Since the Federation doesn't do money, the wagers are essentially meaningless. Play seems to be for the bragging rights as to who won or lost, the fun element of the game and the psychological focus on strategic thinking.
The exception to this in TNG is from the episode Quality of Life where Beverley Crusher taunts Will Riker into wagering his beard on the final outcome:
BEVERLY : Okay... what do you say we up the stakes a little? If I win
this hand... you all shave off your beards [and] if one of you wins --
I become a brunette. Are we on?
GEORDI : We'll take that bet.
n.b. script edited for brevity
And in the Voyager episode Collective :
NEELIX: I don't know what you're talking about. I've, I've, this is
the first time I've played. What is it called?
PARIS: Look, why don't we make things a little more interesting.
Forget the chips. Let's bet on tomorrow's work detail, all right?
Whoever wins this hand gets the morning off.
CHAKOTAY: I'm in.
Mirroring Crusher in TNG, Paris says to forget the chips (which obviously have no worth) and offers a physical wager instead.
Out of universe
It's pretty clear that the actors and writers had no idea either. Despite the script constantly referencing Gene Roddenberry's assertion that the Federation is a 'post-scarcity' society with no money, the actress playing Deanna Troi (Marina Sirtis) clearly felt differently:
Generally, with most
beings, I could just sense what they were feeling, so I was empathic.
Why I was in the poker game, I will never know, because poker's about
sensing when people are bluffing, and there I was in a poker game
every week. I don't think you ever actually saw me win bundles of
money but I'm sure, off screen, at some point that was what I did.
as did showrunner Ronald D. Moore:
It is a strange platitude
that we used on the show, the need for money was gone and everything
was about bettering yourself. It was no longer about any kind of
material gain or personal gain, everyone was just trying to be a
better person So none of us could understand what that mean or how
that society functioned. It all seemed very vague. None of the writers
took it seriously. We all kind of laughed about it and joked about it.
We all had to pay homage to it because that was something that was
built into the structure of the show. At every opportunity we tried to
sneak in ways. How do you play poker if you don’t have currency? Again
The Original Series had credits and currency and we never understood
why they could do all these great things and we couldn’t. It was very