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Old 02-08-2019, 09:30 PM   #1
CallMeVernon
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COTM: Bet Sizing (Revisited)

Introduction

I think everyone on the forum, myself included, could stand to improve their bet sizing. Bet sizing is one of the fundamental parts of no limit strategy. We get to choose our bet size every single time we make a bet or raise, and so often people just go on autopilot with their bet sizes. Even players who are good at choosing when to bet can still have issues with sizing.

Bet sizing is such a complex topic that I won't dare to try to cover it all. In this OP, I don't intend to talk about bluff sizing at all (there's an earlier COTM on Reasons for Betting that includes all I'd ever have wanted to say about that topic). I also could never cover all the intricacies of value bet sizing. Maybe there can be some expanded discussion later in the thread on the stuff I did not cover, but I'm going to keep it to one aspect of bet sizing that I feel is important: sizing value bets before the river to make sure that even if you make a mistake later in the hand, your opponent made a bigger mistake by calling your value bet.

1. An Example of Trading Mistakes

Imagine you're playing 2/5, and it's the flop. You have raised preflop with AKo and gotten called by one Villain in the BB. The pot is $35 (after rake), and effective stacks are $450. The flop is A74rb, and your opponent has checked. You have decided to bet.

Let's suppose you choose to bet $20, and your opponent is going to make this call with a wide range. The turn is a 5, completing the rainbow. Your opponent now leads into you for 55 into a pot of 75. You call. The river is a 9. Your opponent leads into you for 125 into a pot of 185. You call again and get shown 86, the turned nuts.

It could be argued in this hand that both you and your opponent made obvious mistakes. Your opponent decided to call the flop with a gutshot getting 2.75:1 immediate pot odds, when his hand was 10.25:1 to hit (4 outs to hit out of 45 unseen cards). You, however, paid off your opponent's bets on the turn and river.

So who won the battle of mistakes in this hand? This is not an opinion question; we can actually quantify this. One quick way to do it is to look at how much our opponent extracted from us over the course of the hand. He called $20 on the flop to win 35 + 20 + 55 + 125 = 235. That means we gave our opponent implied odds of 11.75:1 on his flop call. Since our opponent's EV on the flop call turns out to be positive after counting implied odds, it is actually our opponent who has won the battle of mistakes.

If we want to fix this (and this really is an "if"--more on that later), there are two ways we can do so. The first is to try to fold our hand so that we are not paying off those big bets. That approach might run into the problem that we are potentially opening ourselves up to get bluffed off the best hand. If we know we have good enough reads, we can mitigate this issue, but it is still a potential issue.

The second way to win the battle of mistakes is an approach that the authors of NLHT&P devote a whole chapter to: adjust our bet sizing so that even if we make the mistake of paying off bets later in the hand, our opponents' implied odds are still small enough that we win the battle of mistakes.

2. Sizing to Force a Mistake

To show this idea in action, here's another example. Let's say we are playing 1/2 and after the preflop action, we're $275 deep with KK. We raised preflop and got called; let's say that after rake, the pot is $30. The flop is K95rb, and it's been checked to us.

Clearly, taking the large view, our hand is so good that we wish to get our entire stack in before the hand is over. But in terms of the immediate issue, sizing our bet on the flop, there seem to be several schools of thought that are popular on the forum. One of those is the idea that on flops like this, where there are no "short-odds" draws, we do not "need" to make a big bet to induce a mistake. So if I posted such a hand on the forum, there would probably be a large contingent of people telling me to bet $15 or sometimes even less.

The problem with this idea is that if we bet small enough that many longshot draws will be tempted to call, we are going to have to stack off to those draws if they hit, because we won't know if we are beat, and our hand is just too good to fold. For example, let's say we bet $15, and one person calls. The turn is an 8. We bet again and now we get raised. We obviously will never be folding our hand because it's too good--but did we just give a too-cheap card to 76, or did we induce a terrible call from 98? (Or, of course, sometimes we induced a semi-bluff as well.)

If we bet only $15 on the flop, any opponent with a gutshot was actually correct to call, given that we will stack off later. Let's do the math to confirm. 41 times out of 45, our opponent will miss and lose $15 after we bet them out on the turn. (Let's figure that their backdoor draws are a wash with us sometimes slowplaying board-pairing turns.) 4 times out of 45, our opponent will hit. When this happens, we lose our stack unless the board pairs, in which case we win our stack plus the pot. So our opponent's EV is:

(41/45)(-15) + (4/45)(34/44)(305) + (4/45)(10/44)(-275)
= (-41/3) + (305)(34/495) - (275)(10/495)
= (-41*165 + 305*34 - 275*10)/495
~ 1.73

It's close, but it's positive. Note also that the deeper we are, the more it hurts our EV (and helps our opponent's) to stack off.

What we have just proved is that if we size our bet too small in cases like this, we can give our opponents +EV calls against us, even though we have a monster. If we were to size our bet bigger, then we would be creating a situation where any call by our opponent with any range is -EV for them and +EV for us. In this example, even increasing our bet to $20 would probably do it.

Some of you might be thinking that this example is too simplistic--and by itself, it would be. (I'll have other examples below.) But its main purpose is to introduce a larger theoretical concept. When I'm thinking about bet sizing and planning for future streets, I'm thinking about leveraging or protecting my stack. The size of the pot only matters because it's part of figuring out the implied odds we are offering. Notice that at no time in this analysis did "pot fractions" enter into it. It does not matter (at least not to me) that $15 is half-pot and $20 is 2/3 pot. What matters is that a $20 bet is enough to mathematically ensure that anyone who gives me action is doing so incorrectly, even if they get my stack, while $15 is not.

Playing Against A Range

Staying with the same example, here's a wrinkle that I'm sure many of you would be pointing out if I didn't do so myself. When we make the smaller, $15 bet--the one that allows gutshots to call us profitably--we are hoping that gutshots are not the only hands that call us. So in the example above, when the turn comes an 8, and our opponent wants to play for stacks, we are hoping that our opponent has a range that includes 76 but also includes 98.

Anyone with 98 is, of course, making an absolutely terrible call against our hand. They're going to stack off drawing dead. That means inducing a call from 98 is MASSIVELY +EV for us. It is so +EV, in fact, that if we know a $15 bet leads to us getting stacks in against a range of {76, 98}, the EV from beating 98 will more than cancel out the negative EV of being behind 76. Because of how small our opponent's EV was with 76, this is even true when you account for the fact that our opponent will have 76 more often (if we include all combos it's 16 vs. 9). Based on this reasoning, some people would then argue that $15 is correct sizing.

But in order for this to be true, we still have to know two things that this argument doesn't speak to:

1. That our opponent really does call $15 with hands like middle or bottom pair, and not JUST the gutshots. The above argument, most of the time I see it on the forum, usually takes for granted that this is true.

2. That our opponent calls $15 with middle or bottom pair, but wouldn't call a bigger bet. Again, the above argument often takes for granted that this is true, usually for seemingly no reason. In this particular case, for example, the idea that we can know that our opponent would call $15 but not $20 with 98 or 65 strains credulity.

If our opponent would fold the hands we need him to call with for $15, OR if he would call a bigger bet with those hands, then the $15 bet cannot be correct, and the larger bet is better in both cases.

3. Adding Complexity

As I already said, the above was a very simple example. There are three obvious reasons why this was the case, and changing each of these reasons adds complexity to the bet sizing picture. They are:

1. We knew we had the best hand.
2. We could easily narrow down what draws we wanted to be targeting.
3. The stacks were shallow enough that it made sense to leverage our stack.

When We Could Be Beat

Let's say in the above example, instead of KK, we have KJ. So we have a hand where we would still like to make other hands pay to draw, but we could also now get called by a better hand, such as AK or KQ (or a set). Sometimes in cases like this, it could make sense to size down our bet in anticipation of trying not to value-cut ourselves. But also, sometimes it could make sense to just check. This is going to be dependent on reads a lot of the time--how often you are actually beat versus how much EV you get from sizing to target hands that you can still beat, either to try to induce a mistake or just to protect your hand. I don't want to make this about protection betting because that has been covered in other COTMs, so I'll end this subsection here.

Multiple Draws

Let's change the example so that we still have KK, but now it's the turn: K953 (and suppose the K is in our hand). And let's say we did bet $20 on the flop and got called, so the pot is now $70, and we have $255 behind. Let's also assume that our opponent has called the flop with a range consisting of all 1 pair hands (that he called preflop with) and all flopped gutshots (QJ/QT/JT/87/86/76).

Now we have to pick a turn sizing.

Let's start by imagining we bet $35, or half-pot. The first thing to notice is that this bet size prices out any of the flopped draws (gutshots/9x/5x) that didn't improve on the turn. Now that we're here, though, we don't particularly care about targeting those hands, because there are other hands we can get value from that will call a bet that prices out the longshots. In particular, we can get value from top pair (even though we block it) and from draws that did improve--hands like 76 (double gutter) or any hand with backdoor spades. (We also don't particularly care that much about targeting good hands like smaller sets or 53, because they're going to lose a lot of money to us almost no matter what size we choose.)

So now we have a range that we are targeting for value; but if we stick with the half-pot bet of $35, we run into a problem. Let's say our opponent calls this bet, and we correctly range him as having some kind of draw. We have just offered him 3:1 direct odds. Not only have we given our opponent correct pot odds with all of his better draws, but our opponent might recoup more in implied odds by leading certain rivers that we don't want to fold. For example, let's say the river is an 8, not completing the flush, and our opponent leads $105 into a pot of $140. If we call that bet and lose to 76, we've again given our opponent too high implied odds--6:1 on a double gutshot that was 4.5:1 to hit.

So just like in the simpler example, when we have uncertainty about whether we should fold a later street, we have to size up our bet to slash our opponent's implied odds on a call. This case is tougher than the other one, though, because in order to adhere to the principle of pricing out every possible draw even if we stack off on the river, we'd have to bet almost twice the pot ($135, to price out 76). Do we really want to do that? Many people would claim that the answer is "never", but in fact I personally believe that there is a place for overbetting in certain spots like this, which I'll discuss later. (I don't believe this is one, though I might plan ahead for the prevalence of turn spots like this by sizing up my flop bet.)

Even though we can sometimes tell when a bet is sized poorly, we still haven't answered the question: what is a good sizing here? This is actually extremely tough to answer--to the point that they don't even try to answer it in NLHT&P (they use a different example but they wave their hands at the end with regard to sizing). If it's too complex for them to definitively give an answer, I wouldn't dare try to do it myself. But the relevant factors are how often--and for how much--we will pay off a hand that rivers us, versus how often we might make extra money by inducing a bluff.

When The Stacks Are Deep

Going back to the flop example with KK, let's say that instead of $275 deep, we are now $675 deep, and the pot is still $30. In order to price out every possible draw while still leveraging our entire stack, we would need to make a big overbet! A pot-sized bet of $30 is actually not nearly enough anymore, just because of how much an opponent with a gutshot stands to win off us.

So what is the solution here? I don't think it's to start wantonly overbetting; instead, we simply have to be cognizant of the implied odds that we are offering when we choose our bet size, and sometimes that means not leveraging our whole stack.

For example, imagine we bet $25 on the flop now, and our opponent calls. The turn is an 8. We bet $50 into $80, and our opponent check-raises to $150. We call. So the pot is $380 and we have $500 behind. Imagine the river is a brick and our opponent bets $200. We call and get shown 76.

Who won the battle of mistakes? Our opponent called $25 on the flop and won 30+25+150+200 = 405. This is implied odds of 16.2:1. So it looks as if our opponent did--but also don't forget that our opponent had to dodge a river board pair! Let's pretend, very generously, that if the river pairs the board our opponent shuts down and loses nothing. In that case, our opponent would have lost an extra $150 instead of winning $405. So our opponent's EV on the $25 flop call was (and again this is being generous in subtle ways):

(41/45)(-25) + (4/45)(34/44)(405) + (4/45)(10/44)(-175)
~1.5

This is so close to zero that anything breaking in our favor would push us into +EV territory. If the river is an action-killing card and our opponent still has us beat but feels the need to size down the river bet, we gain. If our opponent loses a river bet on a board pair, we gain. It's hard to argue we don't win the battle of mistakes here--but the reason is because we managed the pot size and smothered our opponent's implied odds.

I feel this is an extremely important part of playing deep, and it's also, as with the other example, so complex that I don't want to end this section with a definitive conclusion about what to do. You just have to plan ahead to try not to put in big bets with a second-best hand--but also try to ensure that when you do, the bets you put in aren't so big that they justify your opponent trying to draw out on you earlier in the hand.

4. Special Cases

Because this is such an overarching concept, I thought it might help to talk about specific sub-cases of it.

Preflop Raising and SPR

Let's say you're playing 1/3 and the effective stacks are $200. Imagine that you open-raise to $25 with AA and get one caller.

That player has called your raise getting 8:1 stack odds. If that player has a pocket pair, he is getting insufficient odds to set mine. If he has anything else, he's in even worse shape. What that means, in line with the above concept, is that you can commit your entire stack postflop, and even when you are beat, you are still winning the battle of mistakes, because your opponent's preflop call is a bigger mistake than any you could make postflop (other than a folding mistake).

The entire concept of SPR is based around this idea. To say that we have offered our opponent 8:1 stack odds, or to say that we have gotten heads-up with an SPR of 3.5, is mathematically the same thing. If you are familiar with the SPR "thresholds" for when it is OK to commit your stack with a good one pair hand, this is exactly the mathematical underpinnings of that.

One thing that is important about using the SPR numbers, though, is that they are only meant for heads-up situations, i.e. where we get one caller preflop. If we raise to $10 preflop and get 4 callers with our AA, now it is much riskier to commit our stack, even though the SPR is still under 4, because we have offered much higher stack odds to each opponent.

Overbetting

In general, when we're trying to extract value from flopped draws, a pot-sized bet offering 2:1 is good enough to make sure that any draw that is behind is getting incorrect direct odds to call. For that reason, many players will never size their postflop value bets larger than pot-sized, unless it is the river and they are trying exploit someone's inelastic calling range. (The original COTM on overbetting had many examples of this, so I won't talk about that here.)

However, if we have a good hand on a wet board, the direct odds don't matter as much as the implied odds we offer. Furthermore, in accordance with the concept that we want to size up our bet when our opponent can have multiple draws, this can sometimes mean that it can be correct to bet more than the pot, offering extremely slim direct odds and smaller-than-usual implied odds.

Here's one example hand that illustrates several different points about bet sizing. It's one where I decided to employ an overbet on the flop, and unlike my other examples, this is from real life. I was playing 2/5 with a $930 stack, picked up KK UTG, and raised to $30. I got 5 callers, so we went to the flop 6 ways with a pot of $180. Most of the callers had me covered, though one or two were playing significantly shorter than I was.

The flop came K63. I was first to act on the flop. Here are some of the things I was considering when I chose my bet size:

1. There are many draws possible. Flush draws are likely to be out, they might be combo draws, and there's also a chance of 54.

2. Because this pot is 6 ways, if I make a "standard" bet, one caller might encourage someone else to call. For example, let's say I bet $100. If one player calls with Kx, the next player is getting good odds to call with many draws. And with top set, I will likely lose future bets if a draw hits on the turn.

3. Making a bet that scares off Kx is less of a concern when I hold two of the kings.

So ultimately, the sizing I decided on here was $240. It's a 1 1/3-pot overbet, offering immediate odds of 1.75:1 for the first caller and 2.75:1 for a possible second caller. But more importantly, I only leave $660 in my stack for the turn and river betting. If one person calls the $240, I have a pot-sized bet left on the turn, and have offered stack odds of 1080:240, or 4.5:1, on a flop call. I can jam any turn here and almost certainly not have to worry about losing the battle of mistakes.

Now, lest any of you think that the overbet "clearly loses me action", the action behind me went: the guy on my left who had me covered shoved over my overbet with a nut flush draw, and then a short stack with 66 cold-called behind. The latter action was obviously a bit of a cooler, but I did induce a shove from a hand that was quite a bit behind!

This is all to say that overbetting isn't just for protection. Sometimes you can induce mistakes, if you trust your opponents to make some. You shouldn't artificially put a floor on the odds you offer your opponents, just because you don't want to bet more than the pot.

5. Conclusion

Bet sizing is probably the most complex topic in no limit, so the above barely scratches the surface. In fact, I'd like to end this COTM by talking about one aspect of bet sizing that I have seen used by others that still makes very little sense to me: the idea that it's OK, and even good, to make small bets offering very good odds on certain boards.

Obviously sometimes it is OK to size your bets smaller. For example, on a K77rb flop, there are no real draws, so none of the above concepts apply. Betting small here is probably fine (depending on reads and on what your hand is).

But I have sometimes seen people bet as small as one-quarter pot on boards where there really are draws that they're giving good odds to. I see people advocating these things on the forum pretty frequently these days as well.

So I would like to conclude by asking someone who is familiar with the theory behind why this is supposed to be good to join the discussion. It would be a good companion to the ideas I've laid out--the theory behind when and why to size up your bets to put drawing hands in lose-lose situations.
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Old 02-08-2019, 09:31 PM   #2
Garick
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Re: COTM: Bet Sizing (Revisited)

Thank you for reviving the COTM!
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Old 02-09-2019, 09:10 PM   #3
browni3141
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Re: COTM: Bet Sizing (Revisited)

CMV, I think the vast majority of players think way too much about the draw parts of villain ranges, when in fact draws are usually a small part of a villain's range. It's not necessary to be so concerned with forcing villain's to make mistake with draws. Also, of course villain's draws are going to be profitable when we have a super strong hand, but we have a range too, and that entire range isn't going to the felt when a villain hits their gutshot.

Bet sizing is best determined with range vs. range thinking. It's very difficult to guess how villain's are going to react to slight changes in bet sizing.

Quote:
Originally Posted by KT_Purple View Post
Optimum sizing should offer villain 0ev. Using the kelley criterion you will find that the optimum sizing ranges from 40-60% of pot depending on flop texture, position, villains range, blockers, your range and maybe some other stuff I can't think of right now. It's more of an art form than a science.

one thing that's interesting about it is that in a vacuum, you can raise 35% of the time opening from the button, c-bet the flop 60% of the time to 60% of the pot and guarantee you break even without ever looking at your cards

this is the only spot that's quantifiable because once you get to 4 hands it becomes increasingly complex and untractable mathematically, but you can learn a lot from studying the simplest and idealized cases
You are just throwing out buzzwords. Do you even know what the "Kelly Criterion" means?
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Old 02-10-2019, 02:09 AM   #4
johnnyBuz
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Re: COTM: Bet Sizing (Revisited)

Brownie the OP is pretty clearly from the perspective of betting with a made hand that is presumably best at the time. Vernon also said he’s not covering bluffing/semi-bluffing so range vs. range doesn’t apply here.

If you want to dig deeper start from the assumption of [your made hand] vs. [v’s range].
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Old 02-10-2019, 03:05 AM   #5
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Re: COTM: Bet Sizing (Revisited)

Quote:
Originally Posted by johnnyBuz View Post
Brownie the OP is pretty clearly from the perspective of betting with a made hand that is presumably best at the time. Vernon also said he’s not covering bluffing/semi-bluffing so range vs. range doesn’t apply here.

If you want to dig deeper start from the assumption of [your made hand] vs. [v’s range].
I don't think that thinking about our hand in isolation instead of how our hand fits into our range is an effective way to think about poker. Maximizing our EV in this case relies very heavily on how well we understand villain's responses to various bet sizes.

Hand vs. range based thinking leads to all kinds of errors, especially with bet-sizing. We are extremely unimaginative with bet-sizing and take lines that contradict each other all the time. For example, let's say we have KK on the BU and iso some limpers, and get called by an ABC villain in MP. We arrive at the river after having bet 3/4 twice on a runout of Q9722 with 2x pot behind. Many people are not shoving here because villain never has better than top pair, but how can villain call such a large bet with only top pair? The contradiction is that none of those people are bluffing all-in either (villains don't like to fold top pair!) Thinking about our range solves problems like this. After all draws brick and not being check-raised villain is capped at maybe KQ. All of our river value bets beat KQ, so we're betting a polarized range vs. a capped range, and all-in is the best sizing. We should start with range vs. range and make conscious adjustments with specific hands from there. Knowing our own hand actually introduces a huge amount of bias into our thought process.

However, that's not really my beef with the OP. While he did mention playing against a range, the vast majority of the post is talking about the profitability of villain's draws, which shouldn't be the focus of our bet sizing.
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Old 02-10-2019, 01:37 PM   #6
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Re: COTM: Bet Sizing (Revisited)

I was initially thinking much along the same lines as Browni here. But are "range vs range" and "winning the battle of mistakes" mutually exclusive poker paradigms?

Either we're striving for balance or we're exploiting weaker opponents.

When aiming for balance most of us probably can't cope with balancing more than one betting range in any given situation. Therefore most of us are picking one bet size for our entire range in each situation.

What size do we choose though? My feeling is we should use whatever is optimal for our strongest hands for all the hands we choose to bet. That way we maximise our value on our strong hands, give little away and put maximum pressure on our opponents whenever we bet.

In that case OP's "winning the battle of mistakes" ideas are crucial to deciding on our bet sizing choices even when we're operating in the "range vs range" paradigm.

Is that right or am I not getting this?
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Old 02-10-2019, 02:06 PM   #7
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Re: COTM: Bet Sizing (Revisited)

This is not a good or useful cotm at all. There's pretty much nothing anyone coming up and trying to get better can learn from it or apply straight into practice. Probably not allowed to have this opinion though.
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Old 02-10-2019, 03:48 PM   #8
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Re: COTM: Bet Sizing (Revisited)

Quote:
Originally Posted by wait View Post
This is not a good or useful cotm at all. There's pretty much nothing anyone coming up and trying to get better can learn from it or apply straight into practice. Probably not allowed to have this opinion though.
It's for people who have never thought much about value bet sizing. We've all been there at some point. If you're a beginner, understanding the idea that you want to win the battle of mistakes is a nice place to start.
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Old 02-10-2019, 04:51 PM   #9
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Re: COTM: Bet Sizing (Revisited)

Analyzing bet sizing in a value-only vacuum is a major mistake. Bet sizing should *always* be about range v. range thinking.

This isn't necessarily about GTO, but some semblance of balance is useful even at 1/2. Especially in spots where Villains consistently make mistakes. Ex. c-betting certain flops at a small size w/ our entire range is massively +EV because Villain's consistently underdefend the backdoors and overcards they need to.

If you have any sort of regs in your game, or even play a longer session with the same people, you can't choose these ridiculous overbets where it's a mistake for V to call with *any* of their range. Learning to hand-read and fold your set when the V is screaming he hit a flush is much better.
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Old 02-10-2019, 05:06 PM   #10
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Re: COTM: Bet Sizing (Revisited)

My suggestion to those that are unhappy with this COTM is to write their own thoughts to how they would approach bet sizing in this COTM rather than say, "you're wrong or useless, you don't know what you're talking about." Use the existing examples or pick your own.

I will note that the OP assumes that the reader is familar with David Sklansky's "Theory of Poker" and Tommy Angelo's "Theory of Reciprocity."

Last edited by venice10; 02-11-2019 at 07:47 PM.
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Old 02-10-2019, 06:30 PM   #11
Garick
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Re: COTM: Bet Sizing (Revisited)

That is not even remotely close to true.

1) We are not trying to "price in" worse hands. We are trying to get value from them while giving them the false impression that they are priced in. This is the primary reason for betting.

2) Sometimes we are trying to get a better hand to fold. This is the second most common reason for betting

3) Sometimes we are trying to set a price, but this is usually not via blocking the ability of better hands to profitably raise, as they would always be able to if they knew that they were better hands. Instead these blocking bets are designed to be big enough that there are also made hands in our range, so that they don't induce, while also small enough for us to continue profitable with our non-made hands. This is the least common valid reason for betting, though it becomes more common if we are playing against Vs who can exploit.

Most importantly though, GTO is not the magic style that wins the most money. It is the (or a, more than one could exist) style that cannot be exploited. It is designed for defense. Most LLSNL Vs are highly exploitable, and we should be exploiting them as much as we can get away with.

KT_Purple, I've been on the fence for quite a while about whether you're confused about high-level strat or trolling in your references to it, but it's reached the point where it really doesn't make a functional difference. Please stop posting theory statements as though you know them cold and they are unassailable. You clearly don't, but our newer posters will not know when you are talking out of your nether regions. I expect a disclaimer like "from how I understand <Theory X>, here is how it would effect <topic of discussion>."
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Old 02-10-2019, 07:14 PM   #12
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Re: COTM: Bet Sizing (Revisited)

This COTM is centered around denying correct continuing odds when we have the nuts. It's great because these situations come up often.

I'll just add that bet sizing is also about setting up bet-fold situations where we don't have the nuts but have a strong hand that should nevertheless probably fold to a raise, e.g., AcAd on K-T-5cc. If we bet too small on flop and turn and get raised on a brick turn, V could very well be value-owning himself with AK and we'll need to call. Choosing a sizing that conveys enough strength to our opponents so that they will only raise extremely strong hands (sets or two pair) saves us money in these situations. So if we bet 1/3 pot on the flop and 2/3 pot ott and still get raised, we can more confidently fold our overpairs/good top pairs.

Thanks, Vernon!
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Old 02-11-2019, 05:18 AM   #13
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Re: COTM: Bet Sizing (Revisited)

I am only half way through the OP but just want to say thanks!
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Old 02-11-2019, 02:06 PM   #14
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Re: COTM: Bet Sizing (Revisited)

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Originally Posted by Ragequit99 View Post
I was initially thinking much along the same lines as Browni here. But are "range vs range" and "winning the battle of mistakes" mutually exclusive poker paradigms?

Either we're striving for balance or we're exploiting weaker opponents.

When aiming for balance most of us probably can't cope with balancing more than one betting range in any given situation. Therefore most of us are picking one bet size for our entire range in each situation.

What size do we choose though? My feeling is we should use whatever is optimal for our strongest hands for all the hands we choose to bet.
This is more or less exactly what I would have said as well.

A range is nothing more than a set of hands, and as such I would want to think about pieces of the whole picture to get a clearer idea of why I focused my OP on what I did.

When we want to bet in these kinds of situations, there are basically 3 things that could be happening:

1. We are bluffing or semi-bluffing, and we are trying to induce a fold. In that case, the optimal bet sizing is the smallest bet size that gets folds from the range we are targeting.

2. We are value betting a strong hand, trying to get value from a second-best hand. In that case, the optimal bet sizing is (usually) the largest that our opponent will call with the range we are targeting.

3. We are value betting a strong hand, trying to get value from a draw. In that case, the optimal bet sizing is (usually) the largest that our opponent will call with the draws we are targeting, OR the smallest that prices out the draws we are targeting, whichever is larger.

So here's the main point of laying it out like this. Out of all these three scenarios, only one of them--#3--suggests any sort of mathematical underpinnings to how to size a bet. The other two, while they are clearly valid in-game considerations, only suggest that bets should be sized based on your opponents' calling/folding tendencies. If we don't know them yet, or if we are trying to disguise our hand by betting all of our range at the same sizing, then the pricing-out consideration of #3 is the most obvious jumping-off point. It sets a floor for your bet sizing that you can use to stop yourself from being exploited (by drawing hands that are hoping to make up the price of their call after they hit).

And as browni alluded to upthread (albeit while trying to make a different point), if this process ever takes you to a sizing you don't want to use because you think it prices out a range you want to get called by, then it's better to add bluffs to your range at that sizing than it is to lower your sizing.
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Old 02-11-2019, 03:25 PM   #15
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Re: COTM: Bet Sizing (Revisited)

^ your no. 3 is an interesting point that I have never properly considered. Makes sense.

Further to your last point about adding bluffs rather than downsizing your bets - intuitively and in my experience I think that's absolutely right.

I've certainly had times where I've oscillated between a "big betting" style and a "small betting" style. Typically if I'm running bad I get to feeling most comfortable with the smaller sizings because I feel like I'm able to read my opponents a little better and get away from second best hands.

Trouble is I think that's often just a feeling - it's not actually true. What I think is actually happening is variance decreases with a small betting style but actually winrate is also decreased because I'm unable to bluff or value bet as effectively.

I think having this mathematical reason to bet bigger on the wetter boards is exactly the thing I need to stiffen my resolve and avoid playing too weak a style.

Certainly the players I see doing well and who I dislike playing against are those who bet bigger and bluff more (but not too much!). They put me under a lot of pressure and force me play more defensive and balanced when they're in the pot.
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Old 02-12-2019, 01:48 AM   #16
Badreg2017
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Re: COTM: Bet Sizing (Revisited)

Thank you for the write up. One criticism I want to offer:

It’s not really reasonable to say that we can measure how 86 played the hand by his implied odds against our exact holding. We happened to have one of the stronger hands we could have flopped. Him calling against our range as a whole is going to have less implied odds because we don’t usually flop this strong. This has important implications for our sizing. The way you measure the hand implies we should size based on our hand strength rather than our range on a given texture

I think sizing based on hand strength is ok in some games, but in more observant lineups it’s questioable.
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Old 02-12-2019, 02:00 AM   #17
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Re: COTM: Bet Sizing (Revisited)

From a theoretical perspective, an example using hand strength creates narrower results that are more suited for purpose of the topic. Using perception could easily derail readers' chain of thought, similar to how you are incorrectly focused on whether the implied odds is calculated correctly.

It isn't at all important whether correct implied odds were given proper consideration in his example.

What is important is that bet sizing mistakes can happen in scenarios in which H has a better hand and the sole purpose of the example was to illustrate such mistake.
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Old 02-14-2019, 01:14 PM   #18
CallMeVernon
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Re: COTM: Bet Sizing (Revisited)

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Originally Posted by Badreg2017 View Post
It’s not really reasonable to say that we can measure how 86 played the hand by his implied odds against our exact holding. We happened to have one of the stronger hands we could have flopped. Him calling against our range as a whole is going to have less implied odds because we don’t usually flop this strong. This has important implications for our sizing. The way you measure the hand implies we should size based on our hand strength rather than our range on a given texture
I don't think I'm implying this at all.

I don't think it is inconsistent to say that if we want to use one sizing for all of our range, it should be the sizing that is preferred by our strong hands. So on any given flop texture, we imagine we have a strong hand, size accordingly, and then, if we choose to go for balance, bet that size with any hand we want to bet with.

The thing is that when we are betting with the weak parts of our range--i.e. we would like to end the hand now--we are not quite as sensitive to sizing as when we are strong. It still matters how much we bet, but only in the sense that we're trying not to waste money when our bluff gets called. When our hand is strong enough to play for future bets, then it matters a lot more how big a mistake we are inducing (or whether we are inducing a mistake at all) with our sizing.
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Old 02-22-2019, 11:10 AM   #19
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Re: COTM: Bet Sizing (Revisited)

Any fans of the "down bet" (a c-bet that is smaller than our PF open was) care to explain the theory behind it? I don't get it at all.
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Old 02-22-2019, 12:30 PM   #20
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Re: COTM: Bet Sizing (Revisited)

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Any fans of the "down bet" (a c-bet that is smaller than our PF open was) care to explain the theory behind it? I don't get it at all.
Stupid in cash useful in tourneys. Only idiot regs do it in cash to try and look cool.
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Old 02-22-2019, 12:50 PM   #21
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Re: COTM: Bet Sizing (Revisited)

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Any fans of the "down bet" (a c-bet that is smaller than our PF open was) care to explain the theory behind it? I don't get it at all.
I haven't had time to actually read the rest of the thread, but just addressing this single point from my point of view...

I'm of the opinion (that not everyone shares, including yourself I believe) that there is pretty much no difference in calling frequency so long as our bet is considered "reasonable". So, with that in mind, we mostly should be leaning towards betsizes that accomplish our overall goal (with the exception being perhaps deviating if we're up against a good hand / betsize reader). Have a hand / small SPR / etc. that wants a big pot? Bet big. Have a hand / huge SPR / etc. that wants a small pot? Bet small (if we're betting). For me, it's really that simple (in the general case, with the usual "it depends" qualifications).

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Old 02-22-2019, 06:32 PM   #22
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Re: COTM: Bet Sizing (Revisited)

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Originally Posted by Garick View Post
Any fans of the "down bet" (a c-bet that is smaller than our PF open was) care to explain the theory behind it? I don't get it at all.
As a bluff, it minimizes the cost of a c-bet in spots where opponents have ranges that will have a difficult time continuing, or we can force the opponent to call with low equity hands when we have value. It's useful for value in spots where we have very few perceived bluffs or in spots where we have no perceived value when we bet small. A lot of people go bonkers when they face a 1/4-1/3 PSB.

This isn't a "c-bet," but another time I use it is when the primary reason for betting is equity denial. For example if I call a 3-bet IP pre and the flop is 772r, and the opponent checks. I am betting much of my range for 1/4 pot to deny equity to overcards and minimize loss when they're trapping an overpair.
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Old 02-22-2019, 06:59 PM   #23
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Re: COTM: Bet Sizing (Revisited)

Finally found some time (while at work at getting paid, lol) to get around to reading OP.

Thanks for taking the time Vernon. It's a daunting task / topic to attempt to cover and can be difficult to implement in the heat of battle. For better or worse, most of my bet sizing boils down to "small hand / small pot vs big hand / big pot" and commitment (whether I am, whether I want to be, what IO I'm offering my opponents if I plan to be, my plan from the start of the hand, etc.). My guess is that it is really difficult to be "optimal" (whatever that means) with regards to betsizing overall, and we just have to hope that we somehow come up with a strategy regarding betsizing that helps us make a lot fewer (and smaller) mistakes than the strategies our opponents are using.

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Old 02-22-2019, 07:29 PM   #24
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Re: COTM: Bet Sizing (Revisited)

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As a bluff, it minimizes the cost of a c-bet in spots where opponents have ranges that will have a difficult time continuing, or we can force the opponent to call with low equity hands when we have value.
But why will they have difficulty continuing? I you bet 1/4 pot, they only need 16.66% direct equity to continue. Even if they just have 2 overs to the board, they're not far from that on just the outs from the next card. Add in some chance of being good already, IOs, some floats, etc. and they should be in great shape to continue with just about anything.

I mean, I pretty much agree with wait here. It makes sense for tournaments, as the value of each chip goes up as you have fewer, but in cash a dollar chip is always worth exactly a dollar. I could perhaps be convinced, but not by the above.
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Old 02-23-2019, 06:13 PM   #25
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Re: COTM: Bet Sizing (Revisited)

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But why will they have difficulty continuing? I you bet 1/4 pot, they only need 16.66% direct equity to continue. Even if they just have 2 overs to the board, they're not far from that on just the outs from the next card. Add in some chance of being good already, IOs, some floats, etc. and they should be in great shape to continue with just about anything.

I mean, I pretty much agree with wait here. It makes sense for tournaments, as the value of each chip goes up as you have fewer, but in cash a dollar chip is always worth exactly a dollar. I could perhaps be convinced, but not by the above.
I'm not even convinced myself. These are just my thoughts on the subject, and possibly thoughts of others that I've remembered.

What about boards where there are not "two overs." Let's say we open UTG and get called by BB, and the flop is A22r. We c-bet 1/4 pot. How many hands is the opponent comfortable calling with? A 1/4 pot bet is clearly very profitable, although it is mostly due to the fact that we have a very big range advantage on this board and BB has very few strong hands. A larger bet would be very profitable as well, but it's a little easier to defend against a larger bet, IMO.
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