Thanks to this, I discovered this - the Sicherman dice. These are 2d6, one of which has sides bearing the numbers 1, 2, 2, 3, 3, 4, and the other bearing the numbers 1, 3, 4, 5, 6, 8. Why, you might ask? Because, you idiot, rolling these two dice gives you the exact same probability distribution for the sum of two normal d6s. Duh.
I don't know if Mr Sicherman was a gamer, but his creation has some quite profound implications.
First, as somebody in the therpgsite thread pointed out, you could use the Sicherman dice to represent, say, speed and quality. Since one of the dice gives quite low results and one quite high, you could roll 2d6 (actually, let's use 2sd6) and have the higher result represent speed and the lower, quality; or the higher quality and the lower, speed - thus nicely representing the way in which you have to sacrifice speed for quality sometimes and vice-versa.
Another possibility is to use 2sd6 for a unified combat roll: one dice representing defence, the other offence. Again, the trade-off between going on the offence but leaving yourself open to attacks versus focusing on defence at the expense of dealing damage is neatly represented in a single roll this way.
Yet another: roll 2sd6 and assign one dice to initiative and the other to damage. The longer you take to pick your moment, the more damage you do. Or, the quicker you act, the more likely it is that you will give a glancing blow as you frantically try to act before your opponent. Perfect for OD&D, actually.
George Sicherman, wherever you are, and whatever you are doing, I salute you and your crazy dice.