The human ambassador should prepare for war, since he will lose this game.

This reasoning is mostly due to user12408's answer, please give credit to them.

First, some observations. When I say a position is losing (winning), I mean that if either player starts there, they will lose (win).

When the smaller of $x,y$ is $0$ or $1$...

• (0,1) and (1,0) are losing. Everything else has one of these as an option, so is winning.

When the smaller of $x,y$ is $2$...

• The alien wins starting from these spots. From (2,2), he wins by moving to (1,0). From anything else, he moves to (2,2).

• The human wins starting from (3,2) and (2,3) by moving to (1,0) or (0,1), respectively.

• The human loses starting from all other squares whose smallest coordinate is 2. If he moves to $(2,y)$ or $(x,2)$, the alien wins [see first bullet in this section]. Else, he must move to somewhere discussed in the first section, which can't be (0,1) or (1,0), so he loses.

When both $x,y\ge 3$...

• The alien loses starting from (3,3). The choices (3,0), (3,1), (0,3), (1,3), (2,1) and (1,2) are bad [see first section]. His other options, (2,3) and (3,2), don't work either [see second section].
• Otherwise the alien wins. When $x>3$, the winning move is $(x,2)$. When $y>3$, it is $(2,y)$.

We have shown the alien wins starting anywhere, except for the "bad" places (0,1), (1,0) and (3,3). Thus, the humans can only win if they can move to one of these places, showing that (170000,170002) is a loss for the humans if they start there. It is also a loss for the humans if the aliens start there, since it is not one of the three "bad" places. Thus, humanity is doomed by their lack of mathematical rigor.

The human ambassador should prepare for war, since he will lose this game.

This reasoning is mostly due to user12408's answer, please give credit to them.

First, some observations. When I say a position is losing (winning), I mean that if either player starts there, they will lose (win).

When the smaller of $x,y$ is $0$ or $1$...

• (0,1) and (1,0) are losing. Everything else has one of these as an option, so is winning.

When the smaller of $x,y$ is $2$...

• the alien wins. From (2,2), he wins by moving to (1,0). From anything else, he moves to (2,2).

• the human wins starting from (3,2) and (2,3) by moving to (1,0) or (0,1), respectively.

• the human loses starting from all other squares whose smallest coordinate is 2. If he moves to $(2,y)$ or $(x,2)$, the alien wins [see first bullet in this section]. Else, he must move to somewhere discussed in the first section, which can't be (0,1) or (1,0), so he loses.

When both $x,y\ge 3$...

• the alien loses starting from (3,3). The choices (3,0), (3,1), (0,3), (1,3), (2,1) and (1,2) are bad [see first section]. His other options, (2,3) and (3,2), don't work either [see second section].
• otherwise the alien wins. When $x>3$, the winning move is $(x,2)$. When $y>3$, it is $(2,y)$.

We have shown the alien wins starting anywhere, except for the "bad" places (0,1), (1,0) and (3,3). Thus, the humans can only win if they can move to one of these places, showing that (170000,170002) is a loss for the humans if they start there. It is also a loss for the humans if the aliens start there, since it is not one of the three "bad" places. Thus, humanity is doomed by their lack of mathematical rigor.

The human ambassador should prepare for war, since he will lose this game.

This reasoning is mostly due to user12408's answer, please give credit to them.

First, some observations. When I say a positions is losing (winning), I mean that if either player starts there, they will lose (win).

When the smaller of $x,y$ is $0$ or $1$...

• (0,1) and (1,0) are losing. Everything else has one of these as an option, so is winning.

When the smaller of $x,y$ is $2$...

• The alien wins starting from these spots. From (2,2), he wins by moving to (1,0). From anything else, he moves to (2,2).

• The human wins starting from (3,2) and (2,3) by moving to (1,0) or (0,1), respectively.

• The human loses starting from all other squares whose smallest coordinate is 2. If he moves to $(2,y)$ or $(x,2)$, the alien wins [see first bullet in this section]. Else, he must move to somewhere discussed in the first section, which can't be (0,1) or (1,0), so he loses.

When both $x,y\ge 3$...

• The alien loses starting from (3,3). The choices (3,0), (3,1), (0,3), (1,3), (2,1) and (1,2) are bad [see first section]. His other options, (2,3) and (3,2), don't work either [see second section].
• Otherwise the alien wins. When $x>3$, the winning move is $(x,2)$. When $y>3$, it is $(2,y)$.

We have shown the alien wins starting anywhere, except for the "bad" places (0,1), (1,0) and (3,3). Thus, the humans can only win if they can move to one of these places, showing that (170000,170002) is a loss for the humans if they start there. It is also a loss for the humans if the aliens start there, since it is not one of the three "bad" places. Thus, humanity is doomed by their lack of mathematical rigor.

The human ambassador should prepare for war, since he will lose this game.

This reasoning is mostly due to user12408's answer, please give credit to them.

First, some observations. When I say a position is losing (winning), I mean that if either player starts there, they will lose (win).

When the smaller of $x,y$ is $0$ or $1$...

• (0,1) and (1,0) are losing. Everything else has one of these as an option, so is winning.

When the smaller of $x,y$ is $2$...

• The alien wins starting from these spots. From (2,2), he wins by moving to (1,0). From anything else, he moves to (2,2).

• The human wins starting from (3,2) and (2,3) by moving to (1,0) or (0,1), respectively.

• The human loses starting from all other squares whose smallest coordinate is 2. If he moves to $(2,y)$ or $(x,2)$, the alien wins [see first bullet in this section]. Else, he must move to somewhere discussed in the first section, which can't be (0,1) or (1,0), so he loses.

When both $x,y\ge 3$...

• The alien loses starting from (3,3). The choices (3,0), (3,1), (0,3), (1,3), (2,1) and (1,2) are bad [see first section]. His other options, (2,3) and (3,2), don't work either [see second section].
• Otherwise the alien wins. When $x>3$, the winning move is $(x,2)$. When $y>3$, it is $(2,y)$.

We have shown the alien wins starting anywhere, except for the "bad" places (0,1), (1,0) and (3,3). Thus, the humans can only win if they can move to one of these places, showing that (170000,170002) is a loss for the humans if they start there. It is also a loss for the humans if the aliens start there, since it is not one of the three "bad" places. Thus, humanity is doomed by their lack of mathematical rigor.