Suppose you're part of a game with a large, unknown number of players, and each player is given 100 coins of equal value to start. Here's how the game works: each round, all players anonymously put an undisclosed amount of coins -- up to 20 -- into the central pot. Once each player has done this, all players are returned the average amount of coins put into the pot (total coins divided by number of players) plus 25% of that average. The game continues for 5 rounds. How many coins would you put into the pot each round, and why?