In the anime Kakegurui, there is a variant of rock paper scissors played where the rules are:
- Initially, each player draws 3 cards from a random set of 20 cards, each card being either rock, paper or scissors
- The maximum number of rounds per game is 3
- On each round, each player picks a card and puts it down at the same time, the winner of the round wins, otherwise the game continues to the next round
How would one go about calculating the probabilities for the card game?
If an additional rule is included, so that when there is a winner on the very first hand (when each player has three cards), the loser can opt to replay that round (each player gets their card back and the round is started again). This can only be done once for each player. Again, how would such a rule affect the probabilities for the game?