reason why we want to bet big/ overbet vs cap range?

say BU raise vs BB call, or UTG vs BU flat, flop come AK2,

I see some advice say, you should make a big bet or overbet, because ur opponent range is cap, but why tho?

why not a 1/3 cbet just work fine? so u can bluff cheap

Thanks

I'm not really sure about specific spots (play a super different game), but the idea is to exert more pressure on the range. A capped range won't struggle as much vs a 1/3 pot bet as vs a pot bet. Especially on later streets, it's easy to take a hand like second pair and call an underbet on the river but much tougher facing an overbet. In some spots (especially if someone is capped to ~TPMK) a big bet can fold out near 100% of someone's range while they'll still have a fair number of calls vs the small bet. Plus, when they do call, your vbets can make a lot of money.

Bluffing cheap is good in a lot of spots too, though. These should both be tools you use to make money.

Funnily enough, I c-bet 2x pot with QJ on AK2r about half an hour ago. (BOOM link).

The theory is that when you bet big, it means villain has to fold more often, which means you can put more bluffs in your range to balance the nutted part, and thus threaten to play for stacks on the turn and river if villain calls on the flop. It's really hard for villain to call down with Ax (let alone his gutshots) if you bomb flop and turn on AK2x, because you could be taking him to valuetown with AA/KK/AK (none of which are in his range).
If you bet small, villain doesn't fold so often, so your bluffs don't work so well.

Theory is often different to reality though. Against weaker opponents, you can often "get away with" bluffing for smaller sizes on the drier boards, especially as they won't check-raise you very often.

P.S. Using multiple sizes in a "GTO-ish" style doesn't massively increase your EV. There are plenty of winning players that hardly ever overbet. And a good player could probably beat 5NL if he was forced to use half pot and no other size. It's more important to get your range correct to fit whatever size you're using. Usually, this means you can bet small at a high frequency, or large at a low frequency, but in some spots (especially in 3-bet pots OOP), it's sometimes the other way around (i.e. you'd bet large at a high frequency to make villain fold underpairs, for instance).

I wouldn't get too focused on trying to develop an overbetting strat if you're a beginner. It's more important to just make sure you're betting hands that make sense as bets, and checking hands that do better as checks. "Optimal sizing" is a bit more advanced.

from a theoretical standpoint, if you're nutted and villain is capped, you want to bet to grow the pot geometrically and be all-in by the end.

it allows you to bet (and bluff) the most, maximizing your profit

Not sure what this means, exactly, but it seems wrong. You bet less often, but bigger.

the way of thinking presented in OP is very outdated and, frankly, wrong. There is no such thing as capped range, only a range that is weak in comparison to some other range - and in this case, you want to bet smaller, not bigger, into the player with range disadvantage

e: I guess I kinda understand where this misconception comes from: it is correct to incorporate some huge bets with extremely polarised range into your strategy. In this case, your opponents range essentially becomes all bluffcatchers (since you either have the nuts/close to nuts or nothing), thus giving a perception of "capped" range. In reality, those bets are simply very low frequency events, except for some extremely polarizing boards (like double paired or 4 flush), which are not generally representative for how overall range building works.

I know this sounds a little rambly, so let me give an analogy - when the board changes on turn or river in a way that vastly favours your opponents range (for example, you cbet polarized flop strategy and middle card pairs on the turn hu), you should generally avoid bluffing - but you should do it SOMETIMES, using large sizings. This doesn't change the fact, that you shouldn't be bluffing much when at range disadvantage, same way you shouldn't bet big with range advantage.

I read this as 'If you oversize bet both your bluffs and value, you maximize the size of bets that a villain will call light with'.

This is definitely not true, at least in hu hypers where bet/big bet/jam is a very common theoretical line on a variety of runouts. In 100bb deep play I guess you're worried about being overexposed ott and so may prefer generally smaller sizes, but in shallower play it's frequently totally standard for the double barrel and triple barrel sizes to be large.

The one thing I agree with here is that you shouldn't bluff too much when at a range disadvantage

Oh, could be. I had read it as "highest frequency" and was pretty confused.

Let's have some fun with numbers:

bluffcatching ev is a function of (%bluffs in opponent's range * %frequency of showdown * pot) = bluffcatching ev.

The more bluffcatchers in the opponent's range, the more often you can put him to the test with a near 0 ev call. This is how the math works:

I call a $100 bet in a $50 pot on the river = 40% investment = I need to win 40% of the time to at least break even, otherwise it's a bad call. My ev vs a good player will be near break even on my call, so where does the rest of the pot go if I have nothing but bluffcatchers in my range? It goes into my opponent's stack, as he has claimed (% of the $50 pot) = [1 - (% of my range that can beat some value hands * avg ev of those hands)]

The fewer hands that I hold which could beat a portion of my opponent's value hands, the higher this % pot claimed by the opponent is. If I have nothing but bluffcatchers, my opponent's ev becomes (pot).

How does this work on the flop or turn? Well when you're on the flop, showdown is pretty far away, thus you will hold a decent number of hands that can potentially beat a bluff or draw, but should be folded on the flop because the draw value isn't there. On the turn, you're a step closer to showdown, but you should still have some decent combination of (showdown value + draw value) to call any substantial bet.

The effect is that we get to the river, hopefully by making +ev decisions, with enough hands that can call overbets that our opponent can't bet too big or he starts losing money.

From there, I suggest looking into the ev of simple (0,1) games and the effect of river betsizing on the % of the pot that the bettor may win with a strong range(hint: river poker is the most asymmetric portion of the game, and as such it results in asymmetric pot distribution, usually favoring the player that put in the last aggressive action on a previous round of betting, and increasing further if that player chooses to bet again).

you could look at the river-only case first.

if you're on the river with either nuts or air, and villain is capped to bluff catchers,

the optimal bet sizing is simply all-in, and you bluff the right frequency to make villain indifferent to bluff catching.

***

before the river, the "geometric growth of pot" bet sizing is analogous to the river-only all-in.

the idea isn't to bluff cheaply, but to get it all-in with the nuts and make the most money.


***

in real situations, ranges aren't so polarized, but this is the theoretical reason to bet big when you're nutted and villain is capped.

Thanks for all the reply above, thanks Arty! haha, funny you actually provide a real example

I got more confuse reading all the reply lol I guess I just half pot, 2/3 all the way

thanks for the reply! this is a bit confuse me, there is some board where
your opponent is cap? like BTN vs BB on AK2, BB can't have AA KK AK AQ.
Arty just provide a example he overbet QJs on AK2, so u think its a mistake?

If we have range advantage we want to bet small? Can you explain a little why?

Thanks!

Sometimes it's just the case that you have lots of "thin value" hands that can get paid by worse if you bet small and get called. (Betting big produces more fold equity, so you often only want to do it if villain only calls infrequently, and your value range gets more from being called than it would if it went smaller).

I liken the concept to the idea of choosing the "max EV" size for the river. Suppose you had the stone cold nuts and the pot is $100.
Suppose that if you bet $200 (2x pot), villain will call 30% of the time.
As well as getting the $100 pot (which you'd win if you checked back), you're winning an extra $200 30% of the time. 30% of $200 is $60.

Now suppose that you bet $100 (1 x pot), and villain calls this bet 50% of the time. Since 50% of $100 is only $50, this option is not as profitable as overbetting. (You'd literally rather villain call $200 thirty percent of the time, than $100 fifty percent of the time).
If villain would instead call the $100 65% of the time, then now your additional profit goes to $65, and the smaller size nets you greater value, so that would be the better size to use.

Naturally, you have to balance your value-bets with your bluffs. Since betting big means your bluffs will work more often, and makes them at least breakeven, you sometimes want to bet big, to push more of your air hands through.
In spots where you have lots of thin value hands, that will do better by betting small, instead of betting large (when they won't get called by worse) or checking back (no additional value), a smaller size (and a lower proportion of bluffs) makes sense.
Unfortunately, it's not always easy to tell how thinly you should value-bet, or how big you can go before you're value-cutting yourself.
There are definitely spots on the river*, however, where your range has lots of top pair type hands that can get called by worse if they bet about 1/3 pot, but that can't get called by worse if they go much bigger. It's only really in the spots where you're much more polarized (to nuts or air) that overbetting is appropriate.

* It can also happen as a c-bet in a 3-bet or 4-bet pot, where betting small with a range advantage "forces" villain to call with very weak hands. If betting small gets called by worse often, while betting big makes villain fold "too often", then betting small with a range advantage makes sense.

To some extent, the "optimal sizing" thing also applies pre-flop. It would be lovely if every time you had AA, you could open jam 100bb and get called by worse. Unfortunately, that doesn't happen. You have to choose a size that gets called by worse often enough to make that size "perfect" for AA, but the size also needs to be "optimal" for the weaker parts of your range. It turns out that the optimal size pre-flop (in cash games) is somewhere between minraising and 3.5bb. (In a tournament, there are spots where jamming 25bb with certain parts of your range might be optimal)
Post-flop, an optimal size for your range clearly depends on the board and the situation, but it might be anything from quarter pot or 5x pot (or more), depending on how the ranges interact and how much the sizing alters the frequency of villain's calls and folds.

in your example, BB should be flatting all those hands sometimes. Balanced player can have all hands at all times, though at different frequencies. The only "cap" I can think of is simply not having certain hands in your opening range, like if you open UTG in 6max you cant flop a straight on 467 board.

As for why we want to bet small with range advantage, it's very simple, "GTO" betsizings should make your opponent indifferent between calling and folding, if they have a weak range they will be indifferent to small sizings, versus large sizings they should simply be folding.

Because of that I disagree with most above posts, you are all describing some situation-specific exploits or low frequency events, rather than theory behind betsizing.

What does "cap range" mean?

A capped range is one that can't include the nuts.
e.g. If you open BTN and BB just calls, he's highly unlikely to have AA (which should be 3-bet). Indeed, if the BB always 3-bets TT+ and AK, then his range is "capped" at 99, since that is the strongest hand in his flatting range. On a flop of AK2, he can't have AA, KK or AK. He is 'capped' at bottom set. It's often quite useful to know what the top of villain's range is (i.e. where he is capped), because then you can work out which hands in your range are 'always' winning and are tantamount to the nuts.

Didnt read all replies so not sure if this has been explained already.

You can explain this by a simple math example.


OTR 2x pot left we are IP and have the nuts, ignoring all blocking effects etc.

By betting pot V needs to call 50% so our EV is 1.5 pot
By betting 2x pot V needs to call 33% so our EV is 1.66 pot


In most cases this is just plain wrong.



On turns and even more so on flops things just get really complicated as the amount of factors needed to take into account just skyrockets compared to simple river spots.