What is the probability that the first seven tiles drawn in Scrabble form a bingo (a seven-letter word...

competition/games/scrabble.opening.bingo New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What is the probability that the first seven tiles drawn in Scrabble
form a bingo (a seven-letter word using the whole rack)?

[ Editor: problem statement reconstructed from the subject "Probability
of an opening bonus (bingo)" of the collected reply, posted to the
crossword-games mailing list in 1994. ]

Show solution

Oops!  How embarrassing.  I had a look at my program which calculates
the probabilities for picking up a bingo, and noticed that one of the
letters was missing; I only had one H.  This changes the probabilities
somewhat.

For OSW, there are now 2 185 046 148 good racks, which is a chance of
13.6500%

For OSPD, there are now 2 007 426 213 good racks, which is a chance of
12.5405%.

(Thanks to Steve Root for questioning the figures I posted, which
prompted me to go back to the program.)

-- Graeme Thomas <Graeme.Thomas@isltd.insignia.com>

[ Editor: OSW and OSPD are the two official word lists.  The earlier,
uncorrected figures are not in the collected material. ]