John and Jane are playing a game. They both go to the bank and each get 1000 euros in two-euro pieces. So each of them has 500 coins at stake. They then find a large rectangle table and decide that whoever wins the following game gets to keep all of the coins currently on the table. The rules are as follows:
- It is a turn-based game, so John and Jane take turns alternately (1 coin per turn).
- The coins are placed on the table and they may not be put on top of each other.
- Coins may not be moved once put on the table.
- Assume the table isn't large enough to hold all the coins.
- If there isn't any room to put coins on the table, the person who placed the last possible coin wins.
What is the winning game strategy?