## Tuesday, August 10, 2010

### Probability Questions

Playing a game of backgammon today with another math dork brought to mind a handful of difficult questions in probability.

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.

#### 1 comment:

1. You and my "math dork" are both certifiable... thanks for playing with him though, and being dorks with him!