This is hypothetical, but it is interesting to think about.

What would happen to starting hand selection in a game where there are infinite stack sizes. Okay, since we can't really imagine that, let's deal with a number that is really big. How about 1,000,000,000BBs deep?

I would imagine that suited aces and pocket pairs would skyrocket in value. I believe there would be a very strong focus on never being capped in any spot. That makes me wonder if suited double gappers would need to be in all your preflop ranges. You would need a hand like 52s opening UTG to keep you from being capped on 43K8A runout. Maybe UTG range would be something like 22+, AQo+, A2s+, KTs+, Q9s+, J8s+, T7s+, 96s+, 85s+, 74s+, 63s+, 52s+, where the crappier stuff is usually folded, but opened at a very low frequency.

Would it ever make sense to 9-bet bluff, or would we need to flat before it reaches that?

Thoughts?

Yeah, we should mainly be playing hands with a good potential of becoming the nuts. Pocket pairs like 22 don't really have that potential though, unless the board is 22X.

About the 9-bet bluff... It depends on the 3-bet/4bet sizings that people would be using in this game. I assume the sizings should be very big in GTO.
If there's still a lot of money behind after the 8-bet, the 8-bet range definitely shouldn't only be AA since that would be very exploitable. Therefore, the 9-bet bluff range should still exist, and it should be very mixed with pretty much any hand that has a nut potential in it.

Also, position would be super important.

100% vpip

RFI in early position would scale down slightly and spread out over more hands

You'd play any two cards from any position. Since raises will be finite until someone goes all-in no amount of lost chips when you fold will make a dent in your stack.
When you reach the river you go all-in 50% of the time for value or 50% of the time as a bluff according to:
F=X/(2X+Y)
where F is your bluffing frequency
X is the amount of your shove (infinite)
and Y is the pot (less than infinite)

Though realistically once your bluff gets called and you lose an inifinite stack you can never regain it (since you cannot buy in again for an infinite size...because if you had that amount of money behind it would have been in your first infinite stack ...infinities are ... weird)

Under thiis terminal risk of ruin the game would effectively devolve into the model game from "Theory of Poker" where everyone folds everyting until they get dealt aces and then go all-in pre...which would only ever lead to grabbing the blinds or AA vs AA confrontations (and eventually someone winning with a flush)

(The 'play any two cards from any position' approach becomes mathematically correct a long time before infinite stacks, BTW)

A few things that I think infinity brings is the enormous weight the hands you will put inf in with can be only nut hands. Actually, I think the discussion can only mean something in this case. An inf bluff isn't a thing, it can't be in a game with inf stacks. The risk of being inf called by a single card is still is still 2% and that times negative inf is always -inf. I don't think any game theoretically sound plan can sustain a -inf.

One thing that might happen is all bets other than inf are so small they are approximated as checks. Ending in a draw where the only theory is Push fold and you just win the "checks" when you inf shove nuts. However when you both hold nuts, you chop. So the end result is just flipping for inf at exactly 50/50 where you basically check to river.

Chips are countable, what if infinite fractional bets were included. They are null by my above argument. But if so, there would be be Aleph1 bet sizes and Aleph null chips in play.

Fold every hand because gaining chips is not increasing our stack. i.e. x/inf=0 where x is any finite number. Fold infinitely.

This answer is both true and filled with memes. I like it. Fold pre.

Guys, April Fools is several months from now.

Wait for aces. Shove vs prior action. Play AT-AKo. Play Axs. Shove with nuts and nut flush blockers. EZ EZ game.

It's an interesting question. I would guess that optimal play wouldn't make use of the full stack after a certain depth, except maybe on boards where it is possible to fully block the nuts. The reason is that at a certain sizing, it will only be profitable to bet with the nuts because the opponent only needs to defend the nuts to not be exploited. If you can only bet the nuts profitably, then that sizing will clearly be suboptimal.

On a board where the nuts can be fully blocked, such as a 3-flush board, it would likely be optimal to size the river all-in with a balanced range of nuts and bluffs. The opponent has to call some non-nut hands since there are many more naked A blockers than nut flushes.

Maybe you can't go all in. If you have to say how many chips you are putting in, then you can't because infinity is not a number.

https://forumserver.twoplustwo.com/5...-deep-1403117/

I would guess there exists some stack depth where two GTO players will never find themselves all-in unless they have the same hand.

Why would you even sit down to play if you already have infinite money?

(If you play just for fun: Why would you risk your entire wealth in one game?)

If you have an infinite bankroll, obviously you only put 1% of infinity on the table.

Aaaah...but how do you count out 1% of an infinite amount

You just put one foot in front of the other. I mean 1% isn't that much.

is there an ante?