The Gambler's Fallacy Dice

The term Gambler's fallacy refers to a misconception about statistics. [...] In statistics, a random event has a certain probability of occurring. The fallacy is that if the event has occurred less frequently in the past, it will be more frequent in the future. -Wikipedia

Well no longer is this a fallacy my friends, these dice are real! If you roll a 20 sided die, and you haven't seen a 20 in a while it is statistically more likely to show up in the next roll with these dice. And the best part, it's still uniformly random for large sample sets!

obligatory chart

How to Use

$ npm install --save gamblers-dice

const RiggedDie = require('gamblers-dice')
const die = new RiggedDie(20) // for a d20

console.log(die.roll()) // 1 -> 20
console.log(die.roll()) // keep using the same instance

Other Languages

The community has ported this to Java (@eukaryote31), Elm (@solkaz), Python (@torvaney), and C# (@MrTarantula). Check them out if these are your languages of choice!

I don't get it

Normally when rolling a 4 sided die, you would have a 25% chance of rolling any given face, at any time. If you rolled a 4, three times in a row it doesn't make it any less probable of happening the next time. Further, a 1 is not "more likely" because "it hasn't been rolled in a while".

This library breaks that standard rule.

Roll	% of 1	% of 2	% of 3	% of 4	Actual Roll
1	25%	25%	25%	25%	1 (⚀)

In the above example, we got out our fancy die from its box, and rolled. Because we are gods, we know the probability of each side being rolled, and see nothing amiss. Every face has a 25%, and we randomly roll a 1.

Roll	% of 1	% of 2	% of 3	% of 4	Actual Roll
2	14%	29%	29%	29%	2 (⚁)
3	22%	11%	33%	33%	?

Whoa, that's different, we are now 11% less likely to roll a 1, and indeed, by luck, we don't. We instead roll a 2, and when we do, we see the probabilities shift yet again. Let's roll the die a couple more times.

Roll	% of 1	% of 2	% of 3	% of 4	Actual Roll
3	22%	11%	33%	33%	3 (⚂)
4	30%	20%	10%	40%	1 (⚀)
5	9%	27%	18%	45%	?

After four rolls, we've yet to see a 4, it is obviously due and indeed there is now a 45% chance of rolling a 4. If you were going to do something rash (like bet on a 4) now would be the time.

This is stupid, why did you make this

I made a chatbot that rolled dice, and it was constantly criticized for being "broken" because four 3's would come up in a row.

These accusations would come up even though they (all being computer science majors) know it's possible (although unlikely) for these events to happen. They just don't trust the black box.

“Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.”

― Terry Pratchett, Mort