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MrDeathTrout

What is a + worth?

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I was wondering about the odds of flipping different cards given different hand sizes, :+fate:-fate (not done yet), etc.  So I generated some tables and figured would be easy to determine exactly what a :+fate was worth.  Once I had the tables it wasn't as easy as I thought.

I posted the tables on line as well as my thoughts what  a :+fate is worth.  Here's a link to the tables: http://glowingsaber.com/math.html

I've put a copy of my thoughts here.  I'm wonder what everyone else thinks a :+fate is worth.

How much is a :+fate worth?

On average a single card flip will yield a 7, a :+fate flip will yield a 10, and a :+fate :+fate an 11. Does that mean Ml 5 with :+fate and Df 8 are equivalent?

No. If each player has an unfiltered hand (no holdovers from last round, no Rush of Magic, etc.) of six cards then an attacker with :+fate has 8 cards to choose from and the defender has 7 to choose from. If you look at any given result (e.g. having a 6 +) the attacker has at most a 4.8% advantage and the advantage is less than a 1% for a little over half the results. In a nutshell early in the turn the attacker will need to cheat in a card 3 at least higher than the defenders to with the duel.

No assume both players have exhausted their hands are relying on just top decking what they need. The attacker now has a significant advantage. They have a better percentage chance of getting any given result or better, peaking at a 25.3% advantage for a 7+ or 8+. A 13+ only has a 8.5% advantage, but that is nearly double the chances of the defender flipping a 13+. Then again if the defender flips a 10 they need a 13+ just to tie.

I though once I generated these probability tables it would be easy to answer this question, but it definitely is not simple. IMHO, a :+fate is definitely not as good as +3, is probably not as good as +2, and is probably better than +1. I would say a :+fate is roughly equal to +1.5.

 

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I always thought the average result with a  :+fate was 9.

 

The real answer ends up depending on so many variables that  it not the same for everyone. if you really want something to succeed then :+fate is worse than a +2, stat because you don't have the same range of possibilities. But if you want to preserve your hand as much as possible then :+fate  is probably better than +2 stat, because you are much less likely to need to cheat first, and so get maximum value from your hand

 

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On a throwaway model you aren't going to cheat for the :+fate is amazing. As an anecdotal observation crews where almost everything has a :+fate also seem to work a lot better for me, flipping through your entire deck in a turn is very good and can give you the red joker twice apart from meaning you likely win a lot ofduels or force cheats. While playing elite crews with few :+fate I've gone whole games without ever seing the red joker.

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3 hours ago, Adran said:

I always thought the average result with a  :+fate was 9.

You might be right.  I depends on how you define average.  I went with odds are you will flip it at least 50% of the time.  My math could also be off, but while I'm not 100% sure it is correct I have very high confidence it is.

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This is related:

On 1/26/2018 at 6:11 PM, Myyrä said:

I did some really basic stuff this time, because I think most people might not be aware of this and have not seen the previous thread where I posted more or less the same info (which is no wonder considering even I don't remember when that was).

So, here you have the hit probabilities as a function of the difference between attack and defense values (atk-def):

hitprob.png?dl=1

and also as a figure, because why not

hitprob_fig.png?dl=1

As you can see, having a :+fate is more or less equal to having a 2 points higher attacks stat and :-fate equal to having a 2 points lower attack stat.

One would easily think that hitting something with Df 9 would be impossible when you have Ml 5 and :-fate but it's only about equal to having to throw a 6 on a normal 6-sided die.

 

 

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3 hours ago, MrDeathTrout said:

You might be right.  I depends on how you define average.  I went with odds are you will flip it at least 50% of the time.  My math could also be off, but while I'm not 100% sure it is correct I have very high confidence it is.

The distributions for the :+fate and :-fate are not symmetrical, so median is different from mean.

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