nabla: Yes, very good.  And with just 1 die modified, I've finally come up with 8 5/6 pips per roll (in the range you expected).

Ok, you sorta lost me there. Why are we changing the dice?

Thad:Someone was caught using altered dice in a European tournament.

Thad: No dice change here, Thad...as far as I know    :-)

I was just exploring the specific difference that would have resulted from the kind of cheating that took place, according to a news story that I provided a link to (below) a few days ago.

That news story wasn't too clear as to whether just 1 die or both of them were changed, nor did it specify how or when the change was made.

Ah, yes, I read about that.

Novice question: Wouldn't having both players use the same dice fix that? The game would be fair even if the dice weren't. Or would that create new problems (other than breaking tradition)?

And as for my original question, the reason I mentioned it is because I was wondering if moving three checkers instead of four would make for an interesting variant. It seems like having to move three checkers would force a player to leave oneself open to a hit more often than when moving four checkers. That might balance out the higher pips per roll of doubles. I thought it would be an interesting variant.

Thad:It would only be "fair" if both players were aware of the substitution, and were equally experienced in playing with the altered dice.