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?
Pick 3 coins, say 50,100,200c. Assign them binary values: 50 is the rightmost bit, 100 the middle bit and 200 the leftmost bit. Heads=1,Tails=0. Flip all three and generate a binary number 0 to 7.
If 0 or 7 come up, ignore this and flip again. Otherwise you have 1 to 6 with uniform probability. That's 1 die. Repeat to get the second die and add.
If binary is foreign to them, then instead do this after flipping the 3 coins specified: Sum the value of the heads-up coins only. Double the total as expressed in dollars. This also generates 0,1,...7 uniformly.
Edited on October 4, 2018, 10:31 am
attempt at simplicity
