But what is the winning strategy? It would be interesting to know whether the decision tree has a compact algorithmic, since that would serve as an explanation

But what is the winning strategy? It would be interesting to know whether the decision tree has a compact algorithmic, since that would serve as an explanation of the strategy. Even if not, I'd be curious if there is some other simple proof of its existence. And failing that, it would be interesting to see an optimal game: a game in which player 2, though doomed, makes the game take as long as possible (presumably 21 moves).