# Probabilities using 3d10 as 1d1000 [duplicate]

This question already has an answer here:

I'm trying to use anydice to figure out the probabilities of the various values of 1d1000 rolled on 3d10.

I want to know stuff like "what's the chance of rolling 900 or higher? How about 950 or higher?"

I'm not sure how to script anydice to give me this information if it's actually possible.

Thanks for the help and keep up the good work!

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## marked as duplicate by SevenSidedDie, doppelgreener, mxyzplk♦Sep 10 at 5:52

Though not fully related to the question, there's an interesting segment in this YouTube video from VSauce about 'What is Random' about dice. –  Paul Aug 18 at 15:27

Just roll a d1000 in anydice.

The probabilities for rolling 3d10 as the 3 tens places will be exactly the same as rolling a d1000.

These answers shows the math for d100 vs 2d10, it's exactly the same story here just times ten.

The point of using d1000 is that probabilities are easy to calculate: the chance of the number or less is equal to the number in per-mille. The chance of rolling less than 900 is 900-1 in 1000 or 899‰ (89.9%); the chance of rolling equal or higher is the remainder in 1000 or 101‰ (10.1%) SevenSidedDie

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Multiple dice give you a discrete, "blocky" distribution similar to normal when they are added together. This occurs because there are more combinations that sum to results in the average range and fewer combinations as you approach the high and low end of the possible results. For example, with 2 6-sided dice, there is only one combination that produces 2, but there are 6 combinations that produce 7. In the case of percentile or d1000, since each die represents a different place value, even though they are combined to get the final result, the strategy retains the uniform distribution each individual die had (equal probability or flat line), as there are still an equal number of combinations (one) that produce each final result, as if you had rolled a single die.

With a uniform distribution, the chance for any particular result is the same for each possible result. Any particular result is one over the total possible results, so with a d20 for example, any particular result is 1/20 or 5%. Rolling a particular number or under is that number/total possibilities so rolling 15 or under on a d20 is 15/20 or 75%. The chances for rolling a particular number or over is the number plus the remaining possibilities, so rolling a 16 or higher on a d20 is 25% (since there are 5 possibilities, 16-20).

The chance of rolling 950 (exactly) on a d1000 (or 3 d10, where one die represents ones, one tens and one hundreds) is 1/1000 or 0.1%, the same as any other particular number. The chances of rolling 950 or under are 950/1000 or 95%. The chances of rolling higher than 950 are 50/1000 (951-1000 or 50/1000) or 5%.

The slightly odd bit about dpercentile or d100, d1000, et al, is that the highest die represents 1-10 (times the place), while the lower die or dice represent 0-9 (times the place). EDIT- Heh, that is NOT correct, at least not most of the time :) The 0 for the highest place ONLY represents 10 (times the place) when all other dice are 0, in order to make the result 1-100 instead of 0-99 or 1-1000 instead of 0-999, and so on.

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The OP is not talking about 3d10 in the sense of `1d10 + 1d10 + 1d10`, but in the sense of `1d10 x 100 + 1d10 x 10 + 1d10`, which represents a 1d1000 perfectly and does not approach normal distribution. –  Angew Aug 9 at 21:21
Hence, the answer. The OP is looking for a probability (as if it was other than uniform), so I merely explained why, in this case, even though multiple dice are used, the probability is still as if only one die was rolled. –  Wyrmwood Aug 11 at 0:58
Perhaps I was too succinct. I'll add a bit more verbiage. –  Wyrmwood Aug 11 at 1:05
Part of the confusion is likely because you begin your answer with a description of the "normal" method of combining dice. –  thelr Aug 14 at 15:34
Yeah, I thought about rewording it, but then again, I think it's important to understand why the two are different. Guess they'll just have to read to the 4th sentence :) –  Wyrmwood Aug 15 at 14:08