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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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3 Answers 3

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
@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

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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It almost seems like you're expecting "exploding dice," which is where when you roll the max on one die. If you had to get values via exploding dice (eg if you could not roll the second die if you didn't roll a 0 aka 10 on the first die, and couldn't roll the third die if you didn't roll a 0 on the second die), then you'd be in a completely different scenario! You'd have a 90% chance of rolling 1-9, and only a 10% chance of rolling anything above that.

But you're not. You roll all 3 dice every single time, and each digit's place is generated independently of each other's. If the ones-place rolls 1, 7, or 0, it makes no difference whatsoever int he interpretation of the tens-place die nor the hundreds-place die.

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Or a bell curve. –  doppelgreener Sep 10 at 5:20
Your first sentence, defining "exploding dice", seems to. –  Ilmari Karonen Sep 10 at 15:55

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