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What if we had a pair of dice for each player. 1 dice with positive values(1 to 6) and the other with negative values(-1 to -6) instead of both dice with positive values?

So the player who rolls the dice will have to move forward for the positive dice and move backward for the negative dice.

This can change the entire strategy of the game.

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closed as unclear what you're asking by doppelgreener, Tom Au, jwodder, user1873, Brian S Feb 7 at 14:50

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Sorry. What's the question? –  ire_and_curses Feb 6 at 16:47
    
"This can change the entire strategy of the game" - surely this makes the game last much much longer? Try playing it on your own without an opponent and count the number of rolls needed to get your pieces home. –  tttppp Feb 6 at 17:57
    
@ire_and_curses I'm asking about making a backgammon variant. –  KSK Feb 7 at 9:02
    
@tttppp, Every game is built on top of possibilities. Backgammon the way it is played, can be made shorter by adding 1 or more dice... if duration of the game is the only concern. Rummy or Bridge can be modified to be short by changing the rules of the game. My question borders on the possibility of a variation. Open your minds. –  KSK Feb 7 at 9:06
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@KSK, first off, welcome to the site! The problem is that you didn't pose a question in your post. This site isn't a regular forum where people come to discuss things. It's specifically a Q&A site, where people come to get answers to questions, and to help people by answering specific questions. Your post simply mentions an idea that you have, but it doesn't ask any specific question that people can answer. –  GendoIkari Feb 7 at 14:40

1 Answer 1

Do some statistical analysis on the possible rolls:

  • The average value of all rolls will be zero.
  • 41.667% (5/12ths) of all rolls will be negative.
  • 41.667% (5/12ths) of all rolls will be positive.
  • 16.667% (1/6th) of all rolls will be zero.

It seems like it would have a random walk type of effect, with no one being able to move very far (as @tttppp pointed out in his comment to the OP). Any positive moves will eventually be offset by negative ones, and vice versa.

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I ran a quick simulation of getting one piece 24 spaces and in 10 runs I saw it usually take between about 100-200 rolls (the lowest was 26). –  tttppp Feb 6 at 19:06
    
I got MUCH larger numbers from my simulation. Over 100 tries, the mean number of rolls needed to get a total sum of 24 was 1,544,901; the max was 7,411,661; the min was 10,340. –  GendoIkari Feb 7 at 14:59
    
If you assume 1 minute per turn, then for one player to get one of his pieces to the end, you will have to play for about 3 years non-stop. –  GendoIkari Feb 7 at 15:00
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Which translates to 90 years non-stop for a 2-person game, with average luck. –  GendoIkari Feb 7 at 15:01
    
@GendoIkari I've just re-entered the code I used and added a loop: ideone.com/LMy49o There are quite a few rules that weren't specified in the question (e.g. what happens when going backwards past the start, what happens if you throw doubles), so I'm not too surprised that we have different results. Sample output from my code: "The average number of turns in 1000 games was 87 (min = 8, max = 631)" –  tttppp Feb 7 at 18:30

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