When is simplifying actually simplifying?

I just thought range betting to 1/2 would be another simplification, probably higher ev than range betting 1/3 or 3/4.

But don't these two sizes no checking range spots play on similar complexity to those where we have a single bet size but also a checking range?

That's like the main thing that made me think more on this, maybe reasonable spots to play two size strategies even for those who prefer simpler strategies? (optional but similar in complexity to one size and a check range).

SB vs BTN?

Sorry, yes. Typo.

SB vs BTN.

I think any of the options are viable, could run myself and post EVs.

1. Many flop sizings

2. 30% SB size

3. 50% SB size

4. 100% SB size

can post sometime later

Perfect interested to check the results : )

1. Many size EV OOP = 129.17 (ran to 0.0674% exploitability)

2. 30% size EV OOP = 127.05 (ran to 0.0722% exploitability)

3. 50% size EV OOP = 129.14 (ran to 0.0565% exploitability)

4. 100% size EV OOP = 127.26 (ran to 0.0757% exploitability)

Settings for all (only changes oop sizing)

With the constraints from above, the simplified sim with 50% sizing lost the lowest EV compared to the 3-sizing sim, because the 3-sizing sim highly prefers to just play a geometric sizing scheme with these constraints and 3e sizing scheme is ~53% pot which is very close to 50%.

Wow, so when given the option to multiple sizes the solver is picking 53% with everything?

In this sim, you are checking some (not range betting).

So some added complexity compared to 1/3 range betting, which is what I assume the solver did when you forced 1/3.

I guess if you forced range betting for 1/2, the EV loss of the extra betting would end up with something similar to range betting 1/3.

So the ev of betting all your range for 1/3 close to range betting all your range for 1/2 (not checking anything), that's a guess.

And I see both of these as a possible worth simplification (some ev loss for actual added simplicity).

The main point of my thread was that when presented with spots with no checking range and multiple bet sizes, one have to be careful to actually simplify, and not just change the strategy for less EV and the same complexity.

Because imagine if you picked the big size here and decided to now have a checking range. You would still be dealing with 2 ranges (bet big and check, compared to bet big and bet small), but with less EV for your strategy, and probably betting some hands that would rather bet another size, making it also less intuitive and actually harder to implement.

Does what I'm pointing make sense to you?

Thanks for the solutions! I definitively want to start working with custom solutions

Well, I think what you're saying is choosing between strategies of ~equal complexity you should choose the one with highest EV.

Exactly.

But a common trap I can think on the fly is thinking less sizes necesarily means more simple.

If you pay attention to checking ranges, that may not always be the case depending on what kind of "simplification" you are doing.

I know a lot of regs use one size per flop nowadays, and I don't know how most of them approach this always.

But I know of some others also using two sizes on the flop, so I think having check ranges in mind is useful to navigate this for whatever personal plan one may have.

If you simplify two sizes to one size but open up a checking range where there was none you end up kind of on the same spot of dificulty with less EV on theory.

Another example, having a range of 66% big bets, 33% small bets, no checking range, and deciding to play a single big size.

Are you betting all your hands for a big size? How much ev are you losing? Is it worth it for simplicity sake?

Or are you checking now some hands? Ending with still two ranges to balance, but less EV?

If thinking on playing two sizes on some flops, spots with no checking range seems to be the first logic pick in terms of simplicity of execution.

You would just need to remember those spots where you range bet for two sizes instead of one and this shouldn't be that harder to implement compared to playing a single bet size and check strategy you do on another spots.

Ofc it would still be harder to implement than a single bet size for 100% frequency, which is the easist one. But it will be also similar in simplicity to creating a checking range where there was none to simplify to a big size, while having a bigger EV.

In theory for being balanced and easy to implement, something like:

Betting range for a single size > one size and check = two sizes no check.

Having all this in mind could help you structure better strategies based on your personal preferences imo.

FWIW I would be looking at a check as a 0% bet.... so 0% bet and 66% bet is roughly the same as 33% bet and 66% bet (with no checks).

I understand what you're saying... it would come down to ease of implementation. Also, these EVs are assuming perfect play (from both oop and ip).

3size:

30%:

50%:

100%

Are these forced sizes betting 100% frequency of total (no checks)?

correct

Practicality kicks in way before this sort of consideration
Be practical, not theoretical

The 1/2 bet range looks very good compared to the one with checks.

Thanks for the responses and solutions!

Yes, I agree with this. Along with when evaluating EV losses you take a look at what the exploit strat looks like.

Instead of using a sim to evaluate the EV, think about what you are capable of and what your opponent's response will be, as you won't be facing a solver in real life. When I look at a spot like this, I look at pure strategies. It's clear vulnerable hands like QQ/JJ want to bet bigger to put the money in, and it's clear that hands like 9x and underpairs don't want to put the money in. When we have different parts of our ranges wanting to perform vastly different strategies, you can split the difference and go for a catch all size or start splitting it. There are pros and cons to both.

Option 1: Catchall

It isn't very efficient, but it makes the flop easier to play. The issue is that we are putting in more money with hands that don't want to put money in, and we aren't putting in enough with hands that don't. This may work itself out, as the population might slightly underfold, and there aren't obvious exploits that the villains can take vs us, because they won't know our full strategy. The issue comes on the turn where we have to split our range. Arriving with every combo to the turn makes them more difficult to play. So you are sacrificing future complexity to make the flop easier to play.

Option 2: Splits

This can be tricky, because someone paying attention could get a feel for what you are doing and craft exploits, as humans are bad at randomizing. You need to make sure you are mixing in some nutted hands in your smaller size, like the solver does, to keep both ranges protected. This does put in the appropriate amount of money for each hand in your range, but it is much more difficult to pull off correctly. It will make turns slightly easier to play, but you may run into issues where you have trouble keeping the hands in the small size properly protected and be open to easy exploits like the opponent overstabbing turns when you check.

Personally, I think the 50% half pot size would be the way to go, as the turn is going to be complex either way.