What is a Wound worth?

[Guy in Suit]

Coming off my second consecutive Adepticon win, I wanted to start a series of Malifaux strategy articles - just to answer a few questions I get when I bump into people at tourney's or on the interwebs, as well as expand on and document some of the ideas that run through my head while playing.

Not to waste peoples time discussing individual models in detail with all the changes on the horizon, as well as to make these relevant to all faction players, (I play Outcasts exclusively) I will not be including any model specific tactics in these articles.

It may all just come out as meaningless drivel, and if so, whoopsie! But I hope some of these ideas prove useful in your games! So, without further adieu...

Item #1 - What is a Wound worth?

A wound is worth 6.8 *grin*

I like to use overly simple math to guide me in the right direction in my games. I find that trying too hard to calculate exact odds or evaluate situations boggles your brain down during a match and gives your opponent the initiative, but having a few simple rules to follow makes your Cheat decisions easier and allows you to focus more on multi-turn play.

To start with, you need a baseline metric to gauge the value of the cards in your hand. This changes from match to match and crew to crew, but usually it is pretty easy to figure out.

My normal metric is as follows-

Weak and Moderate cards - face value

Severe Cards - face value + 5

Red Jokers - 25

Black Joker - 5 x Turns Remaining

Note that the Black Joker is an obvious anomaly. Its only value is that if it is in your hand it cannot be flipped from the fate deck, hence why its value declines overtime. 5xturn count is entirely arbitrary and I discard or change this all the time based on hunches/ how ****ty I will feel if I flip the black joker two turns from now! There are of course myriad crew selection factors that weigh on the value of the Black Joker. Note that this value is only considered during the discard phase or when forced to discard cards. It does not add to the hand value discussed below.

There are of course reasons you might tailor this. Maybe you have an ability that requires you to discard cards, using Jack Daw, or facing a bunch of Headshot/Decapitate. In that case, you may arbitrarily raise the value of cards by 2-3 to account for the intangible value of having control cards to discard.

Maybe you have the ability to draw cards, causing you to lower the value of your cards. (Lowering the value doesn't make them less useful, it just increases the likelihood that you will use them!)

Another variable is to weight cards based on suit, I tend to give +5 to masks when the Viktorias are in range of a juicy whirlwind opportunity!

So, assuming you draw six cards per turn, you will draw about 38 cards during the Scrap. If you draw 7 cards, this would be 45, etc. Note that models like the librarian can complicate things - I tend to just call the need to discard a card of a particular suit vs. the 7th card a push and just use 38 to keep it simple.

Note, your Sue, Jakob Lynch, etc. players who draw additional cards during the game face a tough decision here, do you want to include those potential draws in your strategic calculations (playing loose) or do you want to consider them a mid-match potential bonus, but not to be relied upon (playing tight). Note the alternative is to just lower the value of the cards as discussed above.

So given a 38 total card draw and a 8.84 average card value (don't include BJ here), you get an average hand value of 53 per turn, for a total of about 340 for the match. This is the numerator to determine a wounds value for the game. The denominator is simply the number of wounds needed to guarantee victory. I use the number of wounds in the enemy crew, as that just fundamentally how I play, but YMMV.

So given a typical 35SS game, lets say the enemy crew has a wound count of 50. This pegs my wound value at just below 7. This means that if it GUARANTEES an extra wound, I should be cheating a 6 or lower and holding on to 7's. If it nets me 2 wounds, all cards 10 and lower would be cheated, 11's are still held because they are worth 16! This means I would normally only be cheating in my severe if it would do 3 Wounds more than weak. (I cheat a lot of face cards on Ronin, for example, as the guaranteed number of wounds go from 2-5 if I flip weak on damage, even against opponents with armor.)

The hard part about this calculation is what exactly 'guarantee' means. It is obvious on damage, as before you cheat, you know how much damage you are doing if you don't cheat, and you know how that damage will translate into Wounds.

It's also straightforward on opposed duels where you win the initial flip. After your opponent has cheated, you know exactly what you are getting for your card.

Going back to our Ronin example - she flips a 6 + Cb 5 =11 vs. a Df 4 model who also flips a 6. The opponent cheats an 8 to make the attack miss. In this example, I would very likely cheat any card 10 or lower to make the attack hit, as it guarantees two wounds. (Discount the black joker here, unless you are a near the end of your deck and haven't seen it.)

It is much more complicated on opposed duels where you lose (when the opponent has cards left).

Looking at the previous example, let's increase the defenders Df to 6. Now I know that I have the *chance* to do 2 wounds, worth 13 points, if I tie or win the duel. However, my opponent can cheat over me causing me to do zero wounds. Therefor I have to weigh the odds of this happening. The simplest way to do that is to gauge my opponents remaining hand strength to determine the likelihood that they have the card needed, and then decide what the likelihood is that they will use it. Assuming they had a 6 card hand, their average hand strength is 53 less what they have cheated so far. Lets assume they tossed a low card make a self-inflicted attack hit a canine remains and a high card to summon a Flesh Construct for a total of 18, leaving them at 35. This puts the average value of their 4 remaining cards back at the starting point of approx 8.75.

Here you can really go down a rabbit hole of probability, looking at the standard deviation of card odds to see what the odds are that they can beat a certain total, but lets avoid that for the sake of simplicity/sanity. I like to simply say that my opponent will consider it no skin off their back to cheat a below average card, and a weightier decision to cheat an above average one. Therefor them cheating a 8 or lower in this example is considered automatic, and cheating a 9 or higher has a 50% probability. (Yes, math geeks, this is totally arbitrary!)

Back to our example, although a 7-8 would meet or beat their starting total, potentially netting me 2 Wds, I am assuming my opponent cheats an 8 or lower if needed automatically, resulting in 0 wounds. (Bad deal) There are of course intangibles or specific circumstances that could cause me to value costing my opponent a card much higher than holding onto a card myself, but these are fairly rare, so normally cheating a 7-8 here is a mistake. Cheating a sever here is also a mistake, as the value of the two wounds is less than the value of the severe card, same as above when we won the duel. The hairsplitting comes down to your 9's and 10's. On a 9, you have a 14 total, requiring an 9 or higher to prevent the damage. As we arbitrarily assumed above, there is a 50% chance your opponent is willing to cheat a 9 or higher to prevent you from doing any damage. On balance, this makes cheating the 9 a bad call, as your guaranteed wounds have only a 50% chance of taking place, so only 1 wound after multiplying by the probability. However, the 10 is the sweet spot for you on offense. Now your opponent must cheat a 10 or higher to prevent - which we must assume is less likely than before. If we say it is only 25% likely (it is significantly lower due to the much higher value of face cards, decreasing the likelihood of them being used), then our average number of wounds goes to 1.5 - worth 10.2 points, just under the value of our cheated card!

Spells are obviously even more complicated, as they must generate their totals prior to seeing an opponents resist flip and often have triggers or suit requirements that greatly skew the odds. I will not be expanding on this at this time, but once you play a given mini with spells often enough, you soon are able to gauge the likelihood of causing wounds from it's effects, and can begin to build assumptions that can help you determine the point value of successfully casting a spell. I know for example that I put the value of Entropic Transformation quite high, and cheat for it all the time!

Often in a match, these borderline calls gets influenced by gut feelings, and what I have observed about the strength of my opponents hand by my own count of his cards and his actions during the turn. Also if I have a very good count on my own deck to the point where I can gauge the probability of flipping higher than weak on flips, can will start playing a little loose with my 6-10s on opposed duels. Both of this factors can obfuscate the main point of this thought process though - so we will hold of until a future article!

Please chime in with your thoughts or to pose in game examples that we can work through together. Also, feel free to hit me up on Twitter @andrewweakland.

Edited May 7, 2013 by Guy in Suit

[Ryu]

For severe cards where does the +5 come from, or is that an arbitrary number to reflect their higher weight?

[Guy in Suit]

Yup, it is entirely arbitrary. Part of it comes from being able to use it + a soulstone for an unstoppable total, part of it comes from casting requirements of uber spells, part of it comes from damage spreads on certain models etc. etc.

Its a little buried in the meat of the article - but essentially the strategy boils down to finding a target number using assumptions that you can stick to throughout the match to make your decisions easier.

[Ryu]

Yep, I read the whole thing - very interesting stuff. Just wasn't sure if the base value of the severe was also arbitrary, since the values of the weak-moderates aren't and the jokers obviously have to be abstracted to an extent.

[Guy in Suit]

Yeah, the +5 assumption is just what works for me - it makes the math easy and I like the separation between severe's and the other cards.

I initially started valuing moderates and severes at their average, 8 and 12, since they are all the same on the damage flips and this made the math very easy. However, I found that this tended to undervalue cards on opposed duels, and overvalue them on damage flips.

I've also considered 'regressing towards the mean' to try and capture the fact that 6's are slightly more valuable than their face values and 10's less so due to the nature of damage flips - but this just gets god-awfully complicated and involves decimals soooo NO.

I thought about blending the two as well, using the former during duels and the second on damage but vetoed that as then you create an apples and oranges situation and thereby defeat the point.

[Odin1981]

I like how you put a value to cards in your hand. I often (don't put a value but I don't often play a faction with a bunch of inbuilt +'s to damage) value any card in my hand of a 8 or higher. 6-7's I normally value to cheat to a - flip for damage on an opponent attack or best case scenario I cheat for a - flip then they have to cheat a severe in for a straight flip, don't hit a severe on said flip and then have to spend a second severe out of their hand for 1 severe damage.

[Guy in Suit]

6-7's I normally value to cheat to a - flip for damage on an opponent attack or best case scenario I cheat for a - flip then they have to cheat a severe in for a straight flip, don't hit a severe on said flip and then have to spend a second severe out of their hand for 1 severe damage.

You bring up a very good point, and I didn't really give good examples of how to calculate these odds on defense.

If you use a 7 vs. two severe's (Call them 11s for 32) that's a pretty great deal. They need to cause at least 4 wounds over what they would have otherwise to overcome that 25 point spread - so only in oddball damage spreads like Levi/Hamelin is that the right call.

From your perspective, you saved over 2 wounds (value of the second severe card) from being dealt somewhere else, so a great value for your 7.

I very often find that when opponents use two severe's on a single action it is inefficient overall, and the math backs that up pretty well.

[Odin1981]

Yep to avoid a huge amount of probability turning off a bunch of people viewing this a straight flip for damage on a fresh deck (1-2 activations into a turn) there is only around a 20-25% (math would give a exact but don't wanna turn people away) chance of hitting severe naturally on a straight flip.

Also the average "hand" must will draw from say turn three on (due to building your hand up over first two turns then expending it on two or three) is 1 severe, two moderate, and two weak cards plus an additional "wild card". So most of the time when I construct a list for a non casual game (competitive environment) I make the list up with this in mind.

Often times what this does in a game is that the one severe damage they due that turn turns their (opponents hand) to a few moderates and weaks left for the rest of the turn to cheat their totals with.

[Csonti]

Very interesting stuff. Thanks for sharing!

I need to digest this a bit but I think Malifaux has so much complexity that in many cases this clever but simple algorithm of yours would yield false results and finetuning it all the time just kills the point of having a base calculation system. For example bringing a model from 10 Wd's to 9 can't be compared with the case of 1 Wd to 0. Or hurting a key support model vs an avarage all-around minion. Or causing 2-3 wounds vs pushing the model from a key territory without inflicting damage etc. I would like to hear more from you regarding these "problems".

[CRC]

You value your cards in hand as if you had only them to deal damage to your opponent.

Sometimes your models will damage your opponent without cheating, and sometimes you need to use your cards to defend your models. Are you just assuming these will balance out?

When valuing defensive use of cards, would you still use your opponents wound count for the denominator, or would you switch to your own wound count? (Assuming they differ enough to matter)

[Ryu]

Yeah, it's interesting to see how people do their internal calculations. I simply card count my enemy's severe cards + jokers and try and keep a simple running analysis of what they have in their hand by how and when they cheat.

I weigh killing a model higher than not-killing it and so I'm more apt to spend more resources to make something die than I am to not do so.

This approach is a great baseline though, and I don't think that he's saying to follow the formula explicitly, he says straight up that a lot of times gut feelings are factored in and the weight of cards is variable depending on card draw and other factors.

[Guy in Suit]

For example bringing a model from 10 Wd's to 9 can't be compared with the case of 1 Wd to 0. Or hurting a key support model vs an avarage all-around minion.

Remember, we are already past the target selection step at this point. If you are targeting an unwounded model with you AP rather than a wounded one, you are making a mistake in AP allocation and/or model placement. (Probably would have made sense to do those articles first, eh?)

All wounds are worth the same to accomplish a stated objective - in my examples I used the objective of killing all enemy models, you could simplify it down to killing a specific model. The first wound and the last wound are worth the same until the models dead. Unless of course, it isn't

Special cases such a Rafael Lacroix/Santiago can skew this a bit, obviously. hard to kill is pretty easy as it presents a hard cap on potential wounds. But I find by and large it is a very useful metric in determining the right point of action in a borderline scenario.

As you said, often times the right course of action is obvious and on such a simplification would be a mistake - missing the forest for the trees, if you will.

---------- Post added at 04:04 PM ---------- Previous post was at 04:00 PM ----------

You value your cards in hand as if you had only them to deal damage to your opponent.

I meant for this to be clearer and may go back and revise the article, but you are correct, I consider BOTH wounds caused to the opponent and wounds prevented on myself. And yes, I usually just use the opponents wound count to do the maths. I'd consider taking an average if there was a huge disparity. And don't infer that I am sitting there in a match doing long division to figure out some exact total. Usually Its just to find the magic number, usually 6 or 7, that I can weight borderline decisions on.

[Csonti]

Remember, we are already past the target selection step at this point. If you are targeting an unwounded model with you AP rather than a wounded one, you are making a mistake in AP allocation and/or model placement. (Probably would have made sense to do those articles first, eh?)

You misunderstood my notes. Under A vs. B I didn't compare two things that could be done in the same moment of the game but two different situations that lead to the same conclusion under your system. For example making 1 Wd on a model doesn't worth a 7+ card in your system whether it is from 10 to 9 or 1 to 0.

However "real life" is usually much more complicated. In my book the later case would even justify burning a 13 if that model is a serious threat with its upcoming activation(s). And there are many-many more subfactors (strategic goals, placement, activation order, needed cards for spells/triggers to go off (X+ numbered and/or with a certain suit) etc.) that you should take into account when you need to decide to use or not to use certain cards from your hand.

So all in all I just have a feeling that this base system needs so much in game tweaking that it is probably a waste of brain cells to bother with it. Or to put it in other words: I think your good results are more about your game knowledge, tactical skills, intuition and stuff than this calculation method.

Please don't take this as a malicious critisicm or something. I just wanted to share my thoughts with you.

[Math Mathonwy]

I dunno. It sounds fancy but there are so many variables that I really don't see it as useful the way you have presented it. I mean, as a rule of thumb, sure, but your presentatin makes it sound like you're striving for some kind of soft "scientific credibility" with this stuff and it just doesn't work that way.

A trivial example: the last wound off an Izamu who is about to activate is prolly twenty times as valuable as knocking off one further wound from a previously unscathed Rotten Belle. But wait, what if Izamu is about to kill your Master? Is it then fifty times as valuable? But if the total was fifty to begin with, how can this one wound be fifty on its own? Or is it ten? Or, if the victory of the tournament hinges on it, is it perhaps one MILLION?

[Guy in Suit]

I mean, as a rule of thumb, sure, but your presentatin makes it sound like you're striving for some kind of soft "scientific credibility" with this stuff and it just doesn't work that way.

Sorry if it comes off that way, really the objective is to assign numbers (arbitrary or not) to try and quantify gut feelings about what the right course of action is during a game.

I think I said earlier that this is only worth doing when the best course of action is not obvious! All of these counter points are very obvious, and most players at a tournament will take the same actions when presented with them.

I just find that previously I would always be asking myself 'what the hell should I be doing with this 7:tomes?' and would often find myself sitting with it still in my hand at the end of the turn. I feel that if you can squeeze value out of these borderline sort of cards in middling situations, it can really help you play more efficiently and give you a better shot at winning.

[Kalkris]

A trivial example: the last wound off an Izamu who is about to activate is prolly twenty times as valuable as knocking off one further wound from a previously unscathed Rotten Belle. But wait, what if Izamu is about to kill your Master? Is it then fifty times as valuable? But if the total was fifty to begin with, how can this one wound be fifty on its own? Or is it ten? Or, if the victory of the tournament hinges on it, is it perhaps one MILLION?

I wonder if somehow Soulstone cost might be able to factor into the value of the wounds of a given model, such as the aforementioned Izamu. I can see how, perhaps in a game where the foe's models are as follows (note that I'm using one given example here, and won't represent every scenario by far):

35 Scrap

Master: Lynch (M), 8Wd, Cache 2, Pool 8

Hungering Darkness (M - recursive, totem, costs 0ss for Slaughter), 7Wd (Spirit)

Illuminated (6ss), 6Wd (Regen 1, Armor +1)

Beckoner (5ss), 6Wd

Beckoner (5ss), 6Wd

Stitched Together (5ss), 7Wd ("DND!")

Depleted (4ss), 6Wd (Armor +1, HtK, Feels Nothing)

Depleted (4ss), 6Wd (Armor +1, HtK, Feels Nothing)

This crew has 58 total Wd. Ordinarily this would put value at 340/58 = 5.9, which means anything under a 6 is to be regarded as unhelpful (unless I am mistaken?). Taking the soulstone costs into account, perhaps one would do better to measure ss/Wd before taking card value into account, per model. in this way, we will put a Master's ss at 10 (even for Huggy - I consider Spirit to double the Wd value here, however...):

Perhaps I might do something odd for cache and pool here? so for instance SS user's wds*(total # of ss users/total starting pool)

Lynch = 1.25 +2 (8wd/(2 ss users*8pool)) = 3.25

Hd = 0.71 + .10 for each Wd it has when it recurs, each time + 3.5 (14wd - effectively*(2ss users/8pool)) = 4.21 to start

Illuminated = 1

Beckoner = 0.83

Beckoner = 0.83

Stitched Together = 0.86

Depleted = 0.67

Depleted = 0.67

Total (not counting Huggy's recursions) = 12.32

340/12.32 = 27.60

I would suggest that perhaps if we switch the numerator and denominator here, we might get a more lucrative result. I'm not sure of the significance of the 49.85 or the value of effects (beyond the recursion which is simple enough), but I'm trying, man oh man I am trying (curse my limited math use!)

I also want to factor in extra stones here too. For this I might use (ss users/pool#)*wd of model = addition to model value.

Lynch = .8 + 2 = 2.8

Hungering Darkness = 1.4 + .2 for each Wd it recurs with, each time (this might actually be affected by the cards the foe pitches!!!) + 3.5 = 4.9 starting

Illuminated = 1

Beckoner = 1.2

Beckoner = 1.2

Stitched Together = 1.17

Depleted = 1.5

Depleted = 1.5

Total = 15.27

340/15.27 = 22.26

Personally, I surmise that some of my crunching might assist a little bit. I really don't know squat about when to multiply or divide here; I'm just doing this because it might help out somewhat...

I'm guessing that this means you will want to use soulstones against the masters here and get to such a value or higher in order to make a dent, but I'm really, honestly unsure. I hope I've helped even a slight bit.

~Lil Kalki

[CRC]

It's an interesting theory.

Given a 6 Wd Beckoner that costs 5 SS, we get an SS-value-per-wound of 0.83

If we then recalibrate from card-value-per-wound to card-value-per-ss, giving a new value of 340 / 45 = 7.56.

Then in play, when attacking the Beckoner, we'd need to mutiply 7.56 * 0.83 = 6.3, to get a card-value-per-wound for this flip. Then we could use that to drive our thresholds.

For a master like Lynch, given a cost of 10 (assumed) + 4 (soulstones), and a wound count of 8 + 2*4 (soulstones), this gives a model ratio of 14 / 16 = 0.875

In this case (as will frequently be the case), there are similar ratios across the board. which isn't useful. This sort of exercise would be useful if you're facing a force with models like Yin (8/8=1) and Rotten Belles (4/8=0.5), and you can say that a doing wounds to Yin is twice as valuable as doing wounds to Belles.

Like my earlier comment about the different between our wound total and their wound total, in theory you could use this to get a more accurate baseline, however, I feel that in practice, the math here isn't sufficient to determine the correct course of action.

A far bigger concern is that you need to adjust the value by game size. It may be 6.5 in a 35 SS game, but closer to 8 in a 30 SS game, and 9 in a 25 SS game.

In conclusion, I feel it would be better to take a standard value-per-wound, say 6.5 in a 35 point game, and just use that a baseline, adding concerns like "is this going to kill the model?", "has the model activated yet?", "how valuable are the models wounds?", and "how much do I value offensive wounds versus defensive wounds?", to arrive at a judgment.

TL;DR: I feel the math is useful, but not sufficient. It's just one more bit of information.

[Math Mathonwy]

Sorry if it comes off that way, really the objective is to assign numbers (arbitrary or not) to try and quantify gut feelings about what the right course of action is during a game.

"Arbitrary" and "quantification" aren't concepts that easily go together. The number of wounds is an arbitrary choice that doesn't really tell you much. What about summons? Armor? Heals? Being insignificant? Being fast? Or the myriad other things that affect stuff? It's just that you lucked into getting the needed number (six or seven) out of that and now you feel that this somehow implies causation.

That said, if you feel that it helps you, be my guest. Someone else might use astrology to get the number and if he or she does well with said number, then more power to him or her, I guess. But I would avoid using the pseudo-scientific proto-math reasoning you've presented as a justification, really. *wink*

Edited May 10, 2013 by Math Mathonwy

[The Godlyness]

<---is wondering what level of play you guys are on that this is needed?

i bank on my opponents having the red joker in their hand at all times till i see it. Why well simply from my play experience they seem to always have it in their hand. (heck last game he played it every turn and drew it every turn.)

I am a great believer in fate, in saying that chance. (yes i know Statistics do play are part once cards are missing yaddy yaddy) but i can not say with any regularity that this is that, since every time i play the cards play diff.

i Do like your write up but i cannot fathom it's purpose on the playing field. to many variables.

[Math Mathonwy]

<---is wondering what level of play you guys are on that this is needed?

The OP won a tournament in Adepticon for the second year running so, even though I disagree with his article, his level of play is as high as it can be, basically.