Here the change I am suggesting:
Before any hands are dealt, expose two cards that will be out of play

My impression is that this would create only very modest changes in casual games. But it would exponentially expand the scenarios that solvers must consider, possibly to a degree that would be impossible for human memorization.

As it is also my impression that small changes in probabilities can make huge differences in solver outputs, would this make solvers essentially useless?
Or am I completely off base?

You are probably right, this would be harder for solvers. But it would be less fun for humans for the same reason.

Expose one card but use it as 1 of 3 flop cards.

This might be interesting, would be a -much- bigger change to the game. Honestly, it would probably make the game less fun in the end because it would dramatically increase the difference in equity between strong hands and weaks hands.

The Chinese start doing algebra at age 11 or something. I'm sure they will figure out how to solve this wrinkle quickly.

+ 1 gazillion

I’m not sure what China has to do with poker solvers.

But if you’re suggesting that solvers -could- still work on this version of the game, I agree with you.
The question would be whether the solver results would be so voluminous as to become unusable by humans playing from memory.

FWIW, I took algebra when I was 12; and I wasn’t exceptional…it was the standard 7th grade math curriculum in my program.

No. Good human players play using heuristics, not direct memorization. Exposing some blockers would add some new heuristic patterns to the game, but solver study and pattern recognition would still work pretty similarly to now.

It would hurt current solvers but it would be the easiest adjustment that probably can be made to reprogram them to use this information correctly. You just remove the combos that include dead cards from the pool your running simulations on before you run the simulations and can use the same process and create a GTO strategy.

I dont get it. Do you mean:
A. Feel players who see two dead cards will start to overcome the edge of more gto-oriented players who saw the same cards just because the gto-oriented players havent studied solutions exactly specific to those two dead cards.

B. Fully automated bots or humans with RTA-assistance will fail to outperform the field because their programming cant take the two dead cards into account and thus start to lose.

?
Because I can assure you neither A nor B is correct.

1. The number of hand permutations already far exceeds the capacity of human memory. Players don't memorize solver inputs - they memorize general scenarios and ranges.
2. Exposing two cards is trivial for the solver to incorporate and actually serves to make the solver output more precise for a given hand. Humans can easily adapt by memorizing the base adjustment the exposed cards represent, the same as they do today by excluding the cards on the board and the cards in their hand. For example, for the suit exposed adjusting the odds and weight of flush draws, blockers, etc...

I definitely don’t mean B. I mean something closer to A, though not exactly.

Maybe just that solver output would become so highly specific to rare situations (since all exact situation will be much rarer in this game) that it would become less useful to study solvers and more useful to concentrate on other aspects of the game.

I thought a lot of people at least memorized preflop charts.

Are you implying that humans are able to memorize solver solutions as they are currently?

I really enjoy the fact that ideas and suggestions to modify the game in order to make it hard to solve are more and more often. I am not an expert in this field but I use some sort of math and game theory in part of my regular job and my bet would be to deal with solvers by somehow modifying the game. But I think that it would be best to give this task to some experts on complexity and computations - they will easily work out ideas how to make poker game fun for poor human beings while out of reach to solve on current resources.

We should keep in mind that solvers is one thing, but neural networks playing new game probably still will be easily beating us no matter what complexity is in a game (I might be wrong here) without solution.

The word "just" is doing a lot of heavy lifting in this sentence!

I was thinking the same. It wasn't "standard" per se, but it certainly wasn't uncommon. More of the equivalent of someone taking honors chem or AP U.S. History or something.

To be honest, I'm surprised current solvers don't already have a feature to exclude dead cards. Or at least cards that you can highly discount from your opponent's range because another player likely folded them.

This would be better done the other way, in that there is an additional card duplicated, which remains constant until both instances of the card are displayed in any given showdown, at which point the bonus card is redrawn

We'll get to re-create the Dan Colman-Doug Polk hand in which two queens of clubs appeared on the flop, too.

Not surprised a simple joke wasn't picked up by yous. Here you go dorks.

you have to play the player not the cards
when luck's out the door you have to come in through the window

You change the array for the deck from 52 cards to the 50 cards that aren’t exposed. It’s pretty easy coding. Array.remove(jd); Array.remove(6s)
Done. Honestly I’m sure some solvers already facilitate this to allow for card sharing when they’re creating their strategies. The bots that operate on their own network with multiple accounts almost certainly do.

Adding a draw element to the game especially post flop/turn/river makes it incredibly hard to program.

Poker has switched from a free flowing yet structured game when it was popular to more of playing cards vs poker. Poker players play against the other humans. Card players play against others cards. I remember when poker was popular that it was a flow game now it's boring and just money. We need to establish a poker union with the best poker players from this site I'll be the president of the union. We need to have lawyers, doctors and other in the group including stars to challenge Congress and make online poker legal again. C'mon man y'all Simping if you don't think that poker was becoming to big and there were other reason congress made it illegal. Poker is the most competitive sport in the world and we need to make a stand. On me if interested in becoming a founding father of Major League Poker. We only accept the top 5000 players in the world and we travel and play tournaments and cash games. My name is John Asaro.

I'll be the commissioner the first one of the League. Not one of the 5000 players in the League.

har de har har

I like how you are the cool guy making simple yet complex jokes which the dorks do not get yet it doesn't surprise you