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Does card counting work in what I am assuming is 5 card poker.
No, but it is irrelevant. Data could cheat on a scale that none of them could match, especially since he is dealing. He'd be capable of stacking the deck so fast that it is imperceptible - even potentially a few turns ahead. His advantage here is ridiculous.
He can probably distinguish the cards by miniscule differences on the back
But that’s unethical so he would play the game as if he didn’t know that
Yep, that's how he dealt all those 3s in that time loop episode.
Right but he very specifically would never cheat, right? So that part isn't really a factor.
Card counting can conceivably provide information, but it's not likely to because the deck is shuffled for every hand and there are usually a bunch of cards you never get to see.
Card counting works in blackjack when many hands are dealt from the same deck or shoe, and discards are placed face up so they can be counted.
The more cards you've seen, the more information you have about what's left in the deck.
It does, but not in the way it does in blackjack.
Basically, if you can guess at the cards people have thrown away, you can update your probability map of what is likely to come out.
Most players use a fixed mapping for calculation, since it gets maths heavy. Data could do it in real time and gain a small edge.
He could also correlate betting patterns with historical plays to estimate hands. All good players do this, but data would be excellent at it.
Counting is also significantly more complex for poker than it would be for blackjack. With blackjack you don't have to take the suit into account, and each card except Aces have a static value when trying to add up to 21.
With poker, a single card's value is significantly different depending on the other cards in your hand. A 4 of hearts is only significant of you have several hearts, other 4s of other suits, or consecutive numbered cards for a straight.
That's why most poker players use static probabilities. It gets even worse when there uncertainty involved. E.g. your 40% sure a player had an AK before folding. Along with an 80% they didn't have a spade.
The Human mind is incredibly good at doing calculations like this. Unfortunately it has to be learnt, and is in the form of "feels" rather than actionable probabilities.
It's also important to note that if Poker were just about probability, we would have had computers beating everyone a long time ago. It's a much more complicated problem than that.
It's actually 5D poker.