Five friends play a simple game with the following rules:
- Players play consecutively one after the other.
- Each player must call out a whole number between 1 and 10 (inclusive), such that it hasn't been called out already.
- The winner is the player whose number is the median of all called out numbers.
What should be the optimal strategy for each player to maximise their chance of winning? Which player is the most likely to win if they all play optimally?
Note that if a player only has losing moves then they will just choose randomly. If they have multiple optimal moves then they will also choose one randomly.