How do I fix the statistical distribution of using 3 dice to handle Chance and Community cards in Monopoly?

Question

I bought a Grab & Go edition of monopoly and realized they changed the Chance and Community cards.

Instead of physical cards, they have you roll 3 dice, and pick out of a list (3-18) of effects.

Right off the bat, I know this will bell curve the effects toward the middle.

How would I use 3 dice to best replicate the 16 card distribution of the original game?

Answer 1

If I understand it correctly, you're looking to generate a uniformly distributed random integer in the range 1-16 using only regular d6s.

You'll need two distinguishable dice; if you don't have distinguishable dice, then roll one die, note the result and then one die again. Call the dice "die A" and "die B".

1. Map the result of die A as follows: 1-2 => 0, 3-4 => 6, 5-6 => 12
2. Add die B to the result of step 1 - you now have an integer in the range 1-18.
3. If your total is 17 or 18, go all the way back to step 1. Do not just re-roll die B until you get a value of 1-4.

Answer 2

If you aren't opposed to buying different dice, you can obtain the result directly from two consecutive d4 rolls.

The first roll tells you whether you are looking at the first, second, third or fourth quarter of the list. The second roll tells you whether you want the first ... or fourth item in that quarter. No dice need to be refilled (no empty results) and there are no difficult rules involved (beyond knowing that 16 ÷ 4 = 4).

If you don't want to seek out special equipment, but like the idea of splitting the list gradually, you need just one coin.

At each flip, you take the first or second half of what remains, and "cross out" the rest. After four flips, you have eliminated 15/16 items and are left with one result.

Answer 3

You could get yourself a d8 (eight-sided die, available from any well-equipped game shop). Use the result from that die (multiplied by 2), and the result of a second die to decide whether to add one (low roll, e.g. 1-3 on d6) or two (high roll, e.g. 4-6 om d6) to the result.

That will give you an even distribution from 3 (1 * 2 + 1) to 18 (8 * 2 + 2).

Of course, really well-equipped game stores will have actual d16. They're not common, but they do exist. That would relieve you of any math stunts (other than possibly adding 2 so you get the 3-18 range).

Answer 4

The following grid assigns 13 results each to 8 of the 16 cards (ie: 1, 3, 5, 7, 10, 12, 14, 16) and 14 results to the other 8 (ie: 2, 4, 6, 8, 9, 11, 13, 15).

It requires one distinguished die, here indicated in green, cross-referenced with the sum of the other two die here marked in red.

It features a symmetrical distribution, to please the eye, with traditional die symmetry on the distinguished die: the sum of the values for the distinguished die as rolled and its inverse summing to 17, just as for a traditional 1d6 each pair of opposite faces sums to 7.

This table gives a nicely (though not perfectly - see above) balanced distribution of the cards. It would require many games to differentiate this distribution from that of the original Monopoly game with physical cards.

Note: (14 * 8) + (13 * 8) = 112 + 104 = 216 = 6³.