<s>[INST] Tim and Alice are playing a game where they alternate taking turns. In each turn, the player can either say a number (from a fixed set of numbers, say {1, 2, 3, 4, 5}) or they can say 'stop'. If they say 'stop', the game ends and the other player scores a point. If they say a number, the next player must say a number that is either higher or one lower than the previously said number. The player who cannot say a number loses the turn and the other player scores a point. The game continues until a predetermined number of points is reached.

Here is an example of a possible game:
```
  T: 3
  A: 4
  T: 5
  A: 4
  T: 3
  A: 2
  T: 1
  A: stop
  T: scores
```
The first question is how to decide who starts (we only care about the probability of winning, not the expected number of turns).  
The second question concerns the optimal strategy: how does a player decide which number to say?[/INST]