A Thought Experiment / Puzzle to Entertain You
- On the first day of every month, each person who wants to play produces a single penny, which they will use to play the game.
- Each player flips his/her coin once, with one of the following results:
- Tails: The player is eliminated from the game, and the penny he/she was using is paid as the cost of participating.
- Heads: The player is still in the game and continues to the next round.
- There is only one player left, who is the lottery winner, OR
- There are no players left (because all remaining players flipped tails in one round), and there is no winner for the month.
However, on months when there is no winner, the government will take in the full $3 million as income with no pay-out.
The cost to the government of administering this lottery is $1 million per month.
Here is the question: Assuming 300 million people play every month, will the government make money or lose money with this system?
Assume that the pennies used all have a perfectly 50/50 chance of coming up heads or tails when flipped, and that there is no possibility of cheating by either the players or the government.