Deadliest supernatural warrior: the setup

[Cheesefondue]

A long, long time ago, a contributor on this forum promised to upgrade his combat algorithm to allow many different types of strategies (including clinches) in a battle between werewolves and vampires.

That contributor is me, and that promise is now coming to pass, after a long period lost failing to get neural nets to work.

I'll be comparing the combat power of:

Humans, Wraiths, Risen, Hunters, Demon, Mummies, Ghouls, Dhampirs, Kuei-Jin, Mage, Changelings, Vampires, Werewolves, some Fera, and... one mystery guest. It should be quite exciting ^_^

And at the end of it, I'll reveal the ultimate secret of combat victory in the world of darkness... (which may be, or may not be, what you're expecting)


The rest of this post is just explaining the rules and assumptions I'm using for this battle. If any of the rules seem unfair or objectionable, the time to object is now, because it takes several days (at least) to run each battle. Most of the rules are standard, others are ones I'd had to piece together, some are just there to make the decision tree tractable.

[Cheesefondue]

Basic rules:
*I'm using the vampire V20 rules for combat. Main reason: it's that or werewolf, and vampire doesn't have different difficulties for defending against different weapons.
*The exception is the bite rules, which are better in werewolf. Since werewolves can bite all the time, and vampires only when clinched, it seems more natural to stick with the werewolf rules.
*Characters cannot split their action into multiple attacks against the same target (what, the cheatin' caitiff with a dice pool of 16, you want to let her have 16 attacks?!?)
*Clinch is in. A character can choose to clinch another; if successful, they deal strength damage, and all other actions, from both characters, are cancelled for the turn. From that point onwards, there is no difference between the two characters in the clinch.
*In clinch, characters can inflict strength damage, bite (if they have the required fangs), or try to break the clinch. Breaking the clinch cancels all other actions from both characters.
*The vampire has the option of the Kiss if in a clinch. The rules state that vampires only have the ability to resist the Kiss by making a Self-Control/Instinct roll of difficulty 8. I've changed this to a permanent willpower roll of difficulty 8 (since every creature has willpower, and it's generally higher that self-control), doable by anyone.
*The basic combat manoeuvres are punch/claw, bite, clinch, and armed attack. No other moves have been included.
*The characters can spend willpower to get an automatic success on an attack or defence.
*On a botch, the character damages themselves with their weapon.
*It's hard to tell whether the various supernaturals that can heal, can do so in combat. My reading of it is that only shapeshifters and wraiths can heal themselves in combat.
*All types can spend a willpower to ignore wound penalties for a turn.
*Characters in frenzy avoid all wound penalties.
*Characters in frenzy can spend a willpower to be able to make defensive actions that turn.
*Initiative does not change in the course of combat. This means additional wound penalties incurred in combat will not affect initiative until the next turn.
*This also means that adding extra celerity actions can't change initiative, even though it changes dexterity and hence initiative rating.. Therefore, as a compromise, celerity will be counted as half its value (rounded down) for initiative purposes.
*A vampire with celerity must be able to spend the first blood point for extra actions within their generation limits; subsequent spending can go beyond the limit.
*Humans (and any character unable to soak lethal damage) get dazed if they take more damage than their stamina. So do werewolves, as this is specifically listed in their rules. Otherwise, supernaturals get dazed if they get damaged by more than their stamina+2.

[Cheesefondue]

Character/situation rules:
*In each supernatural splat, there will be one basic non-combat character (generally 2/3/3 on physical stats, with 2 in brawl/melee/acrobatics) and one broken power-character.
*Each character is a beginning character. The broken character has been given 7 extra freebie points from non-combat related flaws.
*EDIT: Since some character types (Vampires, Changelings, Shapeshifters) benefit from backgrounds in single combat, while others do not, no-one gets free background points (but they can purchase it with freebies).
*Each character has the option of a strength+2 lethal short sword, which they will take unless they have better natural weapons. Strength+1 aggravated claws are considered better natural weapons than the short sword.
*How to deal with the weapon when in a clinch? The compromise solution is that characters can't use weapons when clinched, but pick them up again - or have then attacked to their hand on a strap - if ever the clinch is broken.
*The combat takes place in a room, which the combatants cannot escape and where they can reach each other every turn.
*Each character gets one turn to prepare. The preparation is done without knowing their opponent, so is always the same.
*Anything attempted during the preparation is assumed to succeed (eg Visage of Fenris). When the number of successes is relevant (eg the Hunter's Foresee power), I assume they have the whole number number of successes closest to their average successes.*Humans, Hunters, and Mages cannot soak lethal damage. All other types can. Aggravated damage can only be soaked by shapeshifters and those with relevant abilities.
*Each combat lasts up to 30 turns.
*If the combat ends in a draw (30 turns without a winner or simultaneous kills), one winner is assigned randomly. Each combat is thus a win or a loss.

[Cheesefondue]

The algorithm:
*The main problem with this is exponential growth. Suppose each character faces five yes/no decisions each turn, in a combat that lasts 5 turns. Then there are 33,554,432 different strategies they can take. If the decision depend on things like the amount of damage they take, or the blood they have left, or what decisions the other character makes, the number of possibilities explodes. Worse than that, since the outcomes have some randomness in them, each strategy has to be run against each other one hundreds of times.
*So the question was how to test the best strategies without testing them all. Methods of deep learning can be used here have a neural net learn the best strategy. But my neural net failed to stabilise.
*So I decided to go for the second best approximation: each player would choose from a certain number of rigid strategies. Then I would compute the Nash equilibrium of these rigid strategies (roughly, which randomises mixes of rigid strategies would perform best), and use that to get the outcome.
*Computing Nash equilibrium is normally difficult, but it's much easier if the game is zero sum, ie if each battle has a winner or a loser.

The rigid strategies are as follows:
General facts:
*When they suffer from any wound penalty, characters capable of frenzy will frenzy (argument: this is the kind of situations where they might be required to pass a frenzy test, and anyone willing to fail a frenzy test will fail), and will thus avoid any further wound penalties. Recall that frenzied characters can spend willpower to attempt defensive actions.

*If they suffer from any wound penalty and cannot frenzy, characters will spend willpower to ignore wound penalties.
*When their opponent is dazed or stunned, they will attack with the maximal attacks they can.
*Vampires and those able too boost stats with blood (or chi) follow the same rigid plan: if they can spend blood to boost (for instance, if they haven't spent it on celerity) they boost Dexterity to the maximum, then Strength to the maximum, then "overboost" Dexterity (Kuei-Jin, who cannot overboost, instead boost Stamina).
*The best attack and defence is chosen in each situation automatically.


Unconditional strategy elements (number of options in brackets):
EDIT: since a preliminary analysis shows that all the best strategies involve spending willpower early, I've removed the option not to do so.
(2) When not clinched, either best normal attack, or try to start a clinch.
(2-3) When clinched, either try to break clinch, do best normal attack (strength damage or bite) or Kiss (vampires only).
(1-4) If character has the possibility of multiple attacks, add 0, 1, 50% of max number of attacks, or 100% of max number of attacks.
(1-4) If character has the possibility of multiple defences, add 0, 1, 50% of max number of defences, or 100% of max number of defences.
(1-6) Split main action between attack and defence. We don't need every option here: consider my broken Caitiff character, with a dice pool of 16 (!). It doesn't matter much whether they split it 9-7 or 8-8 between attack and defence. So there are a maximum of 7 different splits the character can try. Total defence is not possible here.

Conditional strategy elements:
(2) If the opponent has chosen their actions that turn, and they have not included any defence, then either do the usual choices or go for all-out attack.
(2) If the opponent has chosen multiple actions, or has yet to choose and has the possibility of multiple actions (due to unspent rage, blood+celerity, demon chi, etc...), or is a Hunter using all their conviction, then either do the usual or go for a total defence. This is the only way of getting total defence (one cannot win a battle purely with total defence).

*Each combination of rigid strategies is run a 100 times.
*Therefore the most number of strategies available to a character is 2*3*4*4*6*2 = 1152. If two such characters fight each other, there will be a million combinations, each run a hundred times, and hence a hundred million battles.
*Typically, each fight between two specific characters takes at most a few days to run (though I have multiple cores available, running about 8 fights simultaneously).

[Coridan]

No Dark Age Fae?

[Cheesefondue]

No Dark Age Fae?

Nope, sorry :-) No dark age stuff at all, in fact.

The options available aren't enough? :-P

[Barbelith]

The Garou will win.

[Coridan]

Nope, sorry :-) No dark age stuff at all, in fact.

The options available aren't enough? :-P

I just want to see the Fae mop the floor with everyone, cuz a CtD changeling is gonna get wrecked hard.

[Marcus Smythe]

How are you handling rules differences between games? Just as an example, KoTE does not add accuracy to damage pools, but tends to have higher base damage on powers and weapons to compensate.

[Elphilm]

[nothing]

5 oboli on the Risen (especially if s/he's got Passions that will allow Pathos generation during combat).

Cheers!

[Saur Ops Specialist]

How are you handling rules differences between games? Just as an example, KoTE does not add accuracy to damage pools, but tends to have higher base damage on powers and weapons to compensate.

I would assume that cheesefondue is using a baseline Revised/20th anniversary setup for everyone and converting any attacks. Also, KotE got errata in the Vampire Revised Storyteller's Handbook, so that's not an issue to begin with.

[Cheesefondue]

I just want to see the Fae mop the floor with everyone, cuz a CtD changeling is gonna get wrecked hard.

I wouldn't count them out just yet... Currently working on a Troll Wilder (+1 Strength, +1 Damage levels) from house Gwydion (hence can Fenzy) with wayfare 2 (hence multiple attacks...)

[Cheesefondue]

How are you handling rules differences between games? Just as an example, KoTE does not add accuracy to damage pools, but tends to have higher base damage on powers and weapons to compensate.

I defer to the splat's rules if it's a different number (like werewolves getting stunned at stamina, rather than stamina+2), not if it's a different system. There is some subjectivity, I'll admit it.

[Cheesefondue]

Two minor edits:

EDIT: Since some character types (Vampires, Changelings, Shapeshifters) benefit from backgrounds in single combat, while others do not, no-one gets free background points (but they can purchase it with freebies).

EDIT: since a preliminary analysis shows that all the best strategies involve spending willpower early, I've removed the option not to do so.