Number picking II. Race to 15

[bonanova]

You and a friend play a game.

This time the computer prints the digits 1, 2, 3, ..., 7, 8, 9

Players take turns erasing one of the digits and adding it to their score.

The first player to score 15 points is the winner.

Do you choose to play first or second?

This qualifies as an Aha! puzzle.

[phil1882]

if its 15 points or more, then clearly player 1 has the advantage.

if its exactly 15 points then player 2 does.

the second case is more tricky so let's go over that one.

if player 1 picks 9, player 2 picks 8. now player 1 can't pick 7,

becasue that puts him over, yet he can't neglect picking it as it gives player 2 the win.

so player 1 picks 1. then player 2 picks 2.

then if player 1 picks 3, player 2 picks 4, forcing player 1 to pick 9.

the score is now 6 to 13, with player 1 having no chance of winning,

because all the low numbers have been chosen.

so player 1 picks 9 after player 2 picks 2. then player 2 pick 8, and the score is 10 to 10.

so player 1 picks 3, as the 7 puts him over. then player 2 picks 4, but now player 1 has no move.

therefore player 2 wins.

Edited May 31, 2014 by phil1882

[k-man]

Hmm... when I read the puzzle, I interpret 1, 2, 3, ... 7, 8, 9 as all digits from 1 through 9 including 4, 5 and 6. Phil's solution appears to include only 6 numbers 1, 2, 3, 7, 8, 9. Also, it's not clear from the OP that going over 15 means losing the game, but if so, then...

Player 1 has the advantage.

Player 1 chooses 6. Player 2 is forced to choose 9.

Player 1 chooses 2 (total 8). Player 2 is forced to choose 7 and go over 15 or choose any other number and let player 1 win by choosing 7.

If going over 15 simply means you can no longer win the game, but can continue playing then neither player can win if both play correctly.

[bonanova]

Truth be told, the puzzle is a flawed attempt to present the "non-race" version,

which I posted as separate problem once answers were posted here.

I mean all the values from 1-9.

My bad.