[Guest]

i fould a neat little game on the internet.

there are 8 cards numbered in acending order. they alternate between green and red. player 1 takes red.

each player takes a turn switching any two cards, such that the card on the right is smaller than the card on the left after the switch.

the goal of the game is to get your 4 colored cards in decending order. if after yor move, both are in decending, its a draw. the game also has the pie rule: if your first move is viewed as too strong by your opponent, he may switch colors as his move.

so, what's the optimal first move for each side?

example game:

1 2 3 4 5 6 7 8 <- initial state

1 5 3 4 2 6 7 8 <- player 1 swaps 2 and 5.

1 6 3 4 2 5 7 8 <- player 2 swaps 5 and 6.

1 6 7 4 2 5 3 8 <- player 1 swaps 7 and 3. (if player 2 now swaps 1 and 8, it would be a draw.)

1 6 7 4 2 8 3 5 <- player 2 swaps 5 and 8.

1 6 7 5 2 8 3 4 <- player 1 swaps 4 and 5.

1 6 8 5 2 7 3 4 <- player 2 swaps 8 and 7.

1 6 8 7 2 5 3 4 <- player 1 swaps 7 and 5.

1 6 8 7 3 5 2 4

1 6 8 7 5 3 2 4

1 6 8 7 5 4 2 3

2 6 8 7 5 4 1 3

2 6 8 4 5 7 1 3

2 6 8 4 7 5 1 3

3 6 8 4 7 5 1 2

4 6 8 3 7 5 1 2

8 6 4 3 7 5 1 2 <- player 2 wins.

[CaptainEd]

1 2 7 4 3 5 6 8

7 and 6 (is met by 8 and 2)

1 4 6 2 3 5 7 8

2 and 4 is met by 4 and 6...

4 2 6 1 3 5 7 8

1 and 4 is met by...?

4x5, yielding

5 2 6 1 3 4 7 8

looks like P2 wins in two more moves each.

If I follow the thread right, we're demonstrating that P1 has no good counter to

P1: 35

P2: 56

1 2 6 4 3 5 7 8

isn't this a surprise! I sure wish I could state a human-oriented strategy, a way for P2 to create each move in response to P1's, without exhausting the game tree.

What a counterintuitive belief!

Edited November 2, 2011 by CaptainEd

[Molly Mae]

P1: 35

P2: 56

P1: 76

1 2 7 4 3 5 6 8

P2: 87 is met with P1: 71 or 35

1 2 8 4 3 5 6 7

P2: 32 is met with P1: 35 or 16?

1 3 7 4 2 5 6 8

Edited November 2, 2011 by Molly Mae

[Guest]

P1 can now swap 4 and 7, yielding

7 5 6 1 3 2 4 8

i think you spoke too soon capt'n :-)

player 2 swaps 8 and 7

8 5 6 1 3 2 4 7

now what for player 1?

[CaptainEd]

Spoke too soon, indeed! Thanks.

But look, Molly Mae believes P1 has the win after

P1: 35

P2: 56

P1: 76

I wonder if he's right...

Edited November 2, 2011 by CaptainEd

[Guest]

1 2 3 4 5 6 7 8

1 2 5 4 3 6 7 8

1 2 6 4 3 5 7 8

1 2 7 4 3 5 6 8

1 2 7 4 3 8 6 5 <-- i personally like swapping 8 and 5 here.

P1 response? if 5,4

1 2 7 5 3 8 6 4 p2 swaps 4 and 3;

1 2 7 5 4 8 6 3

[Guest]

I think that every game leads to a drawish situation.

Both the player have a move to stop the opponent from winning.

So ultimately both the group of nos. are arranged in a decending order!

[Guest]

i) Player A should not move no 1 during his move!

ii) Player B should also never move no 8 during his move!

i.e. if player A is the first to move the 1 during his move he'll eventually lose.

Also if player B is the first to move the 8 during his move he'll lose.

iii) If the other player does the reverse>> like player B moves no 1,

even then Player B will lose.(Same with player A moving no 8)

So generally a game will result in draw (coz the last move is interchange of 1 and 8)