Hey all, posted a few times a few years ago, just more out of curiosity than anything else. But now I'm designing a traditional RPG with GM narration and all that jazz and have a couple of questions about resolution mechanic I'm thinking of.

Characters have skills( in the D and D sense) that have a die type attached depending on how skilled they are. Much like savage worlds. However instead of rolling against a target number, they roll against another die that is dependent upon the difficulty of the task. tasks that are hard enough to warrant a roll will be rolled against a d6. skills start at a d4.

So a character wants to leap a gorge, and is only of average fitness and strength. They would roll a d4 against the gorges difficulty of a d6, if the players roll is equal or higher to than the d6 they leap over all the alligators or whatever.

So my questions are
1. I am not a mathematician, will the maths be there to ensure fairness and scalability over the long run?

2. Is this easy to learn and apply (obviously this would be easy to answer with a playtest, but my game is not at that stage yet)?

3.is it interesting?

also, I find question extremely helpful. please ask away : )

I'm not 100% positive, but I believe that Earthdawn used a dice step system similar to what you're looking at.  It would be a good starting point for you to examine how they created theirs.

I just looked up their mechanic. While similar it doesn't have the players rolling against a different die, just a target number. any math wizards out there see any probability problems with this?

Assuming that a tie is not a success, a d4 beats a d20 only 15% of the time.  I got this value by comparing the number of successful rolls versus the total number of possibilities. A d4 can only beat a d20 on three rolls: 4, 3, 2.  There are twenty possibilities on a d20.
[pre]d4 vs d20: 15%
d4 vs d12: 25%
d4 vs d10: 30%
d4 vs  d8: 37.5%
d4 vs  d6: 50%
d4 vs  d4: 75%[/pre]
For the d20, you just have to subtract the percentage it loses to the other dice from 95% (-5% to represent a tie). For example, the d20 beats the d4 on sixteen numbers (5 through 20) and ties only on four numbers (1 through 4).  That means it beats a d4 80% of the time.  This may seem odd because the d4 only wins 15% of the time isntead of 20%, but that's because a d4 can tie on the "defense" four times instead of three times.

At least I hope that's how this probability stuff works. I'm not that great at math and used google to take a crash course in it haha.

Hrm, I had another thought, but this time, the d20 loses to the d4 12.5% of the time. I came to this value by adding together the chance of failure and averaging them.

5% + 10% + 15% + 20% = 50 / 4 = 12.5%

The 5/10/15/20 is the chance of failure vs a 1, 2, 3, and 4 on a d20.  I'm not sure which way would work better though.  Hoplefully someone else will chip in.

OK,
  I suck at this kind of thing, but I think this is how you calculate this:
Odds of 1d4, winning or tying vs 1d6
1d4 - Odds
1 - 1 in 24
2 - 2 in 24
3 - 3 in 24
4 - 4 in 24

  Meaning 10 out of 24 times (About 42%) you try, you will succeed. The odds go down to 6 in 24 (about 25%) if ties don't count as a success.

  I will add that roll vs. roll creates a really wide range of outcomes, and can add too much randomness to tactical/competitive games.

  I hope this helps.

Actually, I was part of a game design group that used d4 through d20 as stats for a tabletop wargame.  The math wiz ran 10,000 rolls of each die versus another die and we used those statistics to calculate the cost of the dice.

d4 - 2pts
d6 - 3pts
d8 - 4pts
d10 - 6 pts
d12 - 7 pts
d20 - 14 pts

We found that it was pretty well balanced.  Tactics and special abilities / traits played a greater role in defeating your foe than the dice did.

Here are the probability stats you're looking for.  Attacker is on the left, defender on top.  Assume attacker wins ties.

[code]A/D    4      6      8      10      12      20
4      0.625  0.41666 0.3125  0.25    0.20833 0.125
6      0.75    0.58333 0.4375  0.35    0.29166 0.175
8      0.8125  0.6875  0.5625  0.45    0.375  0.225
10      0.85    0.75    0.65    0.55    0.45833 0.275
12      0.875  0.79166 0.70833 0.625  0.54166 0.325
20      0.925  0.875  0.825  0.775  0.725  0.525
[/code]

[pre]
A/D   d4    d6    d8   d10   d12   d20
d4   52%   42%   31%   25%   21%   13%
d6   75%   59%   44%   35%   29%   18%
d8   81%   69%   56%   45%   38%   23%
d10  85%   75%   65%   55%   46%   28%
d12  88%   80%   71%   63%   55%   33%
d20  93%   88%   83%   78%   73%   53%
[/pre]

Cleaned it up, made it a little easier to read and rounded all the numbers to whole percentages.  Thanks for the proper math Jim D!

Thanks guys. That actually helps a lot.
But in terms of "feel" what do you guys think about it?

Obviously rolling dice vs dice is going to introduce more of a random element to your outcomes than dice vs fixed number.  Which do you prefer for your game?

Oh... crap. I just remembered we used exploding dice which greatly threw off the odds.  From my experience however, both sides rolling dice worked for a tabletop war game, but I don't know about an rpg.

@Luminous I'm a bit of a systems/math twink.  One of the things that attracts me to RPG systems is the complex probability and interaction between various rolls and situations.  If you ever need any other computations done, let me know.  :D