Donkey Kong Forum

Other Classic Arcade Games => Classic Arcade Game Discussion => Topic started by: Weehawk on July 07, 2018, 11:54:50 am

Title: The Die Is Cast
Post by: Weehawk on July 07, 2018, 11:54:50 am


(http://www.slither-gdi.net/kongsaw.jpg)


We have before us a standard cubical die, like they use for Craps or many well-known board games. It's faces are numbered with the integers 1 though 6, usually represented with dots, in one of these layouts:


(http://mathworld.wolfram.com/images/eps-gif/Die_1000.gif)


The two arrangments are mirror images of each other, and for our purposes are interchangeable. The important thing is that the 1 is opposite the 6, the 2 is opposite the 5, and the 3 is opposite the 4.

One player starts this game by rolling the die. The number is noted and becomes our total thus far. The players then take turns, starting with the other player (not the one who rolled), turning the die one quarter turn, that is, to an adjacent side to the one that was previously "up". The new "up" number is then added to the running total. The players continue taking turns in this fashion until the total is 31 or greater.

The winner is the player to make the total exactly 31, without going over. If the player goes over 31, he or she loses. The player must turn the die each turn, no passing.

Brave volunteers may initiate a game with me by requesting to roll first, which I will do for them (actually I don't have a die handy and will use random.org to pick a number between 1 and 6), or may defer the first roll to me.

Please allow one volunteer to lose before another begins.

For the first member to beat me by making the total 31 or forcing me to go over, I have a DK Forum t-shirt. If you already have one, you're playing just for fun. (And I'll play until somebody without one beats me.)


(http://www.slither-gdi.net/finalmockup.jpg)
Title: Re: The Die Is Cast
Post by: homerwannabee on July 07, 2018, 12:18:50 pm
Roll it!
Title: Re: The Die Is Cast
Post by: Weehawk on July 07, 2018, 12:21:04 pm
Roll it!

I have rolled a 1. The total is now 1.

You may turn to 2, 3, 4, or 5.
Title: Re: The Die Is Cast
Post by: Weehawk on July 07, 2018, 05:21:51 pm
Well, George has obviously met with some sort of foul play.

While others plan his memorial services, if he doesn't post in an hour or so, I will declare a forfeit.
Title: Re: The Die Is Cast
Post by: Weehawk on July 07, 2018, 06:26:45 pm
Okay, I'm calling time of death on George at 5:45 PM Anchorage time.

NEXT?
Title: Re: The Die Is Cast
Post by: homerwannabee on July 07, 2018, 06:27:31 pm
I'm a truck driver.  I'd go with 5 if I'm still in.
Title: Re: The Die Is Cast
Post by: homerwannabee on July 07, 2018, 06:30:16 pm
Stuff like this is why trucking long haul isn't a normal job.  33 consecutive days of work.  Not many jobs where you can do that.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 02:14:25 am
I'll volunteer next, if I may, and let you roll first.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 06:11:58 am
I'll volunteer next, if I may, and let you roll first.

I have rolled a 1. The total is now 1.

You may turn to 2, 3, 4, or 5.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 07:47:50 am
Turn to 4.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 07:55:22 am
Turn to 4.

Making the total 5.

I turn to 1 to make the total 6.

You may turn to 2, 3, 4, or 5.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:04:16 am
Turn to 4.  Total is 10.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 08:06:20 am
Turn to 4.  Total is 10.

Turn to 1. Total is 11.

You may turn to 2, 3, 4, or 5.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:10:31 am
Turn to 3.  Total is 14.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 08:12:21 am
Turn to 3.  Total is 14.
Turn to 1. Total is 15.

You may turn to 2, 3, 4, or 5.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:15:15 am
Turn to 4.  Total is 19.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 08:21:17 am
Turn to 4.  Total is 19.

Turn to 2. Total is 21.

You may turn to 1, 3, 4, or 6.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:23:27 am
Turn to 1.  Total is 22.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 08:29:09 am
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.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:46:06 am
Turn to 4.

Thanks, John!  I definitely want a Weehawk shirt.  I'd be happy to pay for it too.
Title: Re: The Die Is Cast
Post by: syscrusher on July 08, 2018, 08:54:11 am
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.
Title: Re: The Die Is Cast
Post by: Weehawk on July 08, 2018, 09:09:58 am
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 (https://en.wikipedia.org/wiki/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.