Dan, Sam and their new friend Dimitri (the one who plays chess), 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 between the number previously said and its double (but not including).

For example, Dan begins saying 1, then Sam says 2, and then Dimitri 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, Dan can choose any number between 3 and 6; that is, he can say either 4 or 5.

The game finishes when anyone reaches 150 (who is the winner). If Dan begins and then goes Sam, who will win? This means, who has a winning strategy?

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