Int/Wis/Cha gambling rolls

[Breccia]

So I got bored during what would have been a 7-hour drive that became a 9-hour drive and thought about gambling-style games in 5th Ed.

I'll preface this with, because I was driving, I didn't look up the answer. But I'm modestly sure that a game like poker or liar's dice does not have a set stat for the relevant checks.

So I thought of this and was hoping for feedback.

The example is poker, but any other game in which you get to conceal your hand/pieces would fit.

Int = you play the odds based on what you can see, regardless of table talk or facial expressions. If you have a pair of sixes and someone raises even a single copper, you fold, because your hand sucks. If you have four kings, you bet the house even if someone else is betting like they have a good hand, because odds are strong they can't beat you.

Cha = you are bluffing (or, for a round/night of playing, you bluff often but not "every" time)

Wis = you play the other players more than the hand before you. You look for tells, or frustration when they bet heavily after losing four times in a row, that sort of thing.

That part feels kind of obvious. (And it means nobody's rolling Charisma chess checks, you can't bluff that you still have three rooks left) Then I thought:

Int = paper, Cha = scissors, Wis = rock.

Cha beats Int, because someone with a garbage hand can scare off someone with a low hand.

Wis beats Cha, because they can read your tells.

And Int beats Wis, because it doesn't matter what tells someone has when they keep checking a flow chart with percentages on it each hand.

"Beats" should not mean "Advantage", because there are other things (Inspiration) that should do that, and I wanted it to stack. I was thinking a +2.

I was also thinking, that if someone uses the same stat/strategy routinely and you beat their score by 5 (or more) twice, you learn what stat they're using and are could therefore swap stats to exploit this information. (In theory you could also get this information about famous gamblers by asking around/hearing about them, or by watching someone play from nearby enough to see the game in detail)

So my questions are:

A) Is there any reason to prioritize stats in Int/Wis/Cha gambling/skill contests like this? Or should each character just use their highest and that's good enough?
B) If you do agree in a stat priority like this, what should the "winner" get? Is +2 too strong, or not strong enough?
C) Have you seen (house) rules for when to use Int/Wis/Cha in games of chance that allow for bluffing? (I personally don't think you can use Cha if both you and your opponent can see all the pieces, again, you can't tell your opponent that you have four knights on the board in a standard game of chess, they can see the board) If so, please share!

Thanks for your time in advance.

[MoiMagnus]

(And it means nobody's rolling Charisma chess checks, you can't bluff that you still have three rooks left)

In situations that are complex enough, you can bluff that you actually have a strategy, making them lose more time than necessary thinking about it, or at the contrary that you made a blunder, which if the opponent is low on time might cause them to fall for the trap.

Additionally, if your opponent has an ego high enough (and not enough self-control), you might be able to play one that too to make them fall in your traps.

But yeah, that's definitely not a major part of the game.

A) Is there any reason to prioritize stats in Int/Wis/Cha gambling/skill contests like this? Or should each character just use their highest and that's good enough?
B) If you do agree in a stat priority like this, what should the "winner" get? Is +2 too strong, or not strong enough?
C) Have you seen (house) rules for when to use Int/Wis/Cha in games of chance that allow for bluffing? (I personally don't think you can use Cha if both you and your opponent can see all the pieces, again, you can't tell your opponent that you have four knights on the board in a standard game of chess, they can see the board) If so, please share!

Thanks for your time in advance.

By default, I'd use the following:
Int VS Int & Cha VS Wis & Wis VS Cha => If you succeed at two of them, you win.

I'd also add that if you obtain on the Int contest a success "by a lot" (exact value depends on games, probably 5 for games like chess, but 10 for games that are less open, and 20 for games that are mostly bluffing) then you get an automatic victory.