possibly dumb, possibly interesting question that popped into my head and im curious for others thoughts:

lets say you are on the btn for 1 hand in a 6max nlhe game (so you wont have to play any of the other positions in later hands), and are given the option to choose how many blinds will be posted. the biggest blind will be 1bb no matter what, then each smaller blind will be half the size of the blind to its left. so, if you choose 4 blinds, they will be .125, .25, .5, and 1bb (starting from left of btn). action is otherwise normal, starting from left of the biggest blind preflop (CO acts first in my example) and left of btn postflop.

what is the optimal number of blinds for btn to choose in this game?

not looking for any specific type of answer, and ofc feel free to make any relevant assumptions (ie stack sizes, relative skill of players, etc) as you see fit

You mean for the other positions to post? It would be the maximum number where you are not forced to put in money.

yes, for the other positions to post

the reason i am skeptical of that answer is that we are giving up preflop position by forcing an additional player to post, so it seems like there is probably a blind amount small enough that it isnt worth it to us. for instance, if we are deciding whether to make the 5th player (CO) post, we are essentially creating a new smallest blind of 1/16bb, and we will now act first preflop with 5 players left to act (and only 1/16th of a bb in additional blind money in the pot).

I don't think that matters as much as forcing everyone else to put in money. You're in the best position and you can decide whether or not to put money in, which is just worth way more.

would your answer change if this was 9 handed so the additional blind was only 1/128th of a bb? it seems like the value of preflop position to the btn should have a value >0, and this line of thinking implies to me that it more or less rounds to 0. keep in mind that even if preflop position has zero value, some (most?) of the value of the additional smallest blind will accrue to the other blinds, who have improved their postflop position by having a new smallest blind (if you think of the example as CO moving to become the sb rather than posting the bb and others adjusting).

I don't think the answer is as many as possible, especially for 9-handed, but I have no idea how to attempt to find the answer.

No, my answer wouldn't change.

You'll definitely get diminishing returns.... but I'd imagine you still get returns. I guess I could be convinced otherwise, but my initial inclination was and still is, "as many as possible."

Wow, this is actually a great theory question!

I don't think it's the max either. At some point you'd effectively become UTG preflop. I imagine there's a very clear threshold where it's no longer worth adding another blind. I imagine how deep you are relative to the maximum blind would be a major factor. Rake probably also plays a big part.

If you're playing 9 handed, then the 8th blind would be putting in 1/128th of a blind, or 0.0078bb. I can't imagine it's worth giving up relative position pre to force such a small concession.

I have no idea what the actual answer is though. We could test this with a nodelocked preflop solver, but that seems like a ton of work and compute time.

I was going to say you could abstract it to just a push-fold game and compare/contrast, but I don't think that would work actually.

This would negate the fact that BTN gets position postflop, which is the underlying advantage of being on the button. But it answers a different question

Seriously though, if you had to take a guess, how many players do you think would maximize profit for the BTN? Assume 9-handed 100bb deep no rake.

I might even run this preflop sim (with a ton of abstraction) eventually.

1 blind: 1bb
2 blinds: 0.5bb
3 blinds: 0.25bb
4 blinds: 0.125bb
5 blinds: 0.065bb
6 blinds: 0.03125bb
7 blinds: 0.015625bb
8 blinds: 0.0078125bb

My guess will be the opposite. I'm guessing 1 blind (SB becomes BB in essence) would be the most profitable for the BTN. Fewer players will open because there's less money in the pot, so it folds to you in the BTN more often. You only have one player ahead of you instead of two. You maximize relative positional advantage preflop. And if you get a **** hand it still costs nothing to fold.

Minimum #

thanks! i think my guess would be 3, but i really dont know. im not sure i agree that fewer players would open with 1 blind (vs 2), since there are also fewer players in the blinds defending that money and there also will be 1 more player to act before us; i would guess players would generally be opening more often, but at a smaller size, except that the new utg (who was the bb in 2 blind format) would open less often than the utg player would have in 2 blind.

would be very interested to hear what you find if you do end up running the sim (but obv understand if you decide not to spend the time on this bizarre question)!

i do not think the answer is trivial. for example in this scenario:

would your answer change if this was 9 handed so the additional blind was only 1/128th of a bb?

I think it is clearly disadvantageous as that is one more player who acts behind you yet puts in what is effectively 0 money preflop. If there is still doubt, change the number to 1/1000000th of a bb. You gain nothing but lose a small bit of preflop positional advantage.

I know sometimes in actual poker the SB is busted or leaves during the hand so it's only 1 blind, do we know if that is better or worse than the standard setup? From just randomly guessing I'm inclined to think either 1 blind or 2 blinds is highest EV for the BTN.

I'd think somewhere in the middle 3-5.
We gain a "significant" amount of money in the pot which is worth sacrificing the pre-flop position for.

Clearly there's going to be a point where the EV of the position is going to outweigh the actual money being added in the pot.
Might be at 2 or 3, or it could be at 15, who knows

can we get plexiq to solve this somehow or would game trees be too large?

I recently learned that you're actually supposed to open tighter in straddled pots on the button. The straddle acts as an extra blind, and apparently, that outweighs the extra money in the pot.

So I'm still thinking that the minimum number of blinds would be the most profitable.

Well ****

missed this response - i agree with this

this is def a good question and would be interesting empirical evidence. one concern i would have it whether a change to btn ev was due to the other players incorrectly adjusting/not adjusting (ie other players do not open wider and it folds to btn too often)

its true that btn should open tighter vs 3 blinds, but i dont think that necessarily implies that its less profitable for btn. if btn was given the choice between 2 blinds posting 1/1 and 3 blinds posting 1/1/1, i think the 3 blind format would be better even though they still need to open tighter than in 2 blind. imo the diminishing blind size is what makes the question so tricky.

Yeah, I'm really glad you've raised this question @jvds. I guess I'm really uncertain as to what the answer is now.

You want the maximum number of blinds. Being in position after the flop more than makes up for being utg preflop. If you implemented limping as part of your strategy you could probably play close to 100% of your hands profitably.