I threw out an idea for a strange rule for NLH off the top of my head on NVG to give an example of something computers would find hard to solve. But after thinking about it I'm starting to wonder not only if it might actually catch on, but also the unique type of strategy decisions associated with it.

There are many possible tweaks to this that could possibly improve it but here is the game I originally thought of:

The hand could start out multiway but the distinguishing rule should probably kick in if there are only two players left when the fourth card is exposed. At that point, before the turn bet, the player who bets first can choose, before betting or checking, to match half (or maybe a different fraction) of the pot, in return for which the second player must expose a card of his choice. If he doesn't, things proceed normally (except that the second player knows that the first declined his option and the first player knows that the second player knows that and the second player knows...…..). If the first player pays up, he sees a card and then decides whether and what to bet.


Lots of stuff to think about here. For instance there is no doubt that such a game effects the right strategy on every street not just the turn. Thoughts?

Where does the money go? Into the pot or to the other player directly?

What is the benefit if the first player declines to pay money to see a card of the second player?

I expect the preflop and flop action to be much more tight and passive for the IP player in this game and he shouldn't polarize himself as much on the flop. The opposite for the OOP player.

If the OOP player declines to see the IP players card, it would actually polarize him quite a bit (to trash/nuts) and he should likely lead turns quite a bit.
If he chooses to see the IP players card, the IP player would usually also be very capped, which would make the OOP player lead a lot with a very polarized range and easily go for the stacks.

This game would have higher variance than normal NLH and the positions would be pretty much reversed (depends on how expensive the info is).
The better than the OOP player is (and the deeper the stacks), the more he will gain with that extra knowledge.

I'd play it.

Into the pot.


Don't understand your other question.

I think paying half the pot would be too expensive. What I believe would happen is the OOP player would choose to never pay the half and game play would continue like a normal poker game. Why donate half the pot to see their card, when you can bet half the pot and get them to fold. Also, you conceal information better by not paying to see.

Just to put it into perspective. If the pot was $100 and you paid $50 to see the other card and then proceeded to make a pot sized bet of $150, you would have spent 2x the pot when you could have just potted and maybe get a fold.

ZKesic has a point about paying the fee only when you have a mediocre hand, but that caps your range and that usually isn't a good spot to be in, especially OOP.

If you are looking for a flush on a 3 suited turn, you have a 50% chance of getting a card that doesn't even help you.

If the first player declines the option, what help does that give the second player? You seem to imply the decline would impart some information, what would it be?

There is already a game or an idea where one might use some side card to get information (or destroy/redeal a card and so on). Ideas from Hearthstone and similar, some TV programs, some chess variants. Some popular, some not.

There are Omahas that show one flop card before the first betting round that might make it just some more difficult for the bots and they are not popular games. What the bots can be programmed to do is underestimated.

Isn't it generally considered wrong to pay for information? It is not an unknown strategy to raise for information, nor is sizing an unknown thing.

In theory, it looks a playable game but what is the EV of paying or not paying and should the other be given an option to decline or should that have a different price? If I want to know if the other may have AA, I might pay for it, and if the other declines, I get information also but what is the EV of that? The bots could master those calculations.

Why do you think that this special action would make the game hard to solve?

Obviously the extra action adds some additional complexity, but nothing in the nature of that special rule is particularly challenging to solve imo.

mainly interested for now in what the fourth st buying and exposing strategy should be

Maybe change the payment to 1/4 the pot instead of half. That would give people at least some incentive to see a card.

Could it be that each player can agree to expose one card to each other on the turn, with both players having to agree?
What you’ve proposed wouldn’t be appealing to me personally

I like more what they use at Power Up that's played as a tournament. The idea from there is that one has additional (random) power cards that one can use any time during the tournament and they do different things like making the opponent to reveal one random card.

So to clarify the second player cannot fold when the oop player chooses the expose option because it's not a bet?

I suppose he could fold but why would he? To avoid showing one of the cards he plays? But there is always the chance that the first guy will match and then check.

Why 4th street?

5th street would be more dramatic IMO, but would is also be less strategically important?

Sweet post ZKesic. Explain why you think it's higher variance. Simply because there another chance for more money to enter the pot?

Also is the 1/2 pot price set in stone? There's gotta be a way to estimate the value of seeing a card--shouldn't the "price to see" be a function of that? Say somehow we build a model that demonstrates that seeing IPs card give us a 10% EV boost at equilibrium, let's set the price to 1/10th pot? Something of that nature?

The ranges are more polarized after turn, which means that players bet more with bigger sizings.

The price should mainly be based on the stack to pot ratio.

Why so?

I would imagine that even with potentially free equity there are situations where revealing a card narrows the information about your range to such an extent that you would be at least indifferent to folding and continuing, if not clearly -EV.

I mean when the ip player reveals information not only do +EV nodes thay were reachable with your hidden range in the context of the current game state become unreachable in the game tree, but +EV nodes that are reachable with your exposed card may become less EV as a result of not being able to reach those other nodes or the fact the villain can play much better vs the smaller subset of potential future streets.

Ah I think I see why--because then we ensure the price is never greater than some percentage of the effective stack?

It would polarize the first player's range, since he'd likely know he's either beat or has the nuts.

Not necessarily.

This alters streets before the turn so much (eg. bloating the pot for the sake of pricing out a card reveal) that I can't think of this as a hold'em game.