Three Players A, B and C play a game with a single die. The rules of
the game are:
Player A ALWAYS goes first.
A rolls the die. If the die lands showing a 1 then A wins the game.
If A does not throw a 1 then B has a turn.
B rolls a die. If the die landing shows a 2 or 3 then B wins the
game. If B does not throw a 2 or a 3 then C has a turn.
C rolls the die. If the die lands showing a 4, 5 or 6 then C wins
the game. If C does not throw a 4 or a 5 or a 6 then A starts again.
This procedure continues until there is a winner.
Investigate any or all of:
1. The probabilities of each of A, B or C winning the game.
2. Who will be the most likely winner?
3. The most likely length of the game in terms of the number of rolls
of the die to produce the winner
