The Exact Value of a Positive Twist

[The Zinc Lich]

I was discussing Guild stuff with my brother a few days ago, and the topic of Ryle versus Sidir came up. The two of them have fairly similar guns: Sidir has +2 range and +1 severe damage, Ryle has a built-in trigger for   on damage. They have similar  triggers for extra attacks, although Ryle's trigger can repeat until everyone has been hit once. However, the view in my brother's meta is that Sidir is the better ranged combatant based on the strength of his Sh of 7, versus Ryle's 5.

 

That being said, Ryle has a built in  on his attack flip. It really got me thinking. Aside from making Ryle better at shooting enemies in cover, what is that   really worth? Is Sidir's Sh of 7 that much better?

 

Playing Warmachine for a few years gave me a pretty good idea of dice math; one additional die is worth, on average 3.5. Adding a die and discarding the lowest (which is the closest they have to a ) is worth a little bit more than 2. Unfortunately, dealing with the probability value of several sets with values ranging from 1-6 is a lot easier than dealing with the probability of a deck of cards, primarily because every card that is removed from the deck alters the probability curve.

So, I pose the question to forumites with a better grounding in mathematics than I have: are there any situations where having a  approaches (or exceeds) a trait value of 2?

[Malal]

Not going to attempt the maths but just some of the factors that would need to be considered are: What cards have gone from your deck/are in your hand, what cards have gone from your opponents deck/in their hand, Def of target and is the target in cover. That's just to hit, if you need to do a specific amount of damage there'd be a whole lot more variables.

[LunarSol]

A  equates closest to the concept of roll 2, drop the lowest.  Grossly simplifying the concept to a raw D13 kind of thing I believe raises the average result from 7 up to a little more than 9, so you can probably treat it as a +2...ish... sorta... not really.  Cards played can easily move it around, though even if the only cards removed are the 4 Kings, its still an 8.5 or so, so "normal" card depletion shouldn't hurt that too badly.  The real advantage to a  is maintaining the ability to cheat though, so its probably even more valuable than that.  

 

EDIT: Since the topic is asking for EXACT value.  On average, a D13 rolls a 7.  If you take the 169 combinations of 2D13 and only consider the higher of the two values as the result, it comes out to an average result of 9.153846.... exactly.

[lusciousmccabe]

If there are only 2 cards left in your deck and they're an ace and a 12 then the positive twist is better. 

 

I think you'd be better off focusing on the value of a positive twist with a fresh deck, otherwise it won't transfer between games and unless you're really good at counting cards you probably can't base your decisions on that anyway.

 

I think Malal mentioned a few important considerations aside from the odds. Higher stats mean you can force an attack through if you have good cards and are willing to use them. A positive twist can allow you to cheat when you couldn't otherwise and gives you better results with a weak hand, but it doesn't increase your maximum duel total.

[Lucidicide]

The value depends on a lot of factors, but mainly the defense of the model you're trying to hit. Other than that, you have to take into account how you want to use your cards.

 

If it is a duel you intend or are willing to cheat, then the higher stat is better. If it's a duel you're not likely to cheat, the + is better. When you take into account things like the defenses of your target (both cover and Df value itself), a lot more gets thrown into the mix.

 

For example, trying to shoot Lilith (Df 7). If you're trying to kill her for, say, assassinate, then you're willing to throw high cards to hit her. In this case, Sidir is better because the Sh 7 is much more likely to hit on the cheat than Sh 5. However, if she's just in your way and you don't need to kill her, you might not intend to cheat. In that case, Sh 5 + is better because you're more likely to have a high starting value (forcing Lilith to cheat) without having to cheat yourself.

 

Honestly, there's just a lot that goes into those considerations in a game like this. I tend to prefer the high stats, but part of that is because I tend to run crews with very few models (and therefore it's easier to allocate resources). The more models I run, the fewer cards I have for each individually... and the more I would want + to my flips.

 

/shrug

[LunarSol]

 

I think Malal mentioned a few important considerations aside from the odds. Higher stats mean you can force an attack through if you have good cards and are willing to use them. A positive twist can allow you to cheat when you couldn't otherwise and gives you better results with a weak hand, but it doesn't increase your maximum duel total.

 

Blah.  Now I'm going to need to factor in the opposed roll and overall chance of success.  

[mythicFOX]

The value depends on a lot of factors, but mainly the defense of the model you're trying to hit. Other than that, you have to take into account how you want to use your cards.

 

If it is a duel you intend or are willing to cheat, then the higher stat is better. If it's a duel you're not likely to cheat, the + is better. When you take into account things like the defenses of your target (both cover and Df value itself), a lot more gets thrown into the mix.

 

For example, trying to shoot Lilith (Df 7). If you're trying to kill her for, say, assassinate, then you're willing to throw high cards to hit her. In this case, Sidir is better because the Sh 7 is much more likely to hit on the cheat than Sh 5. However, if she's just in your way and you don't need to kill her, you might not intend to cheat. In that case, Sh 5 + is better because you're more likely to have a high starting value (forcing Lilith to cheat) without having to cheat yourself.

 

Honestly, there's just a lot that goes into those considerations in a game like this. I tend to prefer the high stats, but part of that is because I tend to run crews with very few models (and therefore it's easier to allocate resources). The more models I run, the fewer cards I have for each individually... and the more I would want + to my flips.

 

/shrug

Very well said.

[Valcurdra]

Actually what the op asked for was the exact value of a positive twist. This can be calculated for certain fairly easily.

I don't have time now but I'll have a go at it in a few days.

What the replies are talking about is the tactical value during a match. This is impossible to work out because of the near infinite number of sample sizes and other conditions that come into play.

[SpiralngCadavr]

EDIT: Since the topic is asking for EXACT value.  On average, a D13 rolls a 7.  If you take the 169 combinations of 2D13 and only consider the higher of the two values as the result, it comes out to an average result of 9.153846.... exactly.

Yeah, but these're cards. That number shifts with every drawn card. So... yeah.

 

 

My 2¢:

 

a [+] in the first half of the turn is mostly reliability, and I prefer higher stats on anything that isn't effectively a throwaway attack over a [+], since I can cheat high on a good stat, while a [+] on a mediocre stat really just means my opponent is more likely to need to cheat (and I won't be able to cheat higher, given a worse starting stat), meaning I'm less flexibile/capable of changing things.

 

Once most cards have been drained, I tend to prefer the [+] due to higher reliability, though a good stat is still a good stat.

[LunarSol]

Yeah, but these're cards. That number shifts with every drawn card. So... yeah.

 

This is true, but it doesn't change that drastically until the deck gets pretty low.  There's an inherent redundancy in the 4 of every card that makes the loss of any particular card fairly negligible in how much a  affects the next flip.  I'd be surprised if you'd see the number vary that greatly even from a deck at half strength unless you'd flipped consistent face cards to that point.  It's definitely more of a guideline than a hard rule, even more so than normal probabilities.

[SpiralngCadavr]

Sure, just giving you shit over "exact"

[ddot]

If you were good at counting cards, then an on-the-fly analysis isn't too bad.

 

If you drew a lot of high cards early on, the positive twist might not mean as much, except for the fact that you can still cheat (probably) if you have cards in your hand. If you drew a lot of low cards, then it means a bit more, because you have good cards lurking in there waiting to be drawn.

 

The exact value is that it makes it that much more likely to be able to cheat if you have to. a + and focus 1 (+) cancels out cover and defensive stance, so you'll at least be at neutral twist and thus able to cheat.

[dancater]

Add to this the Joker vaiable.

 

A [+] means a (slightly) greater chance of flipping either Joker which can be excellent (Red) or catastrophic (Black).

 

Furthermore as already observed the effect of the [+] is to usually place more pressure on your opponent to have to cheat first which can be used to drain their hand which is potentially an excellent advantage.

 

The [+] could also (on a flip of near value cards of different suits) allow you to select for suit triggers more reliably, rare perhaps but useful.

 

However the [+] cycles your deck quickly which may be bad or good and opens the possiblity of the wasted high card (the special pain of flipping two face cards on a [+] twist and thinking how useful the ignored card would be later), of course this may balance with the joy of [+] King and Ace.

 

Finally as also already observed the higher base stat is important and at times essential in completing tasks, most especially where you are willing to cheat high and your opponents stat is also higher end. It also means that your opponent is always looking at an 'x' number disadvantage in the duel and for possible cheating which forces tough decisions.

 

I think in the end this is an example of an impossible question to address meaningfully, Malifaux's card opposed duel mechanic presents so many variables that while you could theoretically approximate the number value of a card flip (for a given deck at a given moment in the game) its influence on other factors makes the raw number negligble as a value comparison anyway.

 

This is one of the intriguing aspects of Malifaux's mechanics while in most games you can fairly accurately break down the value of extra dice or a dice bonus at any given moment with the opposed card duels it is a marvellously complicated and near impossible problem. I do wonder if we have a truly gifted chaos theory math prodigy in the community with say a spare year or two. If I was a math nerd I reckon this would make a marvellous PhD proposal.

[Math Mathonwy]

I ran the numbers and had a big thread about this during the beta testing but that section went the way of the dodo.

I made a program that builds a deck, shuffles it, and flips cards. And then ran the numbers for a couple of million iterations for various stats.

A good rule of thumb is that a single positive twist is about as good as +2 to the stat. It allows you to consider its impact.

But bear in mind that if you are willing to cheat a high card in, then a high stat is naturally better. And similarly if you're getting a negative twist from somewhere, then a positive twist cancelling that is hugely better.

If you want the actual numbers for various combinations, I can provide them (I still have the program).

[dancater]

I told you we need a math nerd and it don't get more made to order then a person named Math.....

 

Nice work.

[Joel]

In games I weigh these odds and move between the two positions instinctually - having a "feel" for what is most likely to be the best option.  never really thought about eh math or the odds of the decisions, just what feels "right" or "optimal" for a particular duel.

[Sholto]

Also bear in mind that while Sidir can buy a positive flip with a soulstone, Ryle cannot buy +2 to his Sh stat.

[Omenbringer]

For example, trying to shoot Lilith (Df 7). If you're trying to kill her for, say, assassinate, then you're willing to throw high cards to hit her. In this case, Sidir is better because the Sh 7 is much more likely to hit on the cheat than Sh 5. However, if she's just in your way and you don't need to kill her, you might not intend to cheat. In that case, Sh 5 + is better because you're more likely to have a high starting value (forcing Lilith to cheat) without having to cheat yourself.

 

Honestly, there's just a lot that goes into those considerations in a game like this. I tend to prefer the high stats, but part of that is because I tend to run crews with very few models (and therefore it's easier to allocate resources). The more models I run, the fewer cards I have for each individually... and the more I would want + to my flips.

 

/shrug

I would agree on a typical Attack Flip that the higher stat value is generally better than a flip but dont think it is so "black and white" with Ryle.

 

Ryle has a built in on his gun which allows his use of the Concentrated Burst trigger (assuming he can use a trigger) on any successful hit throwing a on the damage flip. This effectively increases Ryle's "success range" for cheatable damage over Sirdir. Ryle will score a neutral, cheatable damage flip (assuming only Df in play and not accounting for things like Hard to Wound) while only beating Lilith by 1 (her card +3), where as Sirdir will still be at a damage flip while being up by 5 (Lilith's card +5). This allows Ryle to preserve those High Value cards in the hand for cheating Damage flips instead of using them trying to hit well.

 

This is why I would give the advantage back to Ryle in most situations. Having 2 chances to get to the sweet spot of cheatable damage prior to cheating the Attack flip is a potent option when coupled with the increased "success range" for cheatable damage.

[The Godlyness]

I ran the numbers and had a big thread about this during the beta testing but that section went the way of the dodo.I made a program that builds a deck, shuffles it, and flips cards. And then ran the numbers for a couple of million iterations for various stats.A good rule of thumb is that a single positive twist is about as good as +2 to the stat. It allows you to consider its impact.But bear in mind that if you are willing to cheat a high card in, then a high stat is naturally better. And similarly if you're getting a negative twist from somewhere, then a positive twist cancelling that is hugely better.If you want the actual numbers for various combinations, I can provide them (I still have the program).

Sheesh here I am believing in the heart of the cards. If I flip two deuces then I added +2 to my value my tiny little mind does not comprehend well my Sh 5 is sorta like shoot 7 since I have a . To me it's shoot 5 that has a better chance at flipping higher cards. Or mitigates cover. Damn technobabble

Personally the I like better than +2 stat. Mitigating cover is amazing. Being sh7 is fine but burning a stone to be put on negative to damage (generally speaking. Yeah not worth it. Specially when damage profile is 2/3/5. Also ryle is tankier and hits harder when engaged. So there is that.

[Hateful Darkblack]

Statistically, I think a positive twist will raise the results by an average of like 2-3 maybe?

 

But it makes a bell curve instead of a linear curve.

 

And it does not increase the maximum possible value the way a number bonus would.

 

It also affects card cycling and joker-fishing in complex ways, because cards don't behave like dice, but if you pretend that cards behave like dice, it raises the results by an average of like 2-3 maybe.

[MinimumPhase]

Also bear in mind that while Sidir can buy a positive flip with a soulstone, Ryle cannot buy +2 to his Sh stat.

 

Adding onto Sholto's point, Sidir can also buy a positive twist on attack and damage with a single AP.

[zeeblee]

An interesting point on top of the value of a :  What is the value of :+fate?

[Math Mathonwy]

Sheesh here I am believing in the heart of the cards. If I flip two deuces then I added +2 to my value my tiny little mind does not comprehend well my Sh 5 is sorta like shoot 7 since I have a . To me it's shoot 5 that has a better chance at flipping higher cards. Or mitigates cover. Damn technobabble

You aren't flipping two deuces, you're flipping two cards. The value of those cards is a statistical distribution.

In other words: If you pit a Sh 5 with against a Df 5 model, you will win, on average, as often as a Sh 7 model wins against a Df 5 model.

And now, a special part, only to Godlyness:

"But what if my deck only holds aces left?" Yeah, what if Harry Potter was a cube? What then? How would he hold his wand?

[Math Mathonwy]

An interesting point on top of the value of a :  What is the value of :+fate?

Not as much. I can check it but unfortunately I will be at the computer with the program next time on Friday, so the answer will take a bit.

[Hateful Darkblack]

So, the easiest way to compute the value of a twist is to pretend that the deck is a 13-sided die. It isn't, but this will get you something approximately correct.

 

How much will a second flip help you? Take all the possible answers, average them out, and that's the value of the positive flip.

 

If you flip a 1, then almost every flip will help you (except another 1). A 2 is worth a +1, a 13 is worth a +12. You average those out and it's about a +6.

 

If you flip a 7, then anything between 1 and 7 won't help or hurt you. An 8 is worth a +1, a 13 is worth a +6.  You average those out and it's a little below a 2.

 

If you flip a 13, then another card won't help you (because we're pretending it's a 13-sided die and ignoring jokers here). It's a 0.

 

Anyway, that means it ends up about a 2. A little more because a low flip will benefit so much that it skews the average up.

 

* * *

 

Compare to that a third flip. With two rolls you're averaging about a 9, so a third flip is worth a little less than 1.

 

* * *
 

These are approximations, and they ignore the effects of jokers, of stacking your deck with card filtration, of the clever things you can do with your discard pile, and so on. But they give a fairly decent number.

 

Your first positive flip is worth a little more than +2. Your second positive flip is worth a little less than +1. Your third positive flip is worth a little less than +0.5.

 

That third flip is mostly worth it if you're fishing for a red joker and not worried about the black joker (because it's already come up or it's in your hand).