You and I play a game. We each have 1 die. I win if I roll a 4. You win if you roll a 5. If I go first, what is the probability that I win?
Some quick remarks:
- the game is over when I roll a 4 or when you roll a 5. Until that happens, the game is played ad infinitum.
- the game is played in rounds. At each round, I roll the die, and only then you roll the die. If I get a 4, I win the game and you don’t get to roll your die.
- the probability that I win is the same as the probability that you lose. And vice-versa.
- if you go first, the probability that I win is different (of course).
- note that there are two dice! However, since we roll the dice in a non-simultaneous manner, we actually only need one die. I can borrow yours, or lend you mine.
Hat-tip: Nuclear Phynance