My friends and I wanted to play Monopoly, but the dice were missing from the game.
Searching our pockets, we had 4 coins between us, all different: 10c, 50c, $1, and $2.
How can we best emulate a pair of dice with these coins, assuming that they are fair?
(In reply to re: Why this is difficult
Going toward "The sort of lines" you were actually getting at makes for a much harder problem than simply getting a practical solution with multiple throws. You wished us to emulate the sum (as that is all Monopoly needs) of two dice if possible with a single toss of the four coins. Quickly then the identity of the coins denoted by their valuations reduces just to their distinguishability. It seems a slog to try to replicate the sum distribution needed (shown in my older post), an effort which may be appreciated from watching your posted Matt Parker video. The only encouragement I found is that Galileo himself worked on the three dice throw properties.