Your friend wants to play a game with you. You sit down with them at a round table. They produce a large pile of coins.
“Ok”, your friend says, “We’ll take turns putting coins down, no overlapping allowed, and the coins must rest on the table surface. The first person who can’t put a coin down loses.”
Your friend wants to go first.
Is this game fair?
No, the game isn’t fair. The first player always has a winning strategy.
Proof
The following is the winning strategy for the first player:
Put the first coin exactly in the center.
Next, for each coin player #2 puts down, place one directly opposite it. That is, place it so that the center of the table is exactly half way between the two coins.
This will generate a completely symmetric layout of coins on the table. Whenever the player #2 selects a free space to place a coin in, the space opposite is guaranteed to be free as well. Since player #1 is always guaranteed an open