Sim, o jogo - par ou ímpar - existe em inglês. É comumente chamado de "odds and evens". "Tirar par ou ímpar" equivale em inglês a "play odds and evens".
1. Wikipedia: Odds and evens, also known as choosies, pick, odds-on poke, or bucking up, is a hand game played between two people, used to decide an issue. This game, a variation of the ancient Morra, is played internationally, especially among children. The individuals prepare by deciding who will be assigned odds and who will be evens. Then, one or both people say "One, two, three, shoot!". As the word "shoot" is said, the two people quickly and simultaneously thrust a fist into the center, extending either an index finger, or both the middle and index finger, indicating one or two. The sum total of fingers displayed is either odd or even. If the result is odd, then the person who called odds is the victor, and can decide the issue as he or she sees fit. Often, the participants continue to shoot for a best two out of three.
2. Sun Sentinel - USA: The commercial has the girls stripping off their snow gear down to their Speedos and attempting a game of volleyball in the snow. When the ball is hit into the icy waters offshore, May and Walsh play odds and evens [tiram par ou ímpar] to see who retrieves the ball. Walsh loses out.