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Backgammon variant with slightly non-random dice

Posted By: Timothy Chow
Date: Saturday, 19 April 2014, at 4:30 p.m.

A friend of mine who designs games says that in some computer games, instead of rolling two six-sided dice using a standard random-number generator, he implements the following algorithm:

1. Create a deck of 36 cards, each with one of the 36 possible rolls on it.

2. Shuffle the deck.

3. For the next 18 times that you need a roll, draw the next card from the top of the deck, use that roll, and then discard the card.

4. After 18 cards have been drawn, replace the discarded cards in the deck, reshuffle, and repeat.

The number 18 here is somewhat arbitrary; he has sometimes even changed 18 to 36, i.e., running through the entire deck before reshuffling.

What this procedure does, of course, is to prevent the same rolls from coming up in quick succession. You'll never get boxcars three times in a row, and consecutive boxcars will be rarer than in a truly random sequence. Non-doublets could conceivably occur four times in a row, but even three times in a row would be rare.

According to my friend, his card-shuffling algorithm generates sequences of dice rolls that match people's intuitive expectations more closely than truly random sequences do. People complain about ridiculous sequences of rolls much less often.

This suggests the following question. If we were to play backgammon with these quasi-random dice instead of standard dice, how much would the game be affected? In other words, how much theory would have to be rewritten and how differently would a bot trained on such dice behave from a standard bot?

I'm too lazy to pursue these questions myself but I thought I'd throw it out there for those who might find it interesting. We know that Safe Harbor Games "social dice" enjoy some degree of popularity, but of course the deviation from randomness there is too severe for serious backgammon players to countenance. Perhaps my friend's quasi-random dice might achieve a similar psychological effect with negligible change in perfect play.

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