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I'm trying to figure out what is the probability with 3 D10's if I were to roll them one after another."001" is one and "000" is a thousand. Would every number have the same probability or doubles and triples be less common?

And please explain.

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On a side note, this would have been a better fit on the math StackEx rather than here. – Oblivious Sage Nov 19 '12 at 5:41
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Seams like a reasonable beginner role-player question to me. But then I forgot we all need to have passed a doctorate in maths, physics and memorised the entire rule book before we can ask questions here. – David Allan Finch Nov 19 '12 at 8:44
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@David Right, we're not required to be experts in probability to enjoy RPGs—that's exactly why probability questions fit better at Math.SE, where the probability experts are. Should the asker find our answers lacking, now they know where to go for better answers. :) – SevenSidedDie Nov 19 '12 at 8:50
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@David I'm not sure what your complaint is—we did answer it here. – SevenSidedDie Nov 19 '12 at 15:39
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@SevenSidedDie - agreed. May be it was just the 5 down ticks that annoyed me on what is a reasonable question, IMO. – David Allan Finch Nov 19 '12 at 15:44
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2 Answers

up vote 8 down vote

If you're using 1 die as a hundreds digit, 1 die as a tens digit, and 1 die as a ones digit, then every number between 1 and 1000 has a 0.1% chance of occurring.

If by doubles you mean 155, 944, etc. and by triples you mean 333, 777, etc. then those have the same probability as any other number in the range. Think about it: each d10 should have a 10% chance of getting any given number, so why would rolling a 3 (or any other number) on one die affect the probability of getting a 3 (or any other number) on another die?

All of this of course assumes your dice are properly balanced and not flawed or being manipulated; using a truly random random number generator is recommended if you're worried about that sort of thing.

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Note that each instance of doubles or triples has an equal 0.1% chance of occurring, but the chance of getting ANY double or triple (when you don't care which one you get) is higher: 1% for triples and something like 31% for doubles if I didn't mess up the math. – Gregory Avery-Weir Nov 19 '12 at 6:20
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@GregoryWeir 1% for triples and 28% for doubles, according to this precomputed probabilities for the One Roll Engine which looks for exactly that on pools of d10s. – SevenSidedDie Nov 19 '12 at 7:34
up vote 8 down vote

You're reading them as digits, and the dice are in fixed positions. That means that each position has a equal probability (or a "flat" probability curve) of being 0–9, and that flat probability curve remains because you're interpreting them as digits in a number from 1 to 1000. You only start to get non-flat curves if you're adding them together.

If you plug them into Anydice, you'll see the flat curve.

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+1 for AnyDice. – CatLord Nov 21 '12 at 19:40

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