Play a game of ro sham bo to see which player rolls first. If it's a stalemate, both take 900mg bundy and play Rock Paper Scissors liserd Spock until you get bored
Whoever hits third plateau first gets to roll first
Quantum chess
Roll a a 3 sided dice and flip a coin the number you land on determines which generation of matter your particle is and heads= Quark tails lepton
Basically each player keeps rolling for the duration of the game. When you have enough particles accumulated to form a baryon or a meson you roll a regular dice which determines each particles state up down top bottom strange or charm. Regardless of whose turn it is you can roll to find the type of quark/antiquark at any point of the game.
When both of you have enough hadrons to fill your side of the chess board, play a game of chess. Wait maybe checkers would work better. Idk anyone got any ideas for a good game involving quantum physics?
Chinese checkers for balancing electrons could be cool