How valuable is a positive flip?

[gozer]

This is less of a rules question and more of a maths question but this looks like the best place to ask.

Which is statistically more likely to result in a better final duel total:

 

Stat: 7

or

Stat: 6

[santaclaws01]

A  gives you an average value of +2 to your flip.

[msgfree]

10 minutes ago, santaclaws01 said:

A  gives you an average value of +2 to your flip.

Can you recommend any resources detailing the mathematics of a 54 card deck?

[santaclaws01]

10 minutes ago, msgfree said:

Can you recommend any resources detailing the mathematics of a 54 card deck?

Personally no. The math has been done by multiple different people over time on the forums so that's where I'm getting my information from.

[Adran]

1 hour ago, gozer said:

 

Which is statistically more likely to result in a better final duel total:

 

Stat: 7

or

Stat: 6

Discounting cheating the state 7 has a mean result of 14, and a range of 7 to 21.

The 6+ has a mean of 15, but a range of 6 to 20. 

I can't remember the model or median results off the top of my head. 

From most people's point of view the state 6+ will win more duels, but it does depend a little on the duel you are facing. 

I'm going to move the topic to malifaux discussion, because it's not really a rules question. 

[Maniacal_cackle]

It depends on what you are trying to hit.

If you need a 19 total, a straight six has about a 9% chance to hit, while a positive six has about 17% (ignoring black jokers). A 7 has slightly less than 17% (although if accounting for black jokers, might be better than the 6+, which might drop below 17%).

On the other hand, if you need a 15, the 6+ has a 63% chance of hitting (ignoring black joker) while the 7 only has a 46% chance..

So the mileage will vary. It also makes it easier to cheat against - flips, which I think is an even bigger consideration.

[Maniacal_cackle]

If wanting to calculate odds on something specific, I use a hypergeometric calculator for multi-card flips:

https://stattrek.com/online-calculator/hypergeometric.aspx

Remember that whatever result you get wouldn't account for Black Joker. That gets slightly more complicated so I ignored it here.

[Franchute]

Schemes and stones had an episode on this under second edition. On average, a plus flip is more or less +2 but, if you need more extreme values, a better stat is more suited. Moreover, if you are willing to cheat, a better stat will yield better result too.

[MajorUndead]

I would also mention the case where you are attacking a model with an ability that gives you a (like manipulative or serene countenance)
Having a will counter that and you'll still be allowed to cheat.
So in such a case I'd say stat 6 is probably going to be a lot more useful that stat 7, no?

[mythicFOX]

As others have said your total on a positive flip will average +2 higher than without.   The way Malifaux works mechanically I use this as a rule of thumb;

A flip is worth +2 to your duels until either of you chooses to cheat fate, at which point the stat reverts to normal.

In that respect it works as a combination; stat boost, and makes you more resource efficient by letting you cheat second more often, and forces your opponent to spend resources cheating more.

 

[Adran]

I've just tried to work out the probabilities in excel, so I might have made some errors. But these numbers do include the Black joker effect. (but are only valid for a new deck). (they also ignore cheating)

The most common result in a paired flip is 13, and that will happen 13.8% of the flips, and this leads to a weighed distribution, where the positive flip is more likely to flip high. (This is the the mode value of a paired flip) (the mean is 9.03)

The 7 stat is going to be better if you need to score 21, 20, 7 or 8. The 6 stat is more likely to reach every other target number.

looking at comparing 6+ to 8 you are more likely to hit TN 10-17 with the 6 stat, 9 and lower, and 18+ you are better off with stat 8.

Once you start looking at opposed duels, the maths gets really hard. (There is a different answer for each opposed stat).

10 hours ago, Maniacal_cackle said:

If you need a 19 total, a straight six has about a 9% chance to hit, while a positive six has about 17% (ignoring black jokers). A 7 has slightly less than 17% (although if accounting for black jokers, might be better than the 6+, which might drop below 17%).

 

Those numbers are still close enough, and the 6beats the 7 by an extra 0.8% chance to reach 19

4 hours ago, mythicFOX said:

As others have said your total on a positive flip will average +2 higher than without.   The way Malifaux works mechanically I use this as a rule of thumb;

A flip is worth +2 to your duels until either of you chooses to cheat fate, at which point the stat reverts to normal.

In that respect it works as a combination; stat boost, and makes you more resource efficient by letting you cheat second more often, and forces your opponent to spend resources cheating more.

 

This is a good rule of thumb. If you don't know how to calculate the odds, this rule is probably all you need.

[solkan]

It turns out that some of the old threads are still around:

http://malifauxnoob.blogspot.com/2011/03/009-maths-of-malifaux.html

 

I think that's the sort of explanation the original poster was looking for.

It's weird, finding old threads debating whether it's fair to count cards when M3E lets players look through their own discard pile.  🤔

[msgfree]

13 hours ago, Franchute said:

Schemes and stones had an episode on this under second edition. On average, a plus flip is more or less +2 but, if you need more extreme values, a better stat is more suited. Moreover, if you are willing to cheat, a better stat will yield better result too.

Its Episode 32 - I've listened to it this morning, and a lot the information is still relevant.