[MUD-Dev] Chances of success (Bobby's algorithm)

Bobby Martin bobbymartin at hotmail.com
Mon Aug 20 04:22:45 New Zealand Standard Time 2001


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I had said I was going to publish the algorithm we use in Cosm to
calculate skill successes, so here it is.  I've attached a
standalone java class that does some simple testing and reporting on
the behavior of the system.

First, you "roll" a random number in the interval [0,1].  This is
essentially a d1000/1000, if you prefer to think of it that way.
Call this number 'roll'.

Then, you calculate the chance of success.  The chance of success is
the ratio of your skill level to the sum of (your skill level + the
difficulty).

  Here is that calculation:

    chanceOfSuccess = skillLevel/(skillLevel + difficulty);

A simple comparison of the roll to the chance of success determines
whether the character succeeded at all in his endeavor (roll >
chance of success indicates failure).

If he succeeded, we now find out how well.  This is the hardish
part, you can just kind of take my word for it if you like, or you
can work it out for yourself.  My goal here was first to make it so
that 70% of successes were level 1, 70% of the remaining successes
were level 2, 70% of the remaining after that were level 3, etc.

So, if you compare the chanceOfSuccess to roll*(.7)^level like so:
chanceOfSuccess < roll*(.7)^level to achieve the above goal you need
to find the largest level for which the above equation is true.  I
use some logarithms and come up with:

    degreeOfSuccess = log(roll) - log(chanceOfSuccess)/
                   log(.7);

Unfortunately, once a character has achieved success, this will
distribute the success levels the same regardless of the comparison
of skillLevel to difficulty.  To remedy that, I scale by the
multiplicative inverse of (1 - chanceOfSuccess).  This means if you
have twice the likelihood of succeeding, you will also generally get
twice the degreeOfSuccess.

    degreeOfSuccess *= (1.0/(1.0-chanceOfSuccess));

I have tested this and am pretty pleased with the results.  Note
that difficulty is on the same scale as skillLevel, so skill
vs. skill tests happen the way you would want.  To assign a
difficulty to a task, just pick the skill level that you want to
have a 50% chance of success; that's your difficulty.  Characters
with low skills still have a small but significant chance of getting
a 30-40 degreeOfSuccess, but most of the time will fail.  Characters
with high skills will mostly get 70s & above on degreeOfSuccess, but
still have a small but significant chance of failure.

Anyway, javac the attached file and play with it if you like.

Regards,
Bobby Martin
Cosm Development Team

secure email: bobbymartin at hushmail.com

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