I'm sure this is a very complicated theory but I'm a bit confused on the concept of over betting. I realize if the opponent has a strong range and I have them beat it is a good time to overbet.

What about overbet bluffs etc.?

Any examples would be appreciated thanks

In theory overbetting is the way to put pressure on capped ranges (like in polar vs bluff catcher scenarios).

Overbetting also allows for a wider bluff range.

If you bet 3/4 pot then you can have 30% bluffs.

If you bet 2x pot then you can have 40% bluffs

The ideal situation when you have a range of nuts and air is to go all-in with a balanced range.

Only on the river if Villain hast "only" bluffcatcher and no traps

Close but a couple of important mistakes. The idea betsize if we are on the river, we have a range of only nuts or air, villain has almost no nuts, AND a significant portion of our range is air, is all in. If any of those factors are not true, the ideal betsize is a little more complicated, though it may still be a significant overbet

I'm not really sure overbetting has a place in theory, as in, if it can be proven that with GTO play there are actually postflop spots with high SPRs where we're overbetting pot.

In exploitative sense its real simple, if an opponent will never call or will always call a certain betsize it might be a good idea to overbet as either a bluff or value.

Back to thread: When you have good hand and villain doesnt, why wouldn't we want to be big?

But "pot" is an arbitrary descriptor. Sometimes the optimal bet size will be a fair bit less than the current pot size. Sometimes the optimal bet size is going to be 1.2x pot or 2.5x pot. (Claudico seemed to like shoving 17x pot with ten-five high, but Claudico gonna Claudico. )
It would actually be pretty weird if the optimal bet-size in a particular situation happened to be exactly the size of the current pot. I think we commonly use that sizing in practice because it's reasonably close to what's likely to be good, it makes EV calcs fairly simple, and it's very easy to remember.

basically everywhere where you can represent the nuts. you may overbet raise vs cbet, overbet cbet and even overbet preflop if you think the villain's range is too weak.

How would overbetting be superior to a standard pot sized bet to pressure a capped range?

I wasn't trying suggest pot-sizing is somehow connected to GTO play just that somewhere around there seems like a reasonable upper limit to what a GTO strategy would be betting. Typically against better players it seems like bet-sizing gets reduced. You can't just jam for value knowing you'll get a call and you can't just jam as bluffs in spots where "he never has it" because against good players they sometimes do. I'm sure there are spots where 1.5 pot-allin is optimal or so, but I really don't take it for granted that there are spots much beyond that which are actually a part of GTO play, especially 17x pot sizing. I'm not sure if there's a way to actually prove that there are besides solving NL holdem which the best bots still haven't done.

One spot where it's mathematically correct to over bet the pot is when you have best hand vs 15 outs on the turn. Betting less than the pot gives the draw the right price to call.

On top of that, with a call on a very wet board, you may need to make some calls when some draws complete on the river. Therefore they may have implied odds on top of the pot odds.

To prevent this problem you may need to just shove all in for a large over bet if your committed to calling all-in on a dangerous river card anyways.

River betting is quite a bit different since the person facing a bet is in a situation where a good portion of their calling range relies on pot odds dictated by their actual holding and not their entire range.

Although you still are putting pressure on a range OTR, it's different from applying pressure on a range on previous streets.

In theory, a river bet size is a exploitive adjustment, since balanced betting Vs mdf calling ranges any bet size will be will deliver the same EV if the range is balanced

Now to actually narrow down to the point where you want to have different bet sizes on the river, they would/should be dictated by blockers and card removal.

Saying to overbet pot Vs capped ranges is an adjustment you make Vs a specific opponent and isn't necessarily relevant.

From the reading I've done recently (Expert Heads up NLH Optimal and Exploitative Strategies volumes one and two and TMOP) it seems to me that the optimal bet size in a "polar vs bluff catcher" scenario would almost always be all in on the river.

If villain has no traps and no nutted value hands and we have a polarized range of the nuts and air then our optimal river bet size would be all-in for any reasonable/realistic SPR.

Using a large bet size allows us to put more of our air into a balanced range and, even though any bet size might be correct based on the range of hands we decide to bet, we are able to add more bluffs to our range by using an over bet (and keep villain's bluff catchers "indifferent" between calling and folding.)

If we start our betting on earlier streets then the best bet sizing in a pure polar vs bluff catcher scenario is going to be whatever bet size allows us to go all in on the river and keep the same relative sizing on every street.

In other words, if we have a polarized range vs a range of all show down value type hands, then we would want to bet pot on the flop pot on the turn and pot on the river if the last pot sized bet would be exactly all-in.
If stacks are such that we would need to bet 1.5x pot on the turn and the river to keep us 1.5x pot behind for the river jam then that would be the best sizing to use in these PvBC situations.

At least that is my understanding and does seem to make sense based on the indifference principal.

I didn't read the book but this doesn't make much sense to me based on frequency. If your trying to balance river nuted hands with air, there should be fewer bluffs, not more.

Holding the nuts occurs too infrequently so trying to represent the nuts too often will just attract more hero calls.

If I were Trying to do this, I might want to add some mix of thin value bets to pick off those hero calls, not increasing my bluffing frequency.

It seems to be more of an exploitative strategy rather than some kind of GTO spot.

The equity our opponent needs to call a larger bet increases compared to a smaller bet, therefore, we can incorporate more bluffs relative to our value range and still make our opponent indifferent. They pay more to our value hands which allows us to incorporate a few more bluffs.

It only works in nuts/air vs bluffcatchers, but it is sound in theory.

I could understand this for some polarized ranges such as strong hand/air or even monster/air.

But for balancing the nuts with air, it's hard to imagine any bluff where the equity doesn't already favor a call regardless of the bet/pot ratio.

For example, nuts on a paired board is only 1 combo for quads or 6 combos for nut FH if the high card is paired, nut flush only has 9 combos if no st8flush is possible and opponent isn't holding a blocker, at best a nut straight hand contains 16 combos with no blocker in opponents hand.

Therefore picking only one hand as a bluff can at worst make calling equity 50% and the indifference point would require a 0 sized pot.

I understand that river bluffs aren't really about picking a specific hand to bluff with but some percentage to hit an indifference point. But my point is trying to balance any bluffs with just the nuts alone isn't a practical application, and trying to increase bluffing opportunities to rep only the nuts makes even less sense.

Thanks I see where I misinterpreted your meaning. Thanks.

If your opponent only has bluff catchers all your strong hands are the nuts DUCY?

If your opponent is suspicious and stubborn, overbet for value.

If your opponent is meek and timid, overbet as a bluff.

from the exploitative point of view u want to bet big for value against inelastic ranges (oppoents)

No, the nuts are always the best possible hand on any street. They have an absolute value regardless of an opponents hand or range.

Bluff Catchers on the other hand may be relative to an opponents range and is any hand that can only beat a bluff. Therefore, sometimes even a strong hand can be considered a bluff catcher.

Example: Facing a bet on a four flush board that is representing a polarized range of flush or air then even top two pair can be considered a bluff catcher.

Yes, that is the literal definition of "the nuts", but the mistake you've been consistently making in every one of your posts is not realising that nobody else in this thread is using that definition because in the case we're all talking about (polar versus bluffcatchers) every strong hand is exactly as strong as the nuts i.e. it has the same equity as the nuts versus villain's range.

When people are talking about balancing nuts with air in PvBC, they aren't talking about balancing the single strongest possible hand. They are talking about balancing the part of their range which is stronger than all of villain's hands (which we refer to as "the nuts").

Ok if your talking about a hand range that appears to be ahead of villains "capped range" as being "the nuts" such as TPGK+ on boards where villain would have played TPGK+ for two bets instead of only one on the flop or turn.

So then you start shoving a pol. TPGK+/air range on the river for 90BB into a 10-15 BB pot.

Opponents probably will concede some extra hands to your bluffs. But then they will also be playing their monsters as a weak capped range and letting you pay them off for the max with a 9xP shove on the river.

If you say you'll be adjusting to avoid this, than that huge over-bet shove isn't for finding a GTO indifference point but more like a one-off and not worth discussing.

You'd be far better off discussing only the real nuts for massive over bets on the river as you not making as big a mistake and not nearly as often.

Perhaps by just calling good hands the nuts, you were creating a false axiom that allowed you to throw out risk reward?

The reason PvBC gets talked about a lot is because it's very easy to solve computationally, and in the stric PvBC case you do literally want to shove regardless of the stack-to-pot ratio. As it happens it's not that much harder to solve a nearly PvBC case where villain includes some slowplays, and in this case the optimal betsize still ends up being a very large overbet (at least in the 1-street case). For example, in the case where 5% of villain's range is traps, the optimal betsize for the polay player is still between 3 and 4 times the pot, which is a huge overbet compared to what most people consider "standard" sizing.