## Finger Dice

You and your friends are trapped on a desert island. What better way to pass the time than to play games? But you have no dice! What do you do?

You could whittle some out of coconut, but instead here’s an easy way for a group of people to simulate rolling a six-sided die. I originally laid out this method in Microscope Explorer, but it seems like a useful thing for everyone to have in their toolkit so I’m sharing it here.

- Each person secretly picks a random number from 1 to 6. Simultaneously hold out one hand pointing that many fingers or make a fist for a 6. Don’t discuss what you are going to vote ahead of time. That’s cheating!
- Add up the fingers, with each fist counting as a 6.
- If the total is greater than 6, subtract 6. Keep subtracting 6 until the total is 6 or less.
- You now have a number from 1 to 6. That’s your result.

You’ll find that you can also quickly eliminate sets of six as you count fingers. Drop fists or group together fingers that add up to six and drop them as you go, so long as there are still more fingers remaining (i.e. don’t go down to zero).

Statistically all results from one to six should be equally likely, regardless of how many people you include. Can you cheat and rig the results? Only if *every* player cooperates. If even a single player picks randomly, the result is unpredictable, which is pretty solid.

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Ben Robbinssaid:I ran the numbers, and — surprisingly — if you limited players to only picking 1-5 (instead of 1-6), and then did the rest of the procedure normally (subtracting 6 until you get 6 or less), the distribution is *very* close to the same as using 1-6, so long as you have three or more players.

That would eliminate the ability to “rig” 6’s, and also any false perception that picking a six didn’t change the outcome. It would be become almost entirely unpredictable.

So it’s a trade between perfect math accuracy and human psychology.

Ben Robbinssaid:I failed reading comprehension on Shadow’s suggestion. I get it now, but I think it’s more confusing to tell players they can pick zero, subtract six until you get zero to five, but zero is six. The math result is the same, but this seems like it would take more explaining and jazz hands.

edit: Forget to mention, this discussion did give me another idea. I need to check the math on it first…

Tommi Brandersaid:You are calculating modulo six, so zero and six are precisely the same thing; if the fist is treated as a six, then it will just get cancelled in the cancellation phase, so it is the same as zero.

And yes, this is not quite a random method in the strict sense of word, but it is highly unpredictable method, unless the group manages to synchronize in some manner. Unlikely to happen very fast and accidentally with more than two people.

Ben Robbinssaid:If you treat a fist as zero, 1-6 stop being equal odds.

It’s tricky but because the numbers add up and then rollover, rather than being an average of any kind, even “thinking high” won’t get you a high result necessarily.

I suspect even if you told everyone “let’s get a five” (for example), but didn’t say what each of you were going to vote, it would be hard to get a preplanned result without actually discussing a strategy. The one exception to that is six, since it would be easy for everyone to vote 6 and get a 6. But again, that assumes everyone is cheating. If even one person doesn’t, it becomes unpredictable again.

The Shadowsaid:Thinking about this a bit more, I suspect that in the absence of other factors, people will choose a fist less often than randomness would indicate, simply because it feels like you’re not contributing to the result.

The Shadowsaid:It’s even easier to treat a fist as zero. In the unlikely event that the total is zero, treat it as 6.

The only trouble with this method is unconscious collaboration. If you’re playing a game where you always want to roll high, for example, I suspect that people’s choices will tend to skew a bit high – which doesn’t guarantee a high result but does make it more likely.