Tuesday, August 10, 2010
To make things easier, I'll take away some of the nuances of the game of backgammon--rolling doubles, or the fact that pieces have to be moved in certain ways--and just ask the crucial question:
If we take turns rolling dice and I have to accumulate 100 points and you have to accumulate 100 points, what's the probability that I get there first and "win"? Assume you roll 2 dice at a time, and its my turn.
An alternate question is how many turns will it take to accumulate 100 points. Answering this question suggests that the game should be over in 100 / 7 or probably 15 turns. But it could end as soon as 100/12 or 9 turns, or could take as long as 100/2 or 50 turns. What's the probability that it ends in 9 turns, 10 turns, 11 turns, etc....
But would knowing those probabilities help answer the original question--The probability that I get there before my opponent?
I'll say that these are questions I don't know how to answer, even though I love probability and have worked out many difficult calculations before -- perhaps a little more research will help.