Maths request- the odds on a mechanic

[Bailywolf]

OK, here is the die mechanic I'm working with:

You have a pool of dice ranging from 2 to 10.  To get a result, you roll your dice, and subtract the lowest roll from the highest roll.  The result spread looks like this:

0  Setback- you fail & suffer some other misfortune
1  Failure- the GM describes it
2  Basic Success- player describes it, GM inserts a "BUT"
3  Success- player describs it, GM inserts an "AND"
4  Full Success- exactly what Player intended
5  Success Plus- player describes success plus an "AND"

Difficulty is figured like so:

Typical Task 0
Hard Task 1
Very Hard 2

Outside character's experience +1
Situation difficulty +1
Task is boring, anoying, or against the spirit of the setting +1

A point of difficulty means you have to ditch your highest rolled die... more then one point of difficulty means you have to ditch more than one high die.  


Example:

Darian Peel- catsuited secret agent- is trying to pick a lock.  Her Wits score is 3 and she has 3 levels of Espertise with Breaking and Entering.  She has 6 dice to roll.  The lock is fairly challanging (1 diff) but she left her lock picks at home and is doing it with a hair pin instead (+1 diff).  The total difficulty is 2.  Her 6 dice roll out as follows: 6, 6, 5, 3, 3, 2.  Darian has to ditch the two 6's, so her result is 3 (5-2=3).  A Success- she gets the lock open, and the GM uses the "AND" option to drop a red herring, saying that Darian's notices recent tool marks around the lock...as if she wern't the first person to pick it...



OK.  


So can anyone help me figure the odds on this mechanic?  I'd apreciate any help you can offer.

Thanks

-Benjamin

[DaR]

So can anyone help me figure the odds on this mechanic?  I'd apreciate any help you can offer.

This doesn't break down easily, due to the fact that the difficulty penalty isn't assessed until after the dice rolled.  However, a quick monte carlo simulation provides the following:

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No difficulty:
dice success rating
  0      1    2     3     4     5
2 16.7% 27.8% 22.3% 16.6% 11.1%  5.6%
3  2.8% 13.9% 22.2% 25.0% 22.2% 13.9%
4  0.5%  5.4% 15.4% 25.4% 29.9% 23.3%
5  0.1%  1.9%  9.2% 22.0% 34.0% 32.8%
6  0.0%  0.6%  5.1% 17.4% 35.0% 41.7%
7  0.0%  0.2%  2.8% 13.0% 34.0% 50.0%
8  0.0%  0.1%  1.4%  9.4% 31.7% 57.4%
9  0.0%  0.0%  0.7%  6.7% 28.7% 63.9%
10 0.0%  0.0%  0.4%  4.6% 25.6% 69.4%


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1 die difficulty:
dice success rating
  0      1    2     3     4     5
3 23.6% 34.7% 22.3% 12.5%  5.6%  1.4%
4  5.1% 22.4% 28.9% 24.6% 14.5%  4.4%
5  1.0% 10.7% 24.7% 30.6% 24.0%  9.0%
6  0.2%  4.4% 17.5% 31.2% 31.9% 14.7%
7  0.0%  1.8% 11.1% 28.3% 37.5% 21.3%
8  0.0%  0.7%  6.7% 23.8% 40.8% 28.0%
9  0.0%  0.3%  3.9% 19.1% 42.0% 34.7%
10 0.0%  0.1%  2.2% 14.8% 41.5% 41.4%


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2 die difficulty:
dice success rating
  0      1    2     3     4     5
4 30.6% 38.5% 19.8%  8.4%  2.5%  0.3%
5  8.1% 30.5% 32.0% 20.2%  8.0%  1.2%
6  2.0% 17.1% 32.3% 30.1% 15.6%  2.9%
7  0.5%  8.3% 26.3% 35.4% 24.0%  5.4%
8  0.1%  3.7% 19.1% 36.3% 32.0%  8.8%
9  0.0%  1.6% 12.8% 34.1% 38.7% 12.8%
10 0.0%  0.7%  8.2% 30.1% 43.8% 17.3%


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3 die difficulty:
dice success rating
  0      1    2     3     4     5
5 37.1% 40.2% 16.5%  5.2%  1.0%  0.1%
6 11.6% 37.5% 31.6% 15.0%  4.0%  0.3%
7  3.3% 24.3% 36.8% 25.9%  8.9%  0.8%
8  0.9% 13.3% 34.1% 34.5% 15.5%  1.7%
9  0.2%  6.7% 27.6% 39.4% 23.0%  3.2%
10 0.1%  3.2% 20.4% 40.7% 30.7%  5.0%


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4 die difficulty:
dice success rating
  0      1    2     3     4     5
6 43.2% 40.1% 13.1%  3.2%  0.4%  0.0%
7 15.5% 43.0% 29.2% 10.4%  1.8%  0.1%
8  4.9% 31.4% 38.5% 20.3%  4.7%  0.2%
9  1.4% 19.1% 39.8% 30.2%  9.0%  0.5%
10 0.4% 10.5% 35.3% 38.1% 14.7%  1.0%


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5 die difficulty:
dice success rating
  0      1    2     3     4     5
7 48.8% 39.0% 10.2%  1.8%  0.2%  0.0%
8 19.7% 47.0% 25.6%  6.9%  0.8%  0.0%
9  7.0% 38.0% 37.7% 15.0%  2.3%  0.1%
10 2.2% 25.5% 42.7% 24.5%  4.9%  0.1%


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6 die difficulty:
dice success rating
  0      1    2     3     4     5
8 53.8% 37.3%  7.8%  1.0%  0.1%  0.0%
9 24.0% 49.5% 21.8%  4.4%  0.4%  0.0%
10 9.3% 43.9% 35.2% 10.5%  1.1%  0.0%


It's not clear what happens if you have a difficulty which reduces you to only one die.  Do you automatically succeed with what you roll, or automatically fail?

If the handling time works out well, it's a fairly pretty set of probability curves.

-DaR

[Bailywolf]

Yeah- less than 2 dice means you need to try something else- no chance.