After each Posse the player places, the Rival places one. So the Rival matches the player in Posse members each round.
Okay great, because I placed a character on The Saloon. Then the Rival rolled a dice and ended up there. We dueled. I won, because.. psh. I'm a bounty hunter and that's what we do. Then I assumed that the Rival got a turn with their third player (which I don't have) and they rolled a 6. I was like... "Man, I already gunned down your buddy. Now you want to fall too?"
I maybe tell myself Western stories while I'm playing solo.