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Old 07-10-2021, 12:11 AM   #1
tombos21
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Why do you overbet?

This is a topic that I've realized I don't really understand.

For this question, I'm gonna redefine an overbet as a bet greater than the geometric bet size. This factors in SPR and negates the "its the only way to get stacks in by the river" argument. It's a more useful definition for my purposes.

Ok, so why do you overbet? What are the fundamental underlying reasons, in theory, that would make overbetting a preferred strategy?

There are a few moving parts to consider:

- Range & nut advantage, and the polarity of your range
- The elasticity (price sensitivity) of the ranges
- The value of denying equity (including hands that would have outdrawn you later)
- The value of getting called by worse hands with the top of your range
- Rake

None of these factors are good enough metrics on their own though...
  • There are plenty of spots where one player has the other player's range crushed and will still bet small.
  • There are plenty of high rake cap spots that use or even prefer overbets
  • Denying equity is offset by folding out worse hands that might have called a smaller bet size, and it gives you a worse price on your bluffs

So is there a more fundamental model that explains when and why you'd want to overbet? I know it ultimately comes down to EV, but how do we model which situations are more likely to result in overbetting being higher EV?

Last edited by tombos21; 07-10-2021 at 12:19 AM.
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Old 07-10-2021, 08:49 AM   #2
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Re: Why do you overbet?

Definitely has to do with how equities are distributed. Bluffs with robust equity lead to bigger sizings. Value hands that want to deny/can get immediate value but not necessarily future value aswell

Last edited by aner0; 07-10-2021 at 09:04 AM.
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Old 07-10-2021, 02:44 PM   #3
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Re: Why do you overbet?

Math thats why
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Old 07-12-2021, 03:55 PM   #4
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Re: Why do you overbet?

It's betting theory - it doesn't matter the size.

The bet that puts the highest % of opponent's range in 0 EV spots will be used.

Overbets OTT put most of opponent's flopped top pair in indifferent situations.

Consider two situations.

a) UTGvsBB Q62r board - we 1/3 range flop turn Ace. Overbet spot. All Qx is indifferent OTT

b) UTGvsBB Q62r board - we 3/4 flop. turn Ace. Now we don't OB OTT. We use 50% sizing instead.

We use smaller sizing now because our range isn't the same and neither is our opponent's.

The 3/4 cbet made us less Ace heavy OTT since we mostly check Ax back when using 3/4 sizing. So we use smaller sizing now since we still want to bet our Qx but our Qx doesn't want to OB.

In the 1/3 example we still have all Ax in our range - so now more of our range wants to OB and he folded some Ax OTF so there is more range asymmetry.

With the 3/4 flop cbet - once we get to the turn. Now all Villain's 77-JJ/6x is indifferent OTT vs 50% sizing and maybe even some weaker Qxs.

Last edited by DooDooPoker; 07-12-2021 at 04:19 PM.
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Old 07-12-2021, 09:08 PM   #5
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Re: Why do you overbet?

Quote:
Originally Posted by aner0 View Post
Definitely has to do with how equities are distributed. Bluffs with robust equity lead to bigger sizings. Value hands that want to deny/can get immediate value but not necessarily future value aswell
This is something that doesn't get talked about enough. The strength of your bluffs has a huge effect on sizing. You need way more nutted hands to make villain's top pair or w/e indifferent if your bluffs have 0equity compared to if your bluffs have lots of drawing power.

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Originally Posted by DooDooPoker View Post
It's betting theory - it doesn't matter the size.

The bet that puts the highest % of opponent's range in 0 EV spots will be used.

Overbets OTT put most of opponent's flopped top pair in indifferent situations.

Consider two situations.

a) UTGvsBB Q62r board - we 1/3 range flop turn Ace. Overbet spot. All Qx is indifferent OTT

b) UTGvsBB Q62r board - we 3/4 flop. turn Ace. Now we don't OB OTT. We use 50% sizing instead.

We use smaller sizing now because our range isn't the same and neither is our opponent's.

The 3/4 cbet made us less Ace heavy OTT since we mostly check Ax back when using 3/4 sizing. So we use smaller sizing now since we still want to bet our Qx but our Qx doesn't want to OB.

In the 1/3 example we still have all Ax in our range - so now more of our range wants to OB and he folded some Ax OTF so there is more range asymmetry.

With the 3/4 flop cbet - once we get to the turn. Now all Villain's 77-JJ/6x is indifferent OTT vs 50% sizing and maybe even some weaker Qxs.
"The bet that puts the highest % of opponent's range in 0 EV spots will be used."

This is a guideline that I've been using for a long time now, and it's a metric that intuitively gauges what the right strategy is. When we make our opponent indifferent (between continuing/folding), that part of their range will be 0 EV. I like to imagine we are "capturing" the EV of that indifference region.

But maximizing the % of their range that we make indifferent isn't necessarily the best strategy. It's a damn good metric, but it's not a hard law of game theory. There may be a smaller or larger sizing, that more efficiently captures EV.

Ok so let's move away from overbets and talk about sizing theory in general. How do we formalize the theory of the optimal sizing? Hand-wavy idea's welcome!
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Old 07-13-2021, 12:07 AM   #6
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Re: Why do you overbet?

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This is something that doesn't get talked about enough. The strength of your bluffs has a huge effect on sizing. You need way more nutted hands to make villain's top pair or w/e indifferent if your bluffs have 0equity compared to if your bluffs have lots of drawing power.



"The bet that puts the highest % of opponent's range in 0 EV spots will be used."

This is a guideline that I've been using for a long time now, and it's a metric that intuitively gauges what the right strategy is. When we make our opponent indifferent (between continuing/folding), that part of their range will be 0 EV. I like to imagine we are "capturing" the EV of that indifference region.

But maximizing the % of their range that we make indifferent isn't necessarily the best strategy. It's a damn good metric, but it's not a hard law of game theory. There may be a smaller or larger sizing, that more efficiently captures EV.

Ok so let's move away from overbets and talk about sizing theory in general. How do we formalize the theory of the optimal sizing? Hand-wavy idea's welcome!
Why do you think it isn't necessarily the best strategy?

I don't think it is a metric at all - it is game theory at work.

The best tool we have to study the game is solvers. Once you work backwards from a solver's solution you begin to understand why they choose the sizing they do.

It's the same reason why you overbet on a T94r board but use small sizing on an Ace low low board. These aren't metrics. They are solutions.
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Old 07-13-2021, 03:30 AM   #7
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Re: Why do you overbet?

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Originally Posted by DooDooPoker View Post
It's the same reason why you overbet on a T94r board but use small sizing on an Ace low low board. These aren't metrics. They are solutions.
If you bet small on T94 you put a bunch of Ax and ~66 hands in 0EV spots. If you overbet on A37, you put a bunch of Ax and 7x hands in 0EV spots. This way of thinking isn't very logical if you ask me.
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Old 07-13-2021, 04:55 AM   #8
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Re: Why do you overbet?

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Originally Posted by DooDooPoker View Post
Why do you think it isn't necessarily the best strategy?

I don't think it is a metric at all - it is game theory at work.

The best tool we have to study the game is solvers. Once you work backwards from a solver's solution you begin to understand why they choose the sizing they do.

It's the same reason why you overbet on a T94r board but use small sizing on an Ace low low board. These aren't metrics. They are solutions.
One thing I've learned while studying sims is to not project too much meaning onto what I'm seeing. Sometimes the interpretation is right and sometimes it's not or it's incomplete.

For example, you can justify T94r overbets as a betsize that makes your overpairs able to go for 3 streets on almost every runout, while any smaller would make overcards kill some of your action
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Old 07-13-2021, 10:28 AM   #9
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Re: Why do you overbet?

Quote:
Originally Posted by DooDooPoker View Post
Why do you think it isn't necessarily the best strategy?

I don't think it is a metric at all - it is game theory at work.

The best tool we have to study the game is solvers. Once you work backwards from a solver's solution you begin to understand why they choose the sizing they do.

It's the same reason why you overbet on a T94r board but use small sizing on an Ace low low board. These aren't metrics. They are solutions.
Not sure how checking is supposed to fit in with your theory.
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Old 07-13-2021, 10:45 AM   #10
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Re: Why do you overbet?

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If you bet small on T94 you put a bunch of Ax and ~66 hands in 0EV spots. If you overbet on A37, you put a bunch of Ax and 7x hands in 0EV spots. This way of thinking isn't very logical if you ask me.
Yeah but that's when you look at your own range on T94. None of our range wants to bet small.

The highest frequency used sizing combines what your range wants to do - to what part of your opponent's range you want to target.

Overbetting on A37 doesn't make any sense since we don't put a high % of our opponent's range in tough spots. Mainly his K high/Q high hands/J high hands.

Also we need to look at our own range. There's a ton of hands that don't want to put any money in the pot on Ace high boards. So if these hands do bet - it makes sense they would bet very small.

I guess everyone think's about poker differently though. This way of thinking helped me a lot but maybe it doesn't help you.
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Old 07-13-2021, 10:53 AM   #11
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Re: Why do you overbet?

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Not sure how checking is supposed to fit in with your theory.
In general you just check hands that don't want to put money in the pot. Or if your range checks a lot - you check back some strong hands to not be exploited.

So 54s get's checked back a decent amount on 542r because our range wants to check a ton.

Same thing with AA etc.

The goal is to make a complex topic like bet sizing - accessible and easy enough to understand.

Words like robustness/equity distribution aren't really helpful when discussing this topic. You need practical examples.
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Old 07-13-2021, 10:59 AM   #12
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Re: Why do you overbet?

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One thing I've learned while studying sims is to not project too much meaning onto what I'm seeing. Sometimes the interpretation is right and sometimes it's not or it's incomplete.

For example, you can justify T94r overbets as a betsize that makes your overpairs able to go for 3 streets on almost every runout, while any smaller would make overcards kill some of your action
Well everyone has the same tools. I think of a solver as an open book test, except the book is thousands of pages.

Someone at the micros can have access to the same solutions as a world class player. But they are interpreting the data much differently.

That's why you need to actively study. It's very easy to plateau in this game.
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Old 07-13-2021, 02:59 PM   #13
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Re: Why do you overbet?

Let's be honest here - Pretty much everyone is looking at the same solutions and just coming up with some Ad-hoc justification for why it does what it does. It's not exactly a rigorous process.

Complicated topics often need to be described with complicated language. The truth is there probably isn't some pithy phrase that sums up how to gauge different bet sizing strategies.

That's why I want to look deeper. I want a more fundamental model for bet sizing theory. I want to be able to look at a board, look at the equity distributions, and predict with rigorous accuracy what the preferred bet sizing would look like. Do you guys think that is possible?
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Old 07-13-2021, 03:46 PM   #14
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Re: Why do you overbet?

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Let's be honest here - Pretty much everyone is looking at the same solutions and just coming up with some Ad-hoc justification for why it does what it does. It's not exactly a rigorous process.

Complicated topics often need to be described with complicated language. The truth is there probably isn't some pithy phrase that sums up how to gauge different bet sizing strategies.

That's why I want to look deeper. I want a more fundamental model for bet sizing theory. I want to be able to look at a board, look at the equity distributions, and predict with rigorous accuracy what the preferred bet sizing would look like. Do you guys think that is possible?
That's a fair assessment.

Every book I've ever read about poker has swung and missed completely when it comes to this topic and most of these people are very smart.

You'd probably need to study a superbot like Pluribus - but a few iterations more advanced. Then talk to the someone like Noam Brown to really understand how the superbot is playing. It would be a Herculean task though.
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Old 07-14-2021, 02:15 AM   #15
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Re: Why do you overbet?

So I haven't dove deep into this, but I heard that for a fully polarized range (our opponent only has bluffcatchers, and we ONLY have value or bluffs) we want to bet as much as possible to maximize our EV. So overbetting makes sense in that context that we can incorporate it in real situations in poker.
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Old 07-15-2021, 12:44 PM   #16
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Re: Why do you overbet?

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So I haven't dove deep into this, but I heard that for a fully polarized range (our opponent only has bluffcatchers, and we ONLY have value or bluffs) we want to bet as much as possible to maximize our EV. So overbetting makes sense in that context that we can incorporate it in real situations in poker.
In a one street situation where villain can only call or fold, you should always bet your strongest hands as much as you possibly can so long as: (1) they beat all of villain’s range, (2) you have enough bluffs to support the value bet. Bigger bets require more bluffs, but never more bluff hands than value hands… if you have some non-nut hands that you want to value bet (for less), those have to be supported with bluffs as well, which may take away from some of the bluffs you needed for your nut hands…. balancing bluffs and value across multiple bet sizes is really hard, so most just decide on a single sizing most of the time for a given situation, but that’s definitely not optimal. The whole thing gets even more complicated when villain can raise and there’s multiple streets, because then you start worrying a bit more about keeping strong hands around to protect weaker ranges.
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Old 07-15-2021, 05:46 PM   #17
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Re: Why do you overbet?

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Originally Posted by Aesah View Post
So I haven't dove deep into this, but I heard that for a fully polarized range (our opponent only has bluffcatchers, and we ONLY have value or bluffs) we want to bet as much as possible to maximize our EV. So overbetting makes sense in that context that we can incorporate it in real situations in poker.
Perfectly polarized ranges use geometric sizing to end up all-in with the last bet, which is not overbetting the way OP defined it, unless I misunderstood. A 1/4 pot turn jam would be an overbet, though...
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Old 07-15-2021, 07:37 PM   #18
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Re: Why do you overbet?

You can always count on browni3141 to pay attention to the details!

So the perfectly polarized player should always bet the geometric bet size to get stacks in by the river, using equal pot% bets each street. That's proven in The Mathematics of Poker.

However, I've defined an "overbet" as a bet that's larger than the geometric bet size. In other words, you bet more than what was required to get stacks in by the river. This definition is more useful for my purposes than the arbitrary "greater than pot" definition that is commonly used, for reasons I outlined in the OP. I actually think this is just a better definition in general, but that's just semantics.

So, a perfectly polarized player, using my funky definition, would actually NEVER overbet. That leads me back to the original question - when would you bet more than you needed to, to get stacks in by the river?
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