Dice-based Scrabble

Chinese-style dice; the ace and the four always have red pips, with an extra large one for the ace

Rolling five six-sided dice (5d6) yields one of 26 possible numbers, from 5 to 30, which means it can be used as a means of randomly selecting a letter of the alphabet. Of course, the possible results of a 5d6 roll vary widely in frequency -- with, for example, 17 being 780 times as frequent as 5 -- approximating a bell curve. The letters of the alphabet also vary in frequency, though not quite so widely as 5d6 results, and not in so close an approximation of a normal distribution. Still, if the most frequent letters are mapped to the most probable 5d6 results, the results seem to be serviceable enough. Here's the key for converting numbers to letters.

And here's how the letter frequencies associated with this key match up against the actual empirical frequency of each letter in English.

Using this system, you can play (a reasonably close facsimile of) Scrabble without having a board or tiles. You just need five dice, a sheet of graph paper (with squares large enough to write in), some scrap paper, pencils, and a copy of the key. Instead of drawing tiles, roll 5d6 and jot down the the letter that corresponds to the number rolled. When you "play" a letter by writing it in a square on the graph paper, scratch it off and then roll the dice to "draw" a replacement. In a classroom setting, use a whiteboard instead of paper.