Race To 80
Dan and Sam play a game in which the first to start says the number 1, the next says 2, and the one who's next must say an integer number strictly between the number previously said and its double (not including the endpoints).
For example, Dan begins saying 1; then Sam says 2 and then Dan can say whichever number he wants between 2 and 4; as the only integer between 2 and 4 is 3, he must say 3. Then, Sam can choose any number between 3 and 6; that is, he can say either 4 or 5.
The game finishes when someone reaches 80 (who is the winner). If Dan begins, who will win? In other words, who has a winning strategy?