How do I get a diminishing return curve besides using a dice pool?

Extrakun

Tinker of Games
Validated User
#1
From my understanding, a d6 dice pool mechanic where you count 6 as success has a diminishing return curve. That is, for every +1d you have, the increase in chance of getting one success diminishes. How else get I get this effect without using a dice pool?
 

The Benj

Registered User
Validated User
#2
The chance of getting an extra success from each die diminishes, yes. So the chances of getting 2 successes on 2d6 is less than that of getting 1 success on 1d6.
The closest equivalent I can think of for a linear die is difficulties increasing faster than bonuses.
 

Max

A dapper chap without a doubt
RPGnet Member
Validated User
#3
The chance of getting an extra success from each die diminishes, yes. So the chances of getting 2 successes on 2d6 is less than that of getting 1 success on 1d6.
The closest equivalent I can think of for a linear die is difficulties increasing faster than bonuses.
I think Extrakun was rather referring to how, when you add more dice, the chance to roll at least one success keeps going up, but at a diminishing rate for each subsequent die.

For example, let's say you're trying to roll 4 or higher on d6. On a single die, the probability of doing that is 50%. On two dice, it becomes 75%, an increase of 25 percentage points. On three dice, it becomes 87.5%, a further increase of only 12.5; on four dice, it's 93.75, now only increased by 6.25; and so on. The chances keep going up, but each added die has a smaller effect than the previous one.

The most common way to mimic the large scale outcome, if not the phenomenon itself, with flat dice seems to be escalating costs for stat/skill/whatever modifiers. E.g. a +1 modifier costs 1 point, +2 costs 3 points, +3 costs 6 points. +4 costs 10 points and so on. Or otherwise making higher modifiers exponentially, rather than geometrically, harder and more expensive to achieve.
 
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phatonin

Chaos is a bladder
Validated User
#4
With a fixed dice pool, each decrease of target number below the median has diminishing returns.

For instance 2d6, median 7. A target of 5 is less better than 6, than 6 is better than 7.
 

The Benj

Registered User
Validated User
#5
I think Extrakun was rather referring to how, when you add more dice, the chance to roll at least one success keeps going up, but at a diminishing rate for each subsequent die.

For example, let's say you're trying to roll 4 or higher on d6. On a single die, the probability of doing that is 50%. On two dice, it becomes 75%, an increase of 25 percentage points. On three dice, it becomes 87.5%, a further increase of only 12.5; on four dice, it's 93.75, now only increased by 6.25; and so on. The chances keep going up, but each added die has a smaller effect than the previous one.
Yes, both of these things are true.
 

Knaight

Registered User
Validated User
#6
Static TN games get this. If you need to roll at least a 4, going from a d6 to 2d6 to 3d6 goes from a 50% chance to a 91.7% to a 99.5% chance, a notable decrease. Similarly going from d4 to d6 to d8 to d10 to d12 goes from 25% to 50% to 62% to 70% to 75%. The same applies to variable TN curves, such as a dX-dY system where X is skill and Y difficulty. It's a pretty common statistical phenomenon, largely because 0 and 1 are hard limits and you tend to see squishing if you can get them to act like asymptotes.
 

eeldip

Registered User
Validated User
#7
i hate to say this... but you can always kick it old school and use something like a d100 and a table. i feel like i recommend a vovelle every other post, but they are way more fun than a straight table, and do the same thing.
 

The Benj

Registered User
Validated User
#8
i hate to say this... but you can always kick it old school and use something like a d100 and a table. i feel like i recommend a vovelle every other post, but they are way more fun than a straight table, and do the same thing.
What's a vovelle?
 
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