a multiple size strategy correctly (excluding variable of opponent playing poorly, only looking at equilibrium)?
I think as long as you're within the reasonable bounds for min and max sizing in a given spot it doesn't make a difference. Think of it like this though, poker is an imperfect information game where we approximate the correct response based on limited information, as players get stronger and you come up against those stronger players who can extrapolate a lot from very little limiting their ability to do so becomes more valuable. It's why the term ABC player is not a compliment, all of their decisions make a reasonable amount of sense and they don't make massive EV mistakes but there is an informational asymmetry because their strategy is simpler to execute which allows you to beat them in the long run.
DNegs98 Great point! I like the ABC player analogy.
As a heads up, Kevin Rabichow bet sizing videos are great at explaining the theoretical q being discussed.
I'm glad you're using my method for this! I think you'll find greater gains on different board textures, but here you've shown evidence that multiple sizes aren't worthwhile.
Thx @KRab42. Just finished the 3rd vid of your series and really enjoyed them. Can you throw out a quick example of a texture where gains will be greater?
Simplified Summary of Kevin’s vid for multiple sizing (for those who didn’t watch):
A). Look for EV gain when using multiple sizings vs a single size (play around w diff sizings)
B). Look for multiple sizing strats that target different hand classes (ie if a bunch of hands all have 3 sizing mixes this will make things very complex and difficult to execute)
-watch vids for detailed explanation
Specifically on flop or in any spot? Like you said I'm looking for textures with distinct hand classes that benefit from betting distinct sizes. This is easier to find on turns and especially on rivers, but in heads up single raised pots (one of the harder spots to distinguish these spots imo) you might want to try something like AQ3r or JT5t if memory serves me right...
What I do is solve the flop subset provided with a tree that includes multiple sizes (up to 6). Then I look at each flop to see what size(s) the solver prefers and also whether or not there is a clear correlation between size and hand/hand class. Usually, when it is clear that certain parts of the bettor's range want to use one particular size over others, it tells me that there is more EV to be gained by using multiple sizes. Conversely, when there is no clear correlation such that most betting hands use multiple sizes, almost indiscriminately, where all the different colors run together, I usually discover that I can capture with one bet size (a catch-all size) most of the EV earned by multiple sizes. Then I try different sizes, one at a time using my initial subset as a guide, for each flop to determine which size or two earns the most EV. I also take into account complexity when developing my strategy and I usually only use multiple flop sizes when my range is condensed (3bet, EP open, etc.). My challenge with two flop sizes is randomizing bluffs/draws where many times there is no clear direction. Would love to hear how better players are doing this.
BigFiszh DNegs98
If its all about our opponent errors vs our mixed sizing how we can explain spot where pio prefer one sizing only. BBvBTN Q72r PIO will used just the 1/3P size even if we allow bigger sizes. I understand the logic of protection and push equity on this board but we can bet bigger sizing with lower frequency and gain the same EV.
can you explain the theory ?
The solver does not care about mistakes. He plays in a way that the optimal counterexploitation will not hurt him (more than necessary).
That means, if one betsize clearly has a higher EV than another (given that Villain correctly exploits either), the better will taken 100%.
If two (or more) betsizes yield the same EV (given optimal counterexploit in either), Pio will likely split between these. The split results in a slightly higher EV than deciding for one single option.
If you look at a "solved" scenario, it's useless to say "we could do this or that as well or more, it shows the same EV". The calculated EV's are for that exact split. Any change will result in different EVs.
If for example you see a split between 0.5p and 1.0p of 90 vs. 10%, and the EV is (exactly) the same, that does not mean that you could as well play 10/90 or 0/100. This only works as long as Villain does not (properly) adjust, but it would leave room for exploitation, which reduces your (potential) EV.
BigFiszh
Not sure if I understand you correctly, but I think we do lose significant EV if we don't have a small size on Q72, simply because there are too many advantages to betting 7x.
In fact, on a board like this betting 7x is so good that we end up doing it at a high frequency. So even if we had 2 sizes to begin with, we have to pull down so many strong hands to "support" all the 7x in our small size that there aren't any strong hands leftover to bet big.
Compare this to a board like Q82, where we use a mix of big and small bets. Here we do deny quite a bit of equity by betting 8x, but it's nowhere as effective as betting 7x on Q72. So we end up betting 8x at a lower frequency, and even after pulling down some strong hands to support the smaller betsize, we still have enough strong hands to build a big size around.
Just my interpretation of multiple sizes, not 100% sure about it but seems to hold for most scenarios. Also I think the difference is more apparent if you compare A92 with AT2.
I guess a more technically correct way of putting it would be to say that when we have so many mid-pair type hands in our small bet range, we can expect to face a lot of pressure, which means our strong hands have better ev as a small bet. Whereas on Q83 this effect isn't as pronounced, so we mix between big and small bets with our strong hands.
The reason is the gutshots or the more higher cards to the 7 in BB range 8T 89 8J ? On K82 is same for Q72 ?
Yup, JT/J9/T9o are folding on Q72 but not Q82, so we deny a lot more equity with a small bet.
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