Everything you think about Game Mastering is probably wrong: Part XV - The Other Type of Metagaming
Something that happens all the time is the insertion of a game into the game. If it's something minor like "I play cards at the local tavern to try to win some money for extra supplies" you might resolve it in a single die roll that might include a skill or attribute bonus of some kind. A bit of background flavour for a character and then you move on to the meat of adventuring. That becomes a bit hollow when you come to the inevitable cliché of betting the fate of the world or some other high stakes situation on a game of poker, chess, or dice.
The first and most obvious option is just not to have those types of clichés come up. That is truly the worst option for several reasons. For starters dumb clichés are great and the whole freaking point. Why not just remove dragons, ancient tombs, and pirates as part of your campaign to crush all joy. Secondly, it will almost certainly involve removing player agency because otherwise players will try to engineer these situations themselves for the same reasons I just listed. This type of dumb shit is going to happen, so best to buckle up and prepare for it.
So the next option is just to cut away and play the game itself. This is a solid meat and potatoes answer to the problem. All the real tension of playing through the game is there so it doesn't need much of a discussion. I will discuss something anyway, as this option is a baseline. RPGs are a group game and a lot of games are two player. It can be really fucking boring for three people to watch one player and the GM play chess for 45 minutes. If at all possible, stick to group games like poker.
So this is a good baseline option, but if you play any sort of a game with skills or a luck stat then you get into the fact that a player who built a character to be a card shark gambler suddenly sucks at cards when that skill is clutch because they themselves don't know how to play poker. The response to that might reflexively be "git gud scrub", but if you suddenly threw a lock and a bit of bent wire in the middle of the table when the thief when to pick the lock to the prison cell or took the ranger out back to an archery target when he needed to make a shot I suspect people would find that a lot more of a "fuck you" moment.
My solution is cheating. Seriously. If you've ever played against a computer AI you know that AI difficulty is just how much does the computer cheat. Not only is this easier to program, it is effective at scaling up the difficulty. To scale down the difficulty, just let the players cheat. So what do I mean by this?
For every intangible advantage someone has you give then a "bonus token", and if they have a disadvantage in the same way you give them a "malus token", not because malus is at all a good word for this but because in the event this concept gets popular several people I like will become incredibly irritated by the spread of that word. So what are these tokens used for? So the bit of "fuck you design" is you have to figure it out per game, but in essence its a one time cash in. You can cash in a bonus token to cheat or cancel an opponent spending one of your malus tokens. Your opponent can cash in one of your malus tokens to cancel a bonus or to cheat themselves.
To keep this from being a full "fuck you" moment I will give some examples. A cheat in poker would be dealing you a random card at the reveal that you can (optionally) switch for one of the cards you were really dealt. So if you were playing 5 card stud and you showed 2.2,K,4,4 and your opponent dropped 7,7,J,9,9 then you are about to lose the hand. So you cash in a bonus token (from being a professional gambler as a background) to draw a card. Your opponent could cash in a malus token (from you being cursed by a priestess of the fates) to cancel your cheat. If they do, they win the hand, but then they can't use that token later and even with the cheat you are still statistically likely to lose. You would have to draw a 2,4, or K to win. They decide to gamble on you still losing so they can save that malus token for later when they need it. So you draw a card and get...
It doesn't matter, because it keeps the tension going and makes the character sheet still useful while keeping the player skill first and foremost.
If you ignore my advice and use chess, a cheat is something as simple as undoing the last move you made. If you make a careless move and lose your queen to a bishop you might use a cheat token to redo your last move and try something else. Useful, but far from overpowering.
If you decide to use timers for your game you could also have these tokens simply be flat blocks adding or taking away from your time allotted.
As a recurring theme in this, it's all about using the medium to its fullest extent. That means leaning into player skill while learning to season it with character sheets. This is because traditional RPGs are at their core Risk Management games , potentially more so than anything else. Gygax was an insurance actuary after all.