[RPG] Is it possible to emulate common polyhedral dice rolls using just a d6, and if so, how

dicestatisticssystem-agnostic

This is a question that I've asked myself numerous times, but I've never gotten a really satisfying result.

The issue is this: let's assume we only have one or multiple d6 dice (arguably the most common type of dice outside of pen & paper), but we still want to play D&D 5e or another RPG game. The game doesn't really matter here, we just need to be able to emulate different kinds of dice, such as d4, d8, d10, d12 or d20. I presume that if calculating these dices from rolls of a d6 is possible, any other potentially required dice rolls can be calculated as well in a similar fashion.

Therefore: How can the probability results of a d4, d6, d8, d10, d12 and d20 be emulated by rolling only with a d6?

Best Answer

It's pretty trivial if you allow occasional discarding of rolls/rerolls.

d2 (gonna need this later): if result is odd, read as a 1. If result is even, read as a 0.

d4: discard any results of 5 or 6.^*

d5 (gonna need this, too): discard any result of 6.

d6: done.

d8: roll d2 and d4. Result is d2×4 + d4.

d10: roll d2 and d5. Result is d2×5 + d5.

d12: roll d2 and d6. Result is d2×6 + d6.

d20: roll d4 and d5. Result is (d4-1)×5 + d5. Or result is (d5-1)×4 + d4. It doesn't matter which, but just decide before seeing the results to avoid unconscious bias slipping in.

My kids have spelling tests every Friday, and every Friday at breakfast I take their list of 20 words and the 2d6 that are always in my pocket and quiz them in random order, using the 2d6 to simulate d20, d15, d12, d10, d8, d6, d5, d4, d3, and finally d2.

Once you get a little practice with it, it's second nature.

^{* — Okay, here's how I actually roll a d4, without having to discard any results. 1-4 stay the same. On a roll of five or six I look at the orientation of the die. If the numeral is closer to right-side up than upside-down, read the 5 as a 1 and the 6 as a 2. If it's more upside-down than right-side up, read the 5 as a 3 and the six as a 4. If it's pips (which mine actually are, little 8mm suckers) your read the 5 as a 1 if it looks more like a + than an x, and as a 3 if it looks more like a x than a +. The six you read as a 2 if the "lines" of three pips are closer to vertical than horizontal, as a 4 if the lines are closer to horizontal than vertical. In other words, || → 2, = → 4.}

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[RPG] Is it possible to produce a bowl-shaped probability curve with dice rolls

There sure is!

Pick a size of a pool of d20 dice. The bigger the pool, the stronger the results.
Next grab a d6, d10, a different colored d20, or even a coin.
Roll the die pool and roll the extra die.
If you got an even number on the die, pick the smallest roll from of the pool of die and use this as a result. Odd? You pick the largest die value from the pool.

With a pool of 4d20 I get the following results in Excel (using a total sampling of 10,000 rolls):

1   2   3   4   5   6   7   8   9   10
9%  8%  7%  6%  5%  4%  3%  3%  3%  2%

11  12  13  14  15  16  17  18  19  20
2%  3%  3%  3%  4%  5%  6%  6%  8%  9%

So roughly a 20% chance of critical success or critical fail, and a 4% combined chance of a 10 or 11.

Credit goes to sage for suggesting the even/odd roll instead of a coin.

And now some graphs, because everyone likes graphs, right?

Although technically this is bar-graph land, I included a line graph as well as I thought it made it easier to see in light of the number of bars that were being dealt with. I also increased the sampling to some 100,000 dice.

Bowl Effect From Dice When Taking Min or Max From Pool At Random

[RPG] Call of Cthulhu V6 Dice

You're not missing anything. Based on the description you provided, it sounds like your player purchased one of Q-Workshop's licensed "Call of Cthulhu" dice sets. Strange as it may seem, the license isn't to the roleplaying game necessarily, but to the story by H.P. Lovecraft and the associated Mythos iconography. The set of dice is decorated to look appropriate for Cthulhu-themed games, but isn't designed for a BRP Call of Cthulhu game — they're the seven dice usually found in D&D and other popular roleplaying games.

Best Answer

It's pretty trivial if you allow occasional discarding of rolls/rerolls.

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[RPG] Is it possible to produce a bowl-shaped probability curve with dice rolls

[RPG] Call of Cthulhu V6 Dice

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