This may be too theoretical and abstract, but I'm interested in any theory or math around this,

Let's assume we have AA UTG, at 1/2, full ring, everyone has 500, and we have a fairly elastic bet-to-call supply-demand curve that looks like this:

If we raise to 8 UTG, we get 7 callers for an 83 dollar pot
If we raise to 10 UTG we get 5 callers for a 63 dollar pot
If we raise to 15 UTG we get 2 callers for a 48 dollar pot
If we raise 20 UTG we get 1 caller for a 43 dollar pot

Which one of these would you prefer? You could argue that you want to maximize pot size, but do you really want to be 8 ways with AA? Would it be different if you raised JTs UTG?

Obviously a lot would depend on the players, what you hold, how good you are post flop, their ranges etc. but hopefully you get the idea of what I'm asking for in a generic sense.

Reverse order is preferred. Kewl thread tho

Pot size isn't the primary variable, your EV in the pot is. Take your % equity * Pot size - that should allow you to solve for the ideal solution.

What you are asking is one of the most important questions in live poker. It is also what makes it much more complex than people realize.

Back when I was interested in poker theory I asked a variant of this question to several very strong poker minds with online backgrounds. They all gave different answers, most arrogant, a few insightful.

The 2 "best" players (imo) both agreed with what wait posted, as do I. Mainly bc of what twitch posted.

The answer does change with JTs. We'd prefer the small sizing given your parameters.

Yes, that makes sense.

I think I’m this particular example reverse order is best. Equity*pot size is a reasonable metric, although obviously not perfect.

I agree that a bigger raise and getting it HU is best, and with JTs a smaller raise and going multiway is great....but that's on paper. In real life if you raise bigger with big hands and smaller with speculative/multiway type hands, any good player will eat you alive.

I would always want to be HU because it's much easier to asses ranges and exploit players HU than it is multi-way. You don't make your money at low stakes live NL by coolering people with flush over straight or whatever you're hoping happens with JTss.

i agree with everyone else , I'll take the math any day over having more money in the pot,

The above comments about abstract math are correct. I'm just going to point out some of the problems with actually doing this math in practice.

Your equity changes with each street. You can only make a simple preflop equity calculation if you are shoving preflop. If you are shoving preflop with AA you want as much money in the pot as possible even if that means more callers. Your variance and equity will go up with each additional caller. When your shoving with AK you want 1 caller.

You can only estimate opponents calling ranges and how size changes those ranges. And those are not the same for all players, each one has their own curve. Plus this range calculation can not be done in isolation, each player is aware of the previous players and will adjust their range.

Worse, they are aware of previous hands and what betting occurred on those hands. If you bet small with big pairs and bet bigger with weaker hands somebody will notice eventually.

Years ago, I made a huge thread with a lot of debate on almost this exact topic. Here's what I remember from that thread.

The biggest problem with the answers above is that they are not taking into account the fact that we are $500 deep in a 1/2 game. If we are $200 deep, then sure, I agree that we would prefer the last option.

But when we get deep, it is unclear that we want the same thing. Now we may just have no preference. When I'm deep enough that I'm not happy putting my whole stack in play with 1 pair, but I can also get away from my hand before a significant portion of my stack is committed, then the smaller raise has more upside--a lot of people in the pot who might play with me if I flop top set.

Also, 8*8 = 64, so the pot size is not computed correctly on the first line.

Super interesting theory question, but would be much more practical if somehow accurately adjusted to average 1/2 games and stack sizes

As wait and twitch pointed out, EV is more important than just pot size.

Personally, I think its generally best to have an open size that results in 1 +/- 1 caller. So, you are usually getting 0, 1, or 2 callers.

Against 1 caller with top 50% range, AA is 85% to win and against 4 callers it drops to basically 50/50