Roll a D10. There is a 1 in 10 chance it will score a 10.
This is generally approved as correct.

Roll 10 x D10. There is a 1 in 10 chance it will score 10 x 10.
This is generally disapproved of as improbable.

What happens? How do the odds change?

Quote from: GnosticGoblin on December 08, 2024, 04:00:42 PMRoll a D10. There is a 1 in 10 chance it will score a 10.
This is generally approved as correct.

Roll 10 x D10. There is a 1 in 10 chance it will score 10 x 10.
This is generally disapproved of as improbable.

What happens? How do the odds change?

That's because the probability of each die is independent of each other. The short version is that chance is equal to number of results that produce the results you want divided by the total possible results.

So the odds of a 10 on 1d10 are 1-in-10 because there is one 10 result and 10 possible results so 1/10.

So with two d10's you have a hundred possible results and only one that gets you two tens or 1/100.

Now, if you need just at least one 10 on two d10s, then there are 19 possible results out of a hundred outcomes (1+10, 2+10, etc. and 10+1, 10+2, etc. with 10+10 only counting once) so 2d10 has a 19% chance of at least one 10 and a 1% chance for two tens.

So with ten d10's, the odds they'll all be 10s is 1/10,000,000,000 while the odds of at least one 10 are going to be quite high.

He doesn't say he's rolling two d10s and multiplying them together. He's either rolling 10d10 or 1d10 and multiplying the result by 10, but I'm not sure which by his wording.

Quote from: HappyDaze on December 09, 2024, 04:02:58 AMHe doesn't say he's rolling two d10s and multiplying them together. He's either rolling 10d10 or 1d10 and multiplying the result by 10, but I'm not sure which by his wording.

True, but other than 1d10x1d10, I did give him the answer to how the odds change.

2d10 was just an intermediary step and example to show how probabilities change as you add more dice because I really didn't want to calculate the probability of at least one ten on ten dice in my head at midnight (that said, somewhere in the 95-98% range is likely for 10d10 having at least one 10 result).

Number of successful combinations of dice divided by total combinations (successful or not) will always get you the odds of a given successful result.

Too many potential combos though and I start looking for dice calculation apps.

For clarity, 10 x d10 tends to be inconsistent in interpretation.  That's why the industry either uses d10 x 10 or 10d10 to determine exactly what you want to roll.  In the case of the latter, you have introduced a bell curve where you will you will roll an average sum but very rarely roll 10 tens in a row.

The wording is a bit weird too.

Rolling 1d10 has 1/10 chance of scoring 10. This is not "approved", this is true. In case of physical dice you might want to measure it, but because you will run a finite number of tests, it is expected you are not likely to get 10% chance exactly. You can search for "fair dice": https://www.youtube.com/watch?v=bypuKxLZtZQ
Non-physical d10 dice used in math calculations will always have a flat 10% chance of showing either number from 1 to 10.

Given that, rolling multiple dice results in a bell curve. Each roll is independent. Rolling 10d10 has (0.1)^10 chance of adding up to 100 (10 x 10). The chance of 1/10 is not "improbable", it's inaccurate. The chance is (0.1)^10. Rolling 100 is improbable, because of the low chance.