For a game that ends after four rounds, this reasoning proceeds as follows. If we were to reach the last round of the game, Player "2" would do better by choosing "d" instead of "r", receiving 4 coins instead of 3. However, given that "2" will choose "d", "1" should choose "D" in the second to last round, receiving 3 instead of 2. Given that "1" would choose "D" in the second to last round, "2" should choose "d" in the third to last round, receiving 2 instead of 1. But given this, Player "1" should choose "D" in the first round, receiving 1 instead of 0.