John and Jane are playing a game. They both go to the bank and get 1000 euros in 2 euros. So each of them has 500 euros at stake. They then find a large rectangle table and decide who wins the following game gets to keep all of the coins currently at the table. The rules are as follows:
- It is a turn-based game, so John and Jane take turns alternatively (1 coin per turn)
- The coins are placed on the table and they cannot 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?