I am looking for a game mechanic for a game I am designing, that would let players randomly select other players, but that by the end of the game all the players were selected equally.
My first instinct was the destiny deck from Cosmic Encounters. In that game there is a deck with a few cards representing each player. On their turn the player draws a card, and interacts with the selected opponent. The limitation of this solution is that sometimes players select themselves. Cosmic encounters solves this by having rules for how to interact with yourself, but my game lacks this. Even if i was to simply put the card on the bottom of the deck and draw a new one, there is a chance with the last card being left of the last player who must take the last turn. At this point selecting another player randomly would unbalance the game, giving them an extra time they are selected. Is there any other mechanic that can be used to solve this? (I am in no way set on using cards. Any mechanic would be OK)