Our good friends that like games, Alice and Bob, play a game called "Say 100 and win".
The rules are:
- In the beginning they use one regular 6 faced die to get a random number between 1 and 6. Let's call this number $n$
- Alice goes first and says a number $k$ where $n < k \leq n+10$.
- Bob goes second and says a number $m$ where $k < m \leq k+10$.
- They take turns following the rules above. Each one has to say a number bigger than what the previous said but not bigger than 10+ previous number.
- The person that gets to say 100 wins the game.
As we all know Alice and Bob, they are smart and play the optimal strategy.
What are the chances of each winning the game and what's the strategy?