Lets assume a game of [0,1] with symmetrical ranges from 0-100 percentile.

Both players antes 1$ and oop can only check, bet or call. No check-raising is allowed. Only potsize bets are allowed.

There will be 3 streets of betting. (Similiar to HUNL with restricted rules)

As the button:

For the first round of betting, would you rather:

1) Bet the top x% of your hands and check back and fold the bottom y%.

2) Bet the top x% and bottom y% and check some z% in the middle and have a call/bet range on the 2. round.

3) Some more complex split, which likely will bet/check hands in all of x/y/z %

If anyone want to make an attempt at assigning actual numbers to each x/y/z etc. or would like to discuss splitting ranges with 3 rounds of betting left, then that would be awesome too.

Please give some reasoning for the choice you make though.

If you look at the flop in isolation, you would need a hand in the top 25% to valuebet, as oop will fold bottom 50% to a potsized bet.

Edit: A forum dedicated to poker theory would be great too.

Edit: OOP is forced to check the first round, button is only allowed to bet, check or call on any round. OOP can bet 2. round if button checks first round. OOP can bet 3. round if button checks second round or both of the first two rounds.