The game is 6max NLHE, although it doesn't matter I guess.

Probably a simple question, but in a perfect game theory approach, should the number of hands you play preflop (let's just assume UTG to BTN) increase linearly according to your position? Or should your range be more of a curve peaking at the button?

I probaly explained myself badly so I'm basically asking the difference between:

UTG: playing 20% of hands
MP: 25%
CO: 30%
BTN: 35%

or

UTG: 20%
MP: 23%
CO: 28%
BTN: 35%

I ask because I was thinking about my preflop range recently and noticed I, along with a lot of good players play a lot more like the 2nd example, perhaps even more skewed towards button.

Is positional advantage linear or a curve peaking at the button?

Yeah, thanks for summing up my rambling in one easy line

Wow freaky. About half way through game theory last semister this exact same idea occured to me. I assumed its an upward curve because you open with the goal of taking the blinds, and each position you get closer to the button you face a non-linear percentage decrease in opponents.

From UTG to UTG +1 you go from 5 to 4 opponents, so you have 20% fewer opponents. From the CO to button you go from 3 to 2 opponents so you have 33% fewer opponents.

I think this is most visible full ring, when comparing UTG and UTG+1 to CO and button. From UTG and UTG+1 your opening range is probably almost identical, but from CO and button I think its best to loosen up considerably.

definitely a curve peaking at the button

it's, like, (utility of button in (0,1)) ^ (number of opponents) where you make up the first bit depending on stuff.

its #2 fyi.

Sweet, I'd never have expected a reply from you in here. Thanks.

yea its a curve at the button, i cant prove this mathematically tho cuz its a waste of my time.