the first choice matters insofar that you can choose to stick with it, so while the coin toss in isolation is 50/50, for the game as a whole you need to conside

the first choice matters insofar that you can choose to stick with it, so while the coin toss in isolation is 50/50, for the game as a whole you need to consider the option of sticking with that initial 1 in 3 chance along side the 1 in 2 chance.