Player one has weights 2,4,6,8,…,2022 in a pile. Player two has weights 1,3,5,7,…,2021. Player 1 starts the game and remove weights from her pile, one by one (in any order she likes),until her pile weighs less than the second pile. Then player two remove weights until her pile weighs less than of player 1. The winner is the first to take the last weight of her pile. Who has a winning strategy?
We can write the total weight for player one as N^2+N and for player two as N^2 where N=1011. Then at the first turn player 1 can take at most 32 weights and after that player 2 can take at most 6 weights but I'm not sure how to continue. For the simple cases of a small pile it seems that player 1 has a winning strategy.