Rolling Multiple Dice

[Script Wrecked]

On a couple of occasions, I've seen people use multiple dice to generate a number range, via the "*rolls ...*" emote, particularly when one dice won't cover the whole range desired, for instance, using 2d20 to create a maximum of 40.

However, there are implications to doing this. Firstly, the minimum number generated is now the number of dice rolled, rather than 1. In the example above, rolling two dice, the minimum result is 2, giving a result range of 2 to 40, rather than perhaps the desired 1 to 40.

Secondly, and more importantly, using multiple dice skews the result. Some results are now much more probable than others. This is usually contrary to what is intended; most of the time, people want even probability between the results.

The below graph show the difference between the probabilities of the results between 1d20 and 2d10:

As you can see, the 1d20 has a flat, even probability result. The 2d10 however, has a pyramid probability result, with the "11" result being ten times as likely as the "20" result.

So, what to do about generating that 1d40 result?

Well, it would be nice if the "*rolls ...*" emote would accept any pair of numbers...

However, given that is not the case, you can try breaking it down between units and tens using the dice available. In this example, use 1d10 to generate the units, and 1d4 to generate the tens. However, you have to remember to subtract 1 from the 1d4 to generate {0, 10, 20, 30}, and add the units {1, 2, 3, ... 9, 10} to that.

Hope this helps.

Regards,

Script Wrecked.

[stragen]

Nice one. Also remember that dice are limited to uniform random number generation; even distribution.

With a computer it is possible to create normal (or Gaussian) distributed random numbers. American's would know this as the 'bell curve'.

Using a normal distributions it is possible to have critical success and failures as much rarer events.

As Script Wrecked showed it is possible to create other distributions from adding the results multiple uniform distributions.

For example 3d6 can be used an as approximate normal distribution. This is the distribution used for the GURPS system.

What distribution will be used for the MMO? Uniform? Normal?

[darkstorme]

The other option (though Script Wrecked's is simpler) is to map your value to a larger space.

So if you've got twenty-five people, say, roll 1d100, and let the winner be x (where x is the result) mod 25. (Or you can bucket it, whichever your pleasure.) If you have a number that doesn't fit neatly into your space (3 and 4, say) just let anything that falls outside the domain (in this case, 4) be a "roll again". Even with (for example) 40 targets and a d100, your chance of a re-roll is only 20% (better than the 1/4 in my previous example!), and it maintains the lovely flat distribution that fairness demands.