Math question.

[triqui]

Hi everybody.
I'm cooking my own game system (once again...). I like some ideas from Legends of Anglerre/Starblazer version of FATE system, and also some ideas from Dragon Age RPG.

But I've a math question.

To make it simple:

I'm planning to roll +1d10-1d10 + Ability modifier (which is kinda like LoA but with slightly more granularity). Thinking about the Dragon Age focus system (where skills, named "focus", give +2 to ability rolls with challenges relative to the focus), I find it nice, but I'm thinking about a different approach. Just that I don't have enough math skills to know exactly how much it "weights" compared to a flat +2.

My question is, what about adding a second +1d10, then discard the lower?

So, basically, you roll 2d10, take the higher, roll 1d10, substract it, and add the apropiated ability bonus.

And... would it be very different to roll 1d10, then substract the lower of 2d10?

Thanks in advance to the math savvy people outhere

 

[AeroDm]

I get lazy and so often just tell Excel to run 50,000 trials of something and report the results. The "take the higher of 2d10 and subtract d10" averages to +1.6. The "subtract the lower of 2d10 from 1d10" averages to +1.6. They are identical and equivalent to an ability score boost of +1.6.

 

[triqui]

Mmm, thanks, great idea. I'll try myself with Excel then. However, it's not true that an average of 1.6 is the equivalent of 1.6. Adding +1d6 damage in DnD is not the same that adding +3.5 dmg, couse it has lower minimum, higher maximun, and so on. Similarly, rolling 2d6 is, on average, nearly the same than rolling 1d12, however, the bell curve of 2d6 make "7" much more probable as a result than "12", while in 1d12 has same results.

But I guess I can try with Excel and see a few charts to see what I preffer

EDIT: btw, I bookmarked your blog. Nice reading it seems

 

[AeroDm]

I see your point but if we are looking at the probability of hitting a target DC over, say, infinite rolls, a bonus of 2d6 or +7 really are indistinguishable because all we are doing is measuring the number of times the total result surpassed some benchmark.

Thanks for the props. With regards to the site, this post might actually be helpful. It is the first time I talked about my plan for skills which involves training providing re-rolls instead of flat bonuses. I use d20s, but the concept behind the math is similar to your project.

 

[Nagol]

2d10, keep the larger breaks down as follows:

Result   %     vs. +2
 1       1          0
 2       3          0
 3       5         10
 4       7         10
 5       9         10
 6      11         10
 7      13         10
 8      15         10
 9      17         10
10      19         30

Expected value 7.15 or about 1.65 over the base; leaves a slim chance of a very low roll and doesn't have the jump @ 10.

 

[Nagol]

I lost my last line.

A reasonable fit is to give the +2 but cap at the die maximum. That gives a 7.2 expected value, but is simpler to adjudicate at the table.

 

[triqui]

Yes, that article will be very usefull

 

[SiderisAnon]

I think you are better off with a flat modifier than an additional die for one simple reason: Each additional die increases the amount of time you have to spend on each action and so lowers the "fun" of the game.

While some of us can glance at a handful of rolled dice and process them, many gamers cannot. Every time you add another die (especially in this case where it would be compare die 1 to die 2 and pick one based on criteria), you make the math that much harder. Even for someone who can glance at the dice and do it really fast, you're adding a little extra time every time they have to roll that set of dice. Over the course of a combat or a game session, this can start to add up.

If you are only targeting this to your group and nobody else, then this may not be a worry. You know your audience. If you are targeting this toward the general gamer audience, then just having add one die, subtract another die, and apply one or more bonuses is probably at or beyond the limit of what you want to include.

 

[triqui]

I see your point but if we are looking at the probability of hitting a target DC over, say, infinite rolls, a bonus of 2d6 or +7 really are indistinguishable because all we are doing is measuring the number of times the total result surpassed some benchmark.

However, if we are looking not only to hit a DC, it's not the same. For DMG for example, the average damage is a factor, but being able to do higher maximum damage is also a factor. If the skill checks have something like "success rate", +1.6 might not be the same than 2d10 and keep higher, becouse the later might give you higher chance to get extra success, and so on.

I don't know, for example, if the bell curves for 2d10(higher)-1d10 and 1d10-2d10(lower) are the same. But it might mean one of the methos help you more to achieve a really dificult task compared with the others, even if they both have same average result.

However, you've been of a lot of help

 

[triqui]

If you are only targeting this to your group and nobody else, then this may not be a worry. You know your audience. If you are targeting this toward the general gamer audience, then just having add one die, subtract another die, and apply one or more bonuses is probably at or beyond the limit of what you want to include.

I agree with your post in general (+2 is easier than rolling 2, get higher, etc)

However, the bolded part seems to be a bit too much an exageration. Legends of Anglerre uses this (+1d6-1d6), and it´s system is easy as pie.