Comment by 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.
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.