Maths and probability

[Andeu]

I was toying with the idea of modifing the Blue Planet rules, when it comes to skills and throwing. In short: You have skills with numbers between 1-10. When you roll against any of these skills you roll 2 d10. If the lowest dice rolls equal or under your skill, you have succeded.

Example: Character A have a climingskill of 5. He/She then throws 2 d10 and rolls a 3 and a 7. The lower die indicate a success, the other die is ignored.

So far I like this system. But I would like to know from some of you math people out there how this turns out proabilitywize. At what point does a character have a 50% chance of success. What would be the chance of failing if you got a skill of 7? Is there some easy math formula that I could use?

[Chris S]

Yes, there is an easy way of working it out.
The chance of both dice failing is equal to the square of the chance of a single die failing. Once you know that, the odds of success are straightforward.

Skill	Chance of succeeding
1	19%
2	36%
3	51%
4	64%
5	75%
6	84%
7	91%
8	96%
9	99%
10	100%

I've heard of Blue Planet, but I'm not familiar with the rules. Can you explain how your modification changes things?

[Andeu]

Thanks for the help.

Blue Planet system:
Skills are devided into groups. The firearm group contains shooting with firearms. The Pilot group contains all driving skills ect. During character creation you decide which skillgroups you want to be good at. The skillgroups that are most to your liking gets a roll of 3 d10. Some other skillgroups gets 2 d10, and the rest gets 1d10.

The skills are then paired with a attribute, for either a bonus or penalty. If i have +1 intellect and tries to hack a computer I get +1 to my skill. I then roll either 1,2 or 3d10 depending on how many dices I put into the "tech" skillgroup.

Only the lowest roll counts.

The system is fast and easy. And thats why I like it. The only problem is character developent (in my eyes). During character creation you choose your path, and players follow that path. A "warrior" type character will probably not want to waste alot of xp on skills like first aid, because, even if he gets the skill to 6-7, he still have a good chance of failing the roll (hence only throwing 1d10). I don't like "classes" and anything that resemble the D&D system. I want my characters to be able to choose what they want to be.

So I am going to try a few session with this "all skills got 2d10" and see where it gets me. It might be bad, but thats what playtesting is all about

[Erudite]

[Patrice]

oO rolling?

I mean... Rolling? That's what maths are actually for, to avoid rolling. I wonder where you go rolling 1,000 rolls, I mean you'd re-invent the probabilities and statistics mechanics from a scratch. Sorry for being blunt but, come on, don't roll! The maths involved are pretty simple and there's always a math head around to help you, using a formula that will lead you exactly to the same result (except a finer, clearer one) than rolling 1,000,000 rolls.

[Erudite]

oO rolling?

I mean... Rolling? That's what maths are actually for, to avoid rolling. I wonder where you go rolling 1,000 rolls, I mean you'd re-invent the probabilities and statistics mechanics from a scratch. Sorry for being blunt but, come on, don't roll! The maths involved are pretty simple and there's always a math head around to help you, using a formula that will lead you exactly to the same result (except a finer, clearer one) than rolling 1,000,000 rolls.

Yes, I actually rolled dice dozens of times. Yes, it is a crazy thing to do. Yes, it took a while. However, it was worth while. What I found was interesting. My results did not align directly with the statistical averages or expected outcome.

[LordNyax]

Apparently you don't really get how probability works. The point of mapping the probability of random chance is to get an idea of the most "expected" outcome. It is still random and you will not always get the most expected outcome. I could potentially roll a six sided die 50 times and get a mean of 1 instead of the expected mean of 3.5, but that doesn't mean that probability has warped itself in my presence and that I should always expect to get a mean of 1 when rolling a six sider. Basing a system off one's infinitesimally small sample space of "dozens of rolls" is just silly. No matter what your personal experience is, if you're making a dice roll system and want to know the statistical probability ratio of success to failure or something else like that, using probability theory is far more accurate than rolling the dice a hundred times and expecting the outcome to always stack like that.

[Erudite]

[LordNyax]

There's no point in trying to model randomness though, because any model that you make will be completely inaccurate the minute you start adding more data. It is expected that in practice you won't get the same ratios that you get from mathing it out, but it is still the highest accuracy model one can possibly make to simulate a system like this. While your sample size is so small of course it could be greatly off the expected value, but if you were to create another, equal sample size it could be just as wildly off in the other direction, making your original test worthless.

Just think about it this way: If I were to flip a coin 100 times and get a ratio of 40% heads to 60% tails, should I logically expect this coin to always give me that same ratio? Of course not, because I know that I should expect a 50/50 ratio and that my sample size was just too small. Expecting to use a sample of dice rolls to map a probability system more accurately than the mathematics is the exact same thing, just on a more complicated scale. I'm not trying to be mean XD, just trying to point out that rolling dice a hundred or few hundred times and getting "large differences from the probability" doesn't mean anything other than that you didn't roll the dice enough times to get an accurate ratio.

[dindenver]

Hi!
  I think there is a point to actually rolling.
  As long as it is the whole procedure (Modifiers, target numbers, etc.).
  The point is, you get a sense of how the procedures feels.
  Sure, maybe the math says you will succeed on an "Average" task 50% of the time.  But, does that feel right after an "average" task is defined and the various modifiers are brought into play?
  Maybe a modifier that you thought was inconsequential ends up skewing the success rates. Maybe a modifier that you thought would be a real deal breaker has little or no mechanical impact.
  The more moving parts you add to a machine, the more that can break down.
  I don't know if that is what Erudite was trying to say. But I think it is worth saying either way.

[Vulpinoid]

  I think there is a point to actually rolling.
  As long as it is the whole procedure (Modifiers, target numbers, etc.).
  The point is, you get a sense of how the procedures feels.

I don't want this to sound like a "Me Too" response, but this is a perfectly valid reason to conduct a simulation of the mechanics though the physical act of rolling dice.

Running figures through a program or a statistical analysis might give an impression for how the results should end, but it doesn't really give a good feel for the suspense that develops before a roll is made, or the confusion that develops in the immediate moments afterward as players try to work out how the results of the die roll reflect in the game world.

Of course, this is where playtesting really comes into its own as well.

Back to the original topic though...

Example: Character A have a climingskill of 5. He/She then throws 2 d10 and rolls a 3 and a 7. The lower die indicate a success, the other die is ignored.

Do you consider the option of multiple successes?

What happens if both dice meet the success requirements?

V