Wednesday, April 29, 2009

Probabilities

So, a probability question for those of you who know the maths...

I'm trying to work out the probability of the rolling the following, if using d10s.

From a pool of 3d10, rolling two 10's.
From a pool of 4d10, rolling three 10's.
From a pool of 5d10, rolling three 10's.
From a pool of 6d10, rolling four 10's.
From a pool of 7d10, rolling four 10's.

and so on...

I, of course, took Formal Logic and Pre-Calc rather than Statistics in college, so I'm not sure how to do the numbers on this. I assume there's a basic formula somewhere.

It does seem a little odd that I didn't take Stats in college, but at the time I thought I wanted to be a Physicist. That lasted until half-way through Pre-Calc, and my ass being thoroughly kicked. The first and only course I dropped and then retook. And retook because I was convinced I could figure it out-- so the second time around I went to tutoring sessions, read extra books on the topic, and bulled my way through. And got a C-. After that, the liberal arts looked really, really good.

Anyway, I should have taken stats if only because I'm a gamer...but well, bad life choices. Like Anthropology as a Major, but live and learn.

Also, The Flaming Lips cover "Borderline"-- here. And that's why I love them.

5 comments:

  1. Working with some scrap paper and a pen...

    If you have 2d10: Each die has a 90% chance of NOT rolling a 10. There's a .9 x .9 chance of neither die rolling a 10, 81%. There's a .18 chance of rolling 1x10, and a 1% of rolling 2x10 (a double 0 in percentile).

    If you have 3d10: 72.9% NO 10s (.9 x .9 x .9). There's a 16.2% of only 1x10, 2.2% of 2x10, and 0.1% of 3x10.

    I can whip up a spreadsheet and shoot you the results after I walk my dogs. In any case, the odds of most of the dice coming up 10s is always pretty small.

    ReplyDelete
  2. From a pool of 3d10, rolling two 10's.
    2x10 or better, 2.8%.

    From a pool of 4d10, rolling three 10's.
    3x10 or better, 0.37%.

    From a pool of 5d10, rolling three 10's.
    3x10 or better, 0.856%.

    From a pool of 6d10, rolling four 10's.
    4x10 or better, 0.127%.

    From a pool of 7d10, rolling four 10's.
    4x10 or better, 0.2728%.

    ReplyDelete
  3. Sorry about the multiplication mistake in the first post. 0.27%, not 0.22%.

    Quick and useful rule of thumb, if only a natural 10 is a success. On average, each die will provide 1/10 of a success. If you roll 5 dice, you'll get 1/2 of a success. If you roll ten, you'll average one success. After a hundred rolls, you'll probably roll around 10 successes.

    For 10 dice, the stats are (approx):
    0 successes: 35%
    1 : 39%
    2 : 19%
    3 : 6%
    4 : 1%
    5 : 0.15%
    6 : 0.01%...

    Thus, the average and the median are both 1 success after 10 dice.

    ReplyDelete
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