The Exact Value of a Positive Twist

[The Godlyness]

 

I find your attitude a little confusing since you've pretty much described doing what everyone is discussing in this thread. 

I don't comprehend how an pseudo +2 has any effect on the game. If I am sh5 with a to df5 I have a good shot of hitting since more cards. How some one sees sh5 is sh7 vs df5 is beyond me. If I am sh5 vs df7 and I flip the red joker to their 13 well my ephemeral +2 doesn't mean anything since its not applied to the actual number.

So trying to give a a static number I don't understand when that static number does not apply to...well anything.

A or a change with every flip and every game. So it is quite indefinable. I see how you guys are working with averages of what it statistically should be. I get that. But in my personal opinion which I hope I offend no one. Has no place in a game with so many variables at any given time.

[Myyrä]

I've been following this thread with interest.  I'm not a good enough statistics guy to work this out myself, so special thanks to Myyra and Math Mathonwy for doing the simulations (sorry if I missed anyone else!).

I actually didn't really run any simulations. I just wrote some Matlab code that used tensors to calculate the exact values.

[moxypoo]

I don't comprehend how an pseudo +2 has any effect on the game. If I am sh5 with a to df5 I have a good shot of hitting since more cards. How some one sees sh5 is sh7 vs df5 is beyond me. If I am sh5 vs df7 and I flip the red joker to their 13 well my ephemeral +2 doesn't mean anything since its not applied to the actual number.

So trying to give a a static number I don't understand when that static number does not apply to...well anything.

A or a change with every flip and every game. So it is quite indefinable. I see how you guys are working with averages of what it statistically should be. I get that. But in my personal opinion which I hope I offend no one. Has no place in a game with so many variables at any given time.

Oh, I'm not offended at all, and I hope you didn't take offense at my post!  The tone was a little harsh now that I reread it. 

 

I can see where you're coming from - the examples you give are outliers on the bell curve, and they will occasionally happen.  But over the course of the game, you'll find that most of your flips follow the statistical average.  I think the whole point of this thread is to create a rule of thumb for anything that has a on its attack.  So you can assume that Sh5 is going to behave similarly to a Sh7 on average.  Of course you can have outliers where you flip two aces, but it's equally probable that you flip two 13s. 

 

I doubt there are many people out there who can both count both their own and their opponent's cards while keeping an exact statistical likelihood for every flip in their head.  Most people (like me) probably want general rules to follow to make choices easier. 

[decker_cky]

I'd say you're less likely to flip low cards since you tend to pitch them at the start of the turn after shuffling (barring black joker). It improves both sides, but makes  more reliable since it's that little bit more difficult to flip two low cards.

[Valcurdra]

Ok,

 

I finally got around to working this out. Took me a while as I had forgotten a lot of the math involved that I learnt in school, also the jokers make the math significantly more complicated.

 

The results was that is works out to a +2.33 stat increase.

 

Straight flip mean = 7

 

+ flip mean = 9.33

 

This assumes a full deck for both flips and thus does not take into account the effect of burnt cards or other game effects that would influence a flip.

 

Therefore the answer to the implied question of the OP as to who is better at shooting, the raw math says that overall Ryle will hit more often.

[Myyrä]

Ok,

 

I finally got around to working this out. Took me a while as I had forgotten a lot of the math involved that I learnt in school, also the jokers make the math significantly more complicated.

 

The results was that is works out to a +2.33 stat increase.

 

Straight flip mean = 7

 

+ flip mean = 9.33

 

This assumes a full deck for both flips and thus does not take into account the effect of burnt cards or other game effects that would influence a flip.

 

Therefore the answer to the implied question of the OP as to who is better at shooting, the raw math says that overall Ryle will hit more often.

Comparing means is a terrible way to compare two different probability distributions, and it tells very little about the probability of a random variable generated from one distribution having a greater value than a random variable generated from another distribution.

Proof:

Let red joker have a numerical value 14000.

now has mean value of 513.1865828092243

Straight flip has mean value of 266.

Despite all that only has 0.383919558971970 probability of winning against straight flip when attacking.

[Valcurdra]

Comparing means is a terrible way to compare two different probability distributions, and it tells very little about the probability of a random variable generated from one distribution having a greater value than a random variable generated from another distribution.

Proof:

Let red joker have a numerical value 14000.

now has mean value of 513.1865828092243

Straight flip has mean value of 266.

Despite all that only has 0.383919558971970 probability of winning against straight flip when attacking.

 

Irrelevant since everyone knows the sample size in this example (0-14), so we know there is no outlying values.

 

Mean is a perfectly acceptable way of measuring the difference, using the median is also OK however it is less accurate.

[Omenbringer]

The math is further complicated by the control hand and ability to cheat values (which a positive flip can preserve against negative fate modifiers like shooting into cover). Deck cycling and deck shaping also skew results, Gremlin's are a great example of the potency of these things.

[Adran]

Irrelevant since everyone knows the sample size in this example (0-14), so we know there is no outlying values.

 

Mean is a perfectly acceptable way of measuring the difference, using the median is also OK however it is less accurate.

 

Just as long as you understand what the mean tells you.

After all a Sh 5   might have a mean value of 14, whilst a Sh 6 has a mean value of 13, if you have a TN 20 Duel, you're not going to want the one with a higher mean.

[Valcurdra]

Just as long as you understand what the mean tells you.

After all a Sh 5 might have a mean value of 14, whilst a Sh 6 has a mean value of 13, if you have a TN 20 Duel, you're not going to want the one with a higher mean.

Yes you are.

Unless you plan to cheat and have a card saved. Even then your burning a resource.

[Valcurdra]

While I was at it I worked out the mean value of a -ve flip as 5.18.

 

These flips tend to come up mostly on damage flips and so I found the distribution quite interesting on this one.

 

Black = 3.67%

Weak = 57.61%

Moderate = 30.18%

Severe = 4.94%

Red J = 3.60%

 

Over 60% weak or BJ and over 91% of results are a moderate damage or less. Really shows the value of being able to get a straight flip and cheat these flips, also shows the value of a high weak damage stat.

[Math Mathonwy]

Yes you are.

Unless you plan to cheat and have a card saved. Even then your burning a resource.

Ummm... You can't hit TN 20 with Sh 5 no matter how many positive twists you have. You can hit it with Sh 6. So I'm pretty sure that you will want that Sh 6 even if its mean is lower.

[Valcurdra]

Ummm... You can't hit TN 20 with Sh 5 no matter how many positive twists you have. You can hit it with Sh 6. So I'm pretty sure that you will want that Sh 6 even if its mean is lower.

 

Oh I see what you saying. Sorry miss read that the first time

 

The point of calculating the mean is that you know in the vast majority of cases the +flip is better than a +2 stat increase.

[Adran]

Oh I see what you saying. Sorry miss read that the first time

 

The point of calculating the mean is that you know in the vast majority of cases the +flip is better than a +2 stat increase.

 

My point was that whilst knowing the mean is useful, it doesn't tell you everything you might want to know.

Its like on a triple negative result, you are more likely to score 14, than on a straight flip.

 

So on your negative flip calculations, whilst the mean is 5.18, over 60% of the results are 5 or lower, where as you might think because the mean is higher than 5, you are more likely to score more than 5. You're not. you are much more likely to score below 6 than 6 or above.

[Myyrä]

Irrelevant since everyone knows the sample size in this example (0-14), so we know there is no outlying values.

 

Mean is a perfectly acceptable way of measuring the difference, using the median is also OK however it is less accurate.

You are using the term sample size wrong.

It's also impossible to compare two probability distributions with different shapes just by using mean or median. Using both is always better than using just one of them, but even that doesn't even come close to telling the whole truth.

[entropolous]

I'd say you're less likely to flip low cards since you tend to pitch them at the start of the turn after shuffling (barring black joker). It improves both sides, but makes  more reliable since it's that little bit more difficult to flip two low cards.

Sorry for the minor thread necro...

 

This isn't entirely true.  The biggest benefits of a    comes from situations when you flip something like a 1 and a 13, by removing the low cards from the population you are removing these possibilities.  The benefit of a  actually maxes when there are a lot of middling cards out of the deck. Lets look at two extremes:

 

Say you have 4 cards left in your deck, 12, 12, 13, and 13.  (In other words all of your low cards are flipped.)  A straight flip averages 12.5, a   flip averages 12.75, only a 0.25 increase.  

 

On the other hand, say you still have 4 cards left in your deck but they are 1, 1, 13, and 13. A straight flip now averages 7, whereas a   flip averages 10, an increase of 3.

 

As mentioned above, though, looking at averages (or medians) isn't really the best way of looking at things in this case, because the populations have such a different distribution and additionally because we are looking to meet or exceed values.  Its better to compare these likelihoods, as opposed to just looking at averages.  Below is a chart of the probability of meeting various TNs for three situations, Stat 7, Stat 6, and stat 5 :

 

As you can see the benefit of the  is highly dependent on the TN you are aiming for.   Lets look closer at Tn 15.  In an opposed duel, at this point it is almost only going to take a better than average card either from the deck or the opposing player's hand to stop you.   A 5  is 1.34 times more likely to meet a TN 15 than a straight 6, and 1.14 time more likely than a straight 7.  Looking at just the averages would tell you that a  5  is only an 8% improvement over a straight 6 (ave. 14 vs ave. 13) or a negligible improvement over a straight seven.

 

All that said, the benefit of the  really is only applicable when you are talking about being able to perform independently of your control hand.  If you have a card to cheat to the extreme (TNs 18 and above) stats are king.  But in a given turn in the meat of the game, you can be involved in 20+ duels. With only 6 controls cards (and probably only 2-3 big cards), most of your actions are going to have be done independently of your hand, so this discussion is still a valid one.