Two experts are playing heads up PLO with unlimited stacks plus a wrinkle. One of the players has two known cards . Who is the favorite in each of these scenarios:

The two cards are two random aces.

The two cards are two black aces.

The two cards are two random kings

The two cards are two black kings.

With infinite stack sizes and how infrequently suits would play into it I would think the player with information about 2 of his opponent's cards would always be at an advantage even if the opponent only knows the ranks and not the suits.

If the random aces are faceup, how does that differ from having 2 black aces faceup?

oops. fixing it.

I am not a PLO expert but I think the player with exposed cards would be disadvantaged in every case. Really the only board where the AA player has a nut advantage will be Ax boards and non-paired flush boards. On all other boards it will be hard for AAxx to realize it’s showdown equity when it’s hard to have the nuts.

Similarly, in Holden with arbitrarily large stacks I think AA face up against random cards is losing assuming it’s not all in pre.

Neither is the favorite.

With infinite stacks, you can bet or call an infinite amount of money and still have an infinite amount of money left behind. If you lose, so what? If you win, so what? Both players will wind up with the same stacks as before regardless.

People who post questions about infinite stacks should be banned.

People who think infinity - infinity has to be equal infinity and act like they are smart should be banned and revisit school

Aces definitely lose in pot limit holdem. But they win easily in limit.

Consider the set of integers. This set can be divided into 2 infinite disjoint sets e.g. even numbers and odd numbers. These in turn can be divided in a similar fashion as well and so on, etc.

You can do the same with an infinite stack as well. You split it into 2 infinite sets of chips. Do all your betting and/or calling with just one of these sets and keep the other behind in case you lose. If you "win" nothing is really gained. If you "lose" nothing is really lost. You still have the remaining infinite set of chips.

People rely on their intuition to grok infinity, but unfortunately infinity is completely alien to the human experience. Even a relatively puny number like a billion is too much for a human to truly grok. So it should not be too surprising that people lead themselves astray when they talk about infinity.

Fine. But I only used the word "infinite" because I was too lazy to write "more than enough for any possible scenario against a rational opponent".

There would still be GTO play in the scenarios asked about, and therefore still an expectation for each player, which seems almost certain to me to be finite. I think the only time both players would want to keep raising are when each player end up having exactly 50% equity on any additional money put into the pot - e.g., both players have the nuts on the river. If it's not a 50% equity situation, then to infinitely keep raising, one of the players would necessarily be making a decision that is negative infinity in EV - and this cannot possibly be GTO because it is always possible to keep EV finite. Therefore I am almost certain an infinite betting line results in 0 EV for both players (though I think possibly infinite variance, which is a problem), and there is surely a way to work around this to have a working model of the game.

Anyway... IMO... A pot-limit game (or any other game limiting bets to a finite amount) is perfectly reasonable to consider with infinite stacks.

I think having face-up aces in position in PLO must almost certainly be +EV. We almost always have a hand strong enough to bluff-catch with. As long as we're not bluff-catching more than we're supposed to, I don't see how we'll possibly lose in the long run when aces have as much of an edge as they do vs a random hand.

The ability to threaten having the nuts is very important. It's very difficult to realize showdown equity on boards where it is very unlikely for AAxx to have the nuts, such as non-broadway/wheel straighty boards, flush boards of a suit the AAxx doesn't show, or really any other boards without an A. Meanwhile, we can threaten nutted hands on tons of boards and therefore bluff extremely aggressively. AAxx has a very hard time defending it's equity, getting value or bluffing because it can't really bet with a face-up hand effectively.

The GTO strategy for the random hand player likely involves lots of mixing, but generally a good strategy would be potting all our hands that beat AA and using our highest equity hands as bluffs, and giving up our worst hands will allow us to have something like a 4:1 (very rough guess) bluff:value ratio on the flop and there's not much AA can do about it but try to bluff-catch the combos that have slightly better equity or blockers to our value.

I'm thinking the random AA and KK would still be a favorite, but knowing the suits is too valuable making the black AA and KK an underdog.