Monday, August 03, 2015

A Thought Experiment / Puzzle to Entertain You

Suppose the U.S. government instituted a new lottery for all citizens that worked like this:
  1. 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.
  2. 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.
  3. Repeat (2) until:
    • 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.
  4. If there is a winner, that person gets the total amount paid by all players.  In other words, the prize money is calculated in dollars as: (total number of participants) / 100.
As an example, suppose an average of 300 million people play each month (about 25 million fewer than the total U.S. population).  Each person pays a penny, so the players will pay a total of $3 million to play. If one person wins, that person will win the full $3 million, and the lottery will generate no income for the government.

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.


At 8:38 AM, Anonymous LatinThinker said...

Assuming there's a 50/50 chance to win, probabilities say half of the people will play in the next round. that means every time there's an odd number of people playing the next round the total number will be rounded to a pair number of players. I would think most times will finish up by 2 players on the last round and one big winner almost every month.

Nevertheless, Chaos Theory suggests that a minimum change in initial conditions may provoke a major variation on the final results, so it's also plausible that any attempt of predicting the results for the lottery is completely useless.

Sorry for bad english :)

At 6:49 AM, Anonymous thelotter review said...

And think you are right it is 50/50. Still the things like this are designated to make money for the operator the odds are always against the player. If not, there would be something done or conspired. I'm really skeptical about this.


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