Two players alternatively erase some 9 numbers from the sequence 1,2,...,101
until only two remain. The player that starts wins x−54 dollars from the
player that plays second, x being the absolute value of the difference between the remaining
two numbers.

Would you rather be the first or the second player?

Explain your decision by providing your strategy.

(In reply to

Typo? by hoodat)

I obviously defer to Ady, but I don't think it is a typo. If the players take turns erasing 9 numbers each, then player 1 erases 54 numbers. I don't think it is a coincidence that the payoff function is x - 54. If they took turns erasing 1 number each, then player 1 would erases 50 numbers and the payoff function would have been x - 50, which means that Player 1 could still guarantee a win with perfect play.