In the Vice (HBO) clip AI Poker Bots Are Beating The World's Best Players, it is claimed (at 2:00), that Texas Hold'em has "more possible hands than atoms in the universe".
..this competition featured a complex style of the game called Heads Up No Limit Texas Hold'em, with unlimited bet sizes and more possible hands than atoms in the universe.
Due to the insane size of the universe and the tininess of atoms, I got skeptical of the validity of the claim.
The presenter does not specify what she considers "a hand". For now, I assume she means a unique combination of hole cards and community cards.
We are talking about Heads Up, so there are only two players, each of them gets two hole cards. The order of the hole cards is irrelevant, so the deals of hole cards "Ac Kd" and "Kd Ac" should be considered identical, as they play exactly the same way.
The order of the cards of the flop is also irrelevant, in the same way (in some cases one can get live reads based on order if the flop is dealt in a certain way, but this clip deals with computerised games.)
Then there is the turn and river. The order of the flop, turn and river obviously matters.
The game uses a deck of 52 cards, and all in all, a total of 9 cards are dealt, two to each player and five community cards.
I guess one could also interpret the claim to include player actions as a part of a "hand", so each call, check, bet, raise or fold would be a part of the hand. If this is the intended meaning then I guess it becomes sort of a no-brainer. Since it is no-limit, you can make any arbitrary combination of stack sizes, blinds, and bet/raise sizes, and thus create and infinite combination of "hands" in that way.