The Die Is Cast

[syscrusher]

Turn to 4.  Total is 19.

[Weehawk]

Turn to 4.  Total is 19.

Turn to 2. Total is 21.

You may turn to 1, 3, 4, or 6.

[syscrusher]

Turn to 1.  Total is 22.

[Weehawk]

Turn to 1.  Total is 22.

Turn to 5. Total is 27.

You may turn to 4 for the shirt, 6 to throw the game, or 1 or 3 to prolong the agony.

[syscrusher]

Turn to 4.

Thanks, John!  I definitely want a Weehawk shirt.  I'd be happy to pay for it too.

[syscrusher]

I initially tried to write a program to solve this while I was bored at work last night, but it was easier to just make a table of winning/losing conditions working backwards from 31.  If you had rolled a 4 I would've conceded. Heh.

[Weehawk]

Turn to 4.

Thanks, John!  I definitely want a Weehawk shirt.  I'd be happy to pay for it too.

PM me your address and size.

Regarding the game, for anyone watching, I didn't make a mistake. As Ben has explained, if you must roll first, the only "safe" roll is a 4. With each turn, Ben stayed in a position from which he could be sure of a win by playing correctly.

The simplest explanation of winning strategy involves the digital root of the running total.

1) If you can make the digital root equal 4, do so.

if 1) is not possible, then

2) If you can make the digital root 1, 5, or 9 by turning to 3 or 4, do so.

if neither 1) or 2) is possible then

3) Make the digital root 8 by turning 2 or 5.

If none of the above are possible, then your opponent is in a position to guarantee a win by playing the same strategy.

The only explanation of why this is, that I see in a quick Google search, is:

http://headinside.blogspot.com/2011/06/secrets-of-nim-dice-nim-1.html

http://headinside.blogspot.com/2011/07/secrets-of-nim-dice-nim-2.html

When I was first learning computer programming in the late 70's I looked for games like this for the computer to play against a human opponent.