"1/6^3

1/6^4

2/6^5"

The chance of spelling BID = 1/6 x 1/6 x 1/6 = 1/216

The chance of spelling DIAL = 1/6 x 1/6 x 1/6 x 1/6 = 1/1296

DIAL had to be spelled in the first 4 rolls, as the D could only appear in the first roll to make the rest of the word possible, I on the second roll, etc. The 5th roll was irrelevant, and actually something of a red herring.

The chance of spelling FIELD = 2 (1/6 x 1/6 x 1/6 x 1/6 x 1/6) = 1/3888

There were 2 and only 2 ways that FIELD could appear in 8 consecutive rolls: FIELDxxx and xxFIELDx. The chance of one occurring is 1/7776. You multiply this by 2, since there are 2 possible outcomes that spell FIELD.

This proved to be a bit of a toughee. I don't give you guys too many mathematical problems like this with good reason (including that I might not be able to solve them myself!)

Winner: Nathan Glasser, Somerville, MA

Contest Statistics: Newsletter sent to 309760 subscribers, 8 answers submitted, 4 answers correct, 50.00% accuracy. Chance of a correct answer winning: 25.00%.