A zero-sum game

[jason_t]

A game is played between two players. They choose numbers one at time from {-4, -3, -2, -1, 0, 1, 2, 3, 4} and no number can be chosen twice. The first player to obtain three numbers (out of three, four or five) that sums to zero wins.

Which player, if any, has a winning strategy?

[mmbt0ne]

Now, I've only been thinking about this for about 3 minutes, but it feels like this is a Tic-Tac-Toe kind of game. The first player will always set the pace of the game, but the second player should be able to counteract any moves made.

The only way to get to zero, are:

0,-x,+x
1,2,3
1,3,4

As long as player 2 recognizes this, it should be pretty easy to end every game in a tie. But, I'm still thinking.

[mslif]

I believe the first player will have the winning strategy if he does not pick 0 first. The second player will always be one move behind. Like playing tic tac toe.
Just tought I will give it a try.

[mmbt0ne]

So are you saying that if you go first in tic-tac-toe you can always win?

[mslif]

No it is similar to tic tac toe in the way that the second player is always defending the first player's move. Not actually winning.

[PairTheBoard]

If there were 11 numbers, -5...+5 then I think the 1st player has an easy forced win on the 4th pick. Start with 0. If the second player picks a positive number, pick -5 unless up against 5 in which case pick -4. For the -5 case, this forces the second player to pick +5. Now the first player has an unforced pick. Just pick one of the three remaining positive numbers x such that 5-x was not the first pick of the second player.

Examples:

First Player: 0 -5 2
Sec Player: 1 +5 Can't pick both -2 and 3

First Player: 0 -5 4
Sec Player: 2 +5 Can't pick both -4 and 1

First Player: 0 -4 3
Sec Player: 5 +4 Can't pick both -3 and 1

So I don't think the game is necessarily like tic-tac-toe.

PairTheBoard

[mmbt0ne]

-5 to 5 wasn't the game. Can you make a winning strategy for -4 to 4?

[PairTheBoard]

[ QUOTE ]
-5 to 5 wasn't the game. Can you make a winning strategy for -4 to 4?

[/ QUOTE ]

I realize -5 to 5 wasn't the game. But it's a very similiar game and it's solution might give people ideas for solving the -4 to 4 game if it's not a forced tie. It also might give ideas for proving it's a forced tie if that's the case.

btw, the tone of your post sounded a bit rude to me.

PairTheBoard

[mslif]

The only way for the second player not to lose would be to pick the numbers that the other player needs to get to 0. For example:
P1 P2
-4 4
3 1
2 -1
-3 -2
0

The game will end up with no one winning. If the second player does not follow that strategy and if the first player does not pick 0 first, then the first player will always win.
I hope I am explaining myself correctly

[mmbt0ne]

I'm sorry if I came off rude, I didn't mean to.

However, there are so many more possible ways to sum to zero using just those extra 2 numbers I think it can be misleading.