Probability of Spite Damage and Special Attacks, Revised
Mar 7, 2018 23:40:44 GMT -5
jeffepp, zanshin, and 4 more like this

### Post by gaptooth on Mar 7, 2018 23:40:44 GMT -5

You're designing a monster, and you want to use Spite damage as the trigger for its special abilities. But what is the right Spite cost for the ability?

If it's a powerful ability and you set the Spite cost too low, it could trigger every round, or at least more often than you had in mind. And if it's a utility power and you set the cost too high, it might never trigger at all in a thousand rounds of combat.

The last time I mulled this over, I came up with a formula that turned out to be wrong. But I think Mike's method was in error too.

I'm pretty sure I've cracked it now. For your reference, here is a quick reference table you can use:

Suppose you have a Rhino at MR 100, which gives it 11d6+50 in combat. You want to give it a special Atomic Laser Optic Blast that triggers about once every 6 rounds, on average (about 17% of the time). That would mean it might not even come up once in a whole battle, but it wouldn't be so rare that you'd never expect to see it.

To find out the right amount of Spite to trigger it at least 1 time in 6, find the row for "11" in the Dice column, then go to the "1 in 6" column on that row. According to the table, there is a 1 in 6 chance of rolling

If you required 2 Spite instead, the ability would trigger over 50% of the time, about once in every two rolls on average. If you required 4 Spite for the ability, you might expect it to trigger around 8% of the time. (The actual probability of rolling at least 4 Spite on 11 dice is 9.557%, or about 1 in 10.) Supposing we're happy with it triggering about 1 in 6 rounds, the monster would become:

Let's take another example. You have a jolly old troll whose MR is 88, which gives her 9d6+44 in combat. You want the troll to spend Spite to regenerate damage, but you want to check the probability before assigning the amount of recovery.

Finding the row for 9-die monsters, you notice that this troll is unlikely to roll even 1 spite damage 5 rounds out of 6. Instead, she will get 1 Spite on average at least 2 in 3 rounds. She can roll 2 Spite 1 out of 3 rounds on average, and 3 Spite will only pop up about 1 in 6 rounds, according to the table.

If we make 1 Spite worth 20 hits of recovery, that will give her a 1 in 6 chance of healing 60 hits in one round. (The exact probability is 17.826%.) She could heal 40 hits, nearly half her max MR, 1 in 3 rounds; and she will recover 20 hits more often than not.

Does that make sense?

derv pointed out that it's often desirable for the GM to

In 4th edition D&D, some monsters had abilities—like the dragon's breath weapon—that they could use 1 time only, until it

T&T Spite damage offers a way to do the same thing without rolling any extra dice.

Suppose you want the Rhino to use his Atomic eye-beams once "for free", and then use the dice to see when the ability recharges. After the eye-beam attack, you simple roll its combat dice every round like normal, and when you get 3 sixes, the laser is "recharged" and you can use it again the next round.

Maybe they improved WolframAlpha since I last messed around with it, or maybe I've just gotten better at forming queries. This the way to phrase it: "roll 6 dice probability of at least 3 sixes".

But using WolframAlpha to query every number of dice and sixes rolled would be excrutiatingly tedious, and I knew there had to be a better way. So I read some of the manual for Torben Mogensen's dice roller and probability calculator, coincidentally called Troll, and I figured out how to write a Spite-counting operation in the Troll language:

There might be a better way to do it, but I didn't think of it.

I hope this helps someone in the future!

If it's a powerful ability and you set the Spite cost too low, it could trigger every round, or at least more often than you had in mind. And if it's a utility power and you set the cost too high, it might never trigger at all in a thousand rounds of combat.

The last time I mulled this over, I came up with a formula that turned out to be wrong. But I think Mike's method was in error too.

I'm pretty sure I've cracked it now. For your reference, here is a quick reference table you can use:

Dice | ≥5 in 6 or 83% | ≥2 in 3 or 67% | ≥1 in 2 or 50% | ≥1 in 3 or 33% | ≥1 in 6 or 17% | ≥1 in 12 or 8% | ≥1 in 100 or 1% |

20 | 2+ | 3+ | 3+ | 4+ | 5+ | 6+ | 9+ |

19 | 2+ | 2+ | 3+ | 4+ | 5+ | 6+ | 7+ |

18 | 1+ | 2+ | 3+ | 4+ | 4+ | 5+ | 7+ |

17 | 1+ | 2+ | 3+ | 3+ | 4+ | 5+ | 7+ |

16 | 1+ | 2+ | 3+ | 3+ | 4+ | 5+ | 7+ |

15 | 1+ | 2+ | 2+ | 3+ | 4+ | 5+ | 6+ |

14 | 1+ | 2+ | 2+ | 3+ | 4+ | 4+ | 6+ |

13 | 1+ | 1+ | 2+ | 3+ | 3+ | 4+ | 6+ |

12 | 1+ | 1+ | 2+ | 2+ | 3+ | 4+ | 5+ |

11 | 1+ | 1+ | 2+ | 2+ | 3+ | 4+ | 5+ |

10 | 1+ | 1+ | 2+ | 2+ | 3+ | 3+ | 5+ |

9 | 0+ | 1+ | 1+ | 2+ | 3+ | 3+ | 4+ |

8 | 0+ | 1+ | 1+ | 2+ | 3+ | 3+ | 4+ |

7 | 0+ | 0+ | 1+ | 1+ | 2+ | 3+ | 4+ |

6 | 0+ | 0+ | 1+ | 1+ | 2+ | 2+ | 3+ |

5 | 0+ | 0+ | 1+ | 1+ | 2+ | 2+ | 3+ |

4 | 0+ | 0+ | 1+ | 1+ | 1+ | 2+ | 3+ |

3 | 0+ | 0+ | 0+ | 1+ | 1+ | 1+ | 2+ |

2 | 0+ | 0+ | 0+ | 0+ | 1+ | 1+ | 2 |

1 | 0+ | 0+ | 0+ | 0+ | 1 | 1 | 1 |

**How to use it**Suppose you have a Rhino at MR 100, which gives it 11d6+50 in combat. You want to give it a special Atomic Laser Optic Blast that triggers about once every 6 rounds, on average (about 17% of the time). That would mean it might not even come up once in a whole battle, but it wouldn't be so rare that you'd never expect to see it.

To find out the right amount of Spite to trigger it at least 1 time in 6, find the row for "11" in the Dice column, then go to the "1 in 6" column on that row. According to the table, there is a 1 in 6 chance of rolling

*at least*3 Spite with 11 dice. (The actual probability of rolling 3 or more Spite with 11d6 is 27.322%, which is about 1 in 4.)If you required 2 Spite instead, the ability would trigger over 50% of the time, about once in every two rolls on average. If you required 4 Spite for the ability, you might expect it to trigger around 8% of the time. (The actual probability of rolling at least 4 Spite on 11 dice is 9.557%, or about 1 in 10.) Supposing we're happy with it triggering about 1 in 6 rounds, the monster would become:

Atomic Laser Eye Rhino. MR 100, Goring charge (11d6+50).

3// Atomic Laser Optic Blast. The beast's gaze falls on 1 random target, who must make a L1 SR on LCK. If they make it, they suffer a mere 6d6 damage. On a miss, they are completely atomized, as with a Hellbomb Burst spell.

Let's take another example. You have a jolly old troll whose MR is 88, which gives her 9d6+44 in combat. You want the troll to spend Spite to regenerate damage, but you want to check the probability before assigning the amount of recovery.

Finding the row for 9-die monsters, you notice that this troll is unlikely to roll even 1 spite damage 5 rounds out of 6. Instead, she will get 1 Spite on average at least 2 in 3 rounds. She can roll 2 Spite 1 out of 3 rounds on average, and 3 Spite will only pop up about 1 in 6 rounds, according to the table.

If we make 1 Spite worth 20 hits of recovery, that will give her a 1 in 6 chance of healing 60 hits in one round. (The exact probability is 17.826%.) She could heal 40 hits, nearly half her max MR, 1 in 3 rounds; and she will recover 20 hits more often than not.

Zebajina, a Troll. MR 88, Smashy fists (9d6+44).

1// Trollish Adrenaline Rush. Recover 20 hits for each Spite you spend on troll adrenaline.

Does that make sense?

derv pointed out that it's often desirable for the GM to

*choose*to use a special ability. I dig that, but you can still use Spite triggers as a way to manage the cooldown.In 4th edition D&D, some monsters had abilities—like the dragon's breath weapon—that they could use 1 time only, until it

**recharged**. After using it once, the GM would check every round to see if the ability recharged by rolling a d6, and the ability would tell you what you had to roll.T&T Spite damage offers a way to do the same thing without rolling any extra dice.

Suppose you want the Rhino to use his Atomic eye-beams once "for free", and then use the dice to see when the ability recharges. After the eye-beam attack, you simple roll its combat dice every round like normal, and when you get 3 sixes, the laser is "recharged" and you can use it again the next round.

Maybe they improved WolframAlpha since I last messed around with it, or maybe I've just gotten better at forming queries. This the way to phrase it: "roll 6 dice probability of at least 3 sixes".

But using WolframAlpha to query every number of dice and sixes rolled would be excrutiatingly tedious, and I knew there had to be a better way. So I read some of the manual for Torben Mogensen's dice roller and probability calculator, coincidentally called Troll, and I figured out how to write a Spite-counting operation in the Troll language:

`\ Count the number of Spite`

\ for any given number of dice.

function spite(n) =

x := count 6 = n d6;

if x=0 then x else x

\ Call the Spite counter for 11 dice.

call spite(11)

\ Change the "11" to any other number

\ to calculate the probabilities

\ of Spite counts for different numbers

\ of dice.

There might be a better way to do it, but I didn't think of it.

I hope this helps someone in the future!