"Statistics of results 1d6 x 1d10" Topic

Ok, so our eldest son is well on his way to being a gamer. We've been gaming with him since he was 5 or so, and have introduced him to roleplaying in the past year or two.

A few days ago, he decided to create his own RPG. Keep in mind that he is 10 years old, and statistics have nothing on doing something neat and different (to him).

I won't go into details on what his game was about or any of that. But I did want to ask about the surprising (to me) die mechanic that he came up with.

The game only used a d6 and a d10. He would give you a target number between 1 and 60 and you'd roll both and multiply the results. So, suppose you roll a 3 on the d6 and a 5 on the d10, your result is 15.

I'm no mathematician, but I have a feeling that while this is cerainly an interesting mechanic, it probably doesn't give an even statistical spread between 1 and 60.

So, I call upon the TMP Hive Mind. What sort of result spread do you get from a 1d6X1d10 roll?

And, no, I have NO idea where he came up with this mechanic. It's not like anything in any game we've played with him. In fact, I don't think I've ever played a game with such a mechanic.

Interesting, but certainly not an even spread. Some numbers, obviously, are not represented at all. For example, on a D6xD10, you can't ever get a 17, nor any other prime number greater than 7.

The most common numbers are 6 and 12 with a frequency of 4 each. Seven numbers are have a frequency of 3, eight numbers have a frequency of 2, and fifteen numbers have a frequency of only one. Twenty-eight numbers are not represented at all. And it looks like any prime number greater than 7 or any number that is a multiple of a prime number greater than 7 will not be represented in the list.

And I just graphed the distribution to be sure -- there is no bell distribution, whether skewed to the right or left or not.

Wow… I knew it had to be hinky somehow, but I didn't realize just how screwy it was. LOL!

For the record, I told him after our first "playtest" that it was an interesting mechanic, but that he might want to try something like percentile dice, etc.

But it's really good seeing him try to do something like this. And to see him try to do something different from everything else.

It could still work. You'd only have to gear your results table to your probabilities. It doesn't have to matter that you never get a 17 or a prime number over 7 IF you are not looking for a purely mathematical result (say for number of casualties) but merely a list of random selections.

For instance, it might make a good command mechanic. Since 6 and 12 are your most common numbers (according to jizbrand, I haven't crunched them) then they could represent the 'status quo' while more rarer results could provide alternative courses of action.

Kudos to him for experimenting at any rate! :)

The 50% probability number (roll this number or less) is 15 (exactly) not 30 as one would naturally assume. The probability of the number 30 is 80%. As a game mechanic your sone may want to say you need a 30 for a 50/50 chance while it is really much easier. As long as you chart the probabilities of each number it could work. Watch out for the distribution though, the steps in probability on the low end tend to be far apart while the high end bunch together (1.67% apart for the top 6).

Here's a plot of the 1D6 x 1D10 distribution. Fun with Excel!

picture

This brings to mind an oooold article I read in Dragon magazine waaaay back, about "divided dice". You roll two dice, say your D10 and your D6, and divide the first result by the second. This gives you a distribution weighted towards low numbers, but with the slim possibility of getting a high result. With D10 and D6, on average I guess you'll be getting something around "2", heavily weighted to low numbers, but with the off-chance of getting up to "10". Pretty nifty, but most folks will not want to perform division during a game…

Most people don't want to perform division period.

Thanks for all the info guys! I'll pass this along to him.

Most people don't want to perform division period.

Mainly because they don't do enough. They get really good at it very quickly if they do it a lot.

I the past before telling machines shop assistants, of less than average natural ability, learnt to add really well -- sheer practice. Those selling fabric learnt to multiply well too: 3 yards at 2.75 sort of thing.