Malifaux Theorycrafting

[lipman]

I was hoping to start a discussion on the theorycraft behind Malifaux. I am a numbers nerd, so I enjoy doing this type of stuff, and like talking to others about it as well, so I welcome any input.  A little background on why I started down this path.  I am playing a Shifting Loyalties campaign with some buddies and I was thinking about 2 of the campaign upgrades (skills) that I have had the chance to buy. 

Off Hand Fighting costs 4 scrip to purchase, 0 SS to attach.  It gives you a + to attack flips.

Duelist costs 4 scrip to purchase, 0 SS to attach.  It increases your Ml stat by 1, up to a max of 7.

 

I started down the path of evaluating those two and realized that I needed to take a step back.  First, how do you assign a value to something like that.  I can think of a few ways to measure in Malifaux.

- Soul Stones: Calculate the expected value in SS of the item.  This is great for models and upgrades because you can easily compare it to the actual SS cost.  It also helps you calibrate any formulas you have, as you can find an upgrades and models that have that ability and see if your numbers match up.

While SS cost is a good baseline, it doesn't really capture what the end goal is, and it can really only be applied to models and upgrades.  While you could assign a SS cost to a particular action, I am not sure it would be that easy to translate.

 

- Victory Points: The Performer has an ability that lets her take an interact action while engaged.  That action can easily translates to a VP value.  Just figure out (or estimate) how often she will use that value per game and how many VPs it will gain each time.  And presto, expected VP value!

I don't think VP value is that great of a measure as well, since a lot of actions don't directly influence your VP (either denying opposition VPs, denying them activations, etc).  So what we would likely end up with is a crew where the total expected VP is something like 15 despite the fact that you can only score 10vp in a game.  You could just normalize it down, but then you would lose the clarity of saying something gives me X VPs on average, and I would get to do it Y times a game, the value is X times Y.

 

- Win %: This might be the best option for actions and whatnot, but I think it is going to be a pretty convoluted calculation.  Essentially you are trying to figure out what each action, model, upgrade, etc adds to the chances that you win the game.  In a perfectly balanced game, the two crews add up to 50% each.  This would need to be scaled to the crew size however, as a 10SS model would give a much higher Win % in a 25ss game than he would in a 50ss game.

 

I think the best way to calculate all of these values is an iterative process where you assign a value to the basic building blocks, then use those to assign a value to the next level of complexity, and work your way up.  For example, if you can assign a value to a single point of AP, then you can work from there to assign a value to Imbued Energies that gives a model fast at the expense of the card. 

So what all needs to have a value assigned to it in order to calculate the values of stuff. 

Not an exhaustive list by far, but where I am starting at...

AP

AP manipulations (fast, slow, paralyze, etc)

Activation delay (either an ability, or the fact that you have more models than your opponent)

1 point of each stat (this will need to be on a point by point basis, as going from 3 def to 4 def isn't nearly as valuable as going from 6 to 7)

+s and -s to attack/wp/def/etc flips

Melee/shooting/casting range

Damage spreads

Healing flips and abilities

Control hand card value (being able to have additional cards, cycling through cards, etc)

Generic abilities (attack, walk, interact)

Movement abilities (flight, ignore hazardous terrain, etc)

Push abilities

Wounds

Summoning abilities

Armor and defensive abilities (hard to wound/kill)

And a ton more.

 

The vast majority of my experience with Malifaux is playing Arcanists, so that is where my head is at mostly.  I know that I am missing a lot of Arcanists type stuff that should be on the list, and I haven't played many of the other factions, so I don't really know any of their abilities, so I am likely missing a TON of stuff from that list.  But it is at least a starting point.

 

But after all of that, I am going to jump back to my original question that started me down the path.  Which is better, + to melee attacks or +1 to your Ml stat?

 

I ran some numbers and here is what I figured out.

For a straight Ml vs Def duel, there are 2,916 combos of outcomes (54 cards for attacker * 54 cards for defender).  That isn't the case in practice, as we know what our control hand is, what cards we have already flipped, etc.  But while evaluating these things in a vacuum, it works.

For a Ml vs Def duel where the attacker gets a + to the attack flip, there are 154,548 combos (54 cards for attacker's 1st card * 53 cards for attacker's 2nd card * 54 cards for defender)

I assumed a Ml stat of 6 for both sets of test.

For the +1 Ml stat, it raised your chance of success by anywhere from 5.8% to 7.2% (depending on what Def you are facing)

For the +twist to attack, it raised your chance of success from 13.5% to 15.1%

 

I was pretty surprised at that result, but I guess I shouldn't be as the average straight flip is a 7, while the average +twist flip is a 9.  So +twist gets you 2 pts on average where the other option only gets you 1. Those raw numbers of course aren't the only thing to take into account. 

For the +1 Ml stat, there is an added value to either forcing opponents to have to cheat in higher cards to beat you, or knowing that you can cheat your 13 in and guarantee a success (against somebody who's defense is 1 below your Ml)

There is also value in having a +twist to damage so that it can negate any -twists that you might have and let you cheat that attack flip.  I think this value is much less for a Ml attack than it is for a Sh attack, as the Sh attack will have a lot more -twists due to cover. 

 

I am not sure how to value those two considerations.  My gut says they feel pretty close to each other.  Being able to plan out attacks and know that something is going to hit can be pretty powerful when planning out a turn.  If I can use the 13 in my control hand to all but guarantee that my Performer will paralyze their master, then that is much better than having the +twist (bad example as that is a Ca action, not a Ml one, but you get the idea). 

So there are probably cases where the +1 Ml is preferential, but I think for 95% of the situations, the +twist is going to be the better option.

 

Would love to hear other thoughts on this.

 

Next time, I will try and tackle how valuable fast/slow is.

[H4ml3t]

I like where you are going with this as I'm a numbers nerd too and like getting under the hood and looking at the engines that make games run.

At the moment I'm too tired to contribute anything more than encouragement but in the near future I should have useful things to add...

[Adran]

Its not as clear cut as that as to which is best. Partially because we are using a deck of cards, and whilst the average result is (6+9) 15 for the positive flip, that can't happen more than 4 times in a deck of cards at most. 

The positive flip doesn't effect the range of your final total, it is still between 6 and 20. It doesn't matter how many positives you have, you'll never reach 21, and you'll only reach 20 on very rare occasions (something like 1 in 27 times. although it is possible to pass through a complete deck with out ever reaching 20 if the red joker and black joker appear on the same flip). The case with +1 ml will get to 20 or higher 5 times in 54 from a complete deck, so over 2 and a half times more likely. 

The control hand also throws the odds out a little bit, as that 10 I have in hand is always going to be a 10, so on the positive flips will get me to 16, where the bonus to Ml will get me to 17. The advantage of the positive flip when you take cheating into account is that firstly, it will allow you to cheat in situations when normally you couldn't, and secondly, you are more likely to be able to cheat second, so not wasting a card to no effect. 

 

I'm looking fowrad to what else you think though. Not sure I agree that changing df 6-7 is more powerful than changing 3-4. 

[lipman]

3 hours ago, Adran said:

Not sure I agree that changing df 6-7 is more powerful than changing 3-4. 

Well, my initial logic was that going from a 6 to 7 adds a lot more value because you are most likely going to be +1 against any attack.  So that should give you the advantage of knowing you can pass with a 13 (ignoring the RJ)

But the other aspect that I was considering is that somebody with a def of 6 is designed to be in the thick of things taking hits, so they would get more use out the +1.  A model with a def of 3 is either designed to stay far away from danger, or has other defensive tricks that save them (like the silent one's statue ability), so the +1 def isn't as valuable.

Having said that, it seems disingenuous in a theorycrafting post to throw out comments like that without having any backing.  So I officially recant that statement