[antasvara]

In the style of Texas Hold'em, both players could secretly choose two seats each and write them down. Then, you'd collectively choose 5 seats to be the shared "cards."

This next suggestion would stretch the "poker" definition somewhat, but I think it retains the same characteristics (imperfect information, shared "cards").

You start from a shared list of attributes (coat color, presence of a hat, etc.) and designate a row of seats. Each person gets one attribute secretly. You wager after each stop following poker conventions.

Only downside to this is that unlike poker, your hand can get worse after a stop.

[johannes1234321]

This misses the information your secret hand gives you about the other player's chances. In poker if I got an Ace in my hand the chance of the opponent having an ace lowers.

If I got somebody wearing a black coat, this has no impact on the chance of my opponent having a black coated passenger.

[Retric]

Discard any hands where you pick the same seats, at the end.

You can also play actual poker like this. Each player writes down random numbers 0-51 in predefined order. You reveal some of those numbers to the other player who adds their own number mod 52 to get their private hand. You all slowly reveal both numbers for shared cards. If one of your cards matches the shared card you have to start over, same deal if at the end multiple players end up with the same cards.

It’s a slow process, but when the goal is wasting time and you don’t have cards it’s a poor substitute.

[poincaredisk]

This actually increases their chances, because they can pick the same seat.