James Smith 💾Mar 27

I have these six dice on my desk (from a recent purchase of the Warhammer Spearhead launch mag) and every now and again I roll them, hoping to get 1-2-3-4-5-6…

I think it might take a while…

Show threadJames Smith 💾Mar 27

although, I just rolled twice and got only one duplicate in each, so maybe not as long as I think...

Probability is hard.

Show threadJames Smith 💾Mar 27
Aargh! It only took a few more! My intuition was *way* off.
Show threadJames Smith 💾Mar 27

Now I think, and maths people could correct me here, that it's like rolling a series of dice, with a decreasing chance of getting a number not already rolled on each one:

1 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 0.015

So about 1-2% chance. Is that right?

EJMar 27
Show threadArthur van der Harg

@Floppy Yes. if you throw them all together, you have 6^6 total possible outcomes. 1..6 can be arranged in 6! ways. So you have 720 out of 46,656 possibilities that match your desired outcome. That is 1.54%.

So if you want for something to keep you busy, throw a single dice and try to get 1..6 in order. Wrong number: start over. Now you can expect to need about 46,656 throws.

[Edit: I mistakenly added an extra factor of 6 to the "serial" version]

Mar 27 at 3:26pmWeb
Show threadJames Smith 💾Mar 27
@ArtHarg I think that's what I must have been initially thinking about, hence I had a wildly wrong estimate :)
Show threadSeanBurlington 🌈 🕊️Mar 27

@ArtHarg @Floppy

It's the difference between combinations and permutations

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

Combinations and Permutations

In English we use the word combination loosely, without thinking if the order of things is important. In other words:

Math Is Fun