It was the first meeting of the humans and the aliens, and things were going well: The humans and aliens had learned to understand each other's language and found that both were hoping for a peaceful relationship. In this spirit, the alien and human ambassador decided to play a game.
The human ambassador put a queen on a chessboard. She explained the rules of the game:
We will take turns moving this queen around the board. Each move, it must get closer to the top left corner. Whoever moves the queen to the top left corner, however, loses. The queen can move-
At which point the alien interrupted
Yes, yes. We know how queens move on our planet too!
This exchange proved to produce a fateful misunderstanding: The aliens believed queens could make the same moves as a rook or a knight - that is, they would move the piece straight up or left, or go left two and up one, or go up two and left one. The humans believed queens moved in a straight up, diagonal, or leftward line.
Not realizing this, they began playing the game. If we label the top left square $(0,0)$, the square right of it as $(1,0)$ and the square below it as $(0,1)$ and continue with coordinates analogously, then they started by placing the queen at $(2,3)$.
The human ambassador played first, moving the queen up to $(2,2)$, knowing this was a winning strategy. She was very surprised when the aliens made the knight-leap to $(1,0)$, forcing her to move to $(0,0)$ and lose. The alien ambassador smiled and asked,
How could you not have seen such a standard move?
The human ambassador immediately understood how the aliens believed the game worked, but politely said nothing. They played again, starting at $(4,2)$ this time. The aliens started, moving to $(3,2)$, believing this to be a winning move. They were very surprised when the humans moved the queen to $(1,0)$, diagonally upwards, forcing the aliens to lose. The aliens were too polite to say anything, but realized how the silly humans must believe queens moved.
Both species understanding how their opponent would move queens, they played many more games, and became very confident about it. After a while, the aliens asked,
Shall we make a bet? Whoever wins the next game will be declared the best species in the universe and will be entitled to ownership of their opponent's planet! We will make this fair: We choose the starting position, you choose which player moves first.
The aliens placed an enormous, $1000000\times 1000000$ chess board on the table. The human ambassador quickly accepted, knowing that a queen moving diagonally was far more powerful than one that could merely make knight leaps. The aliens placed the queen at the position $(170000,170002)$.
What should the human ambassador do?