Drop rates and deck selection

[kev]

I got to thinking about what a shame it is that my often used FG grinder, PuppyChow's Unoriginal (http://elementscommunity.org/forum/index.php/topic,1748.0.html), never wins against Divine Glory.  It's a shame because Divine Glory probably has a higher than average drop rate among FGs.  This got me thinking about whether it's possible to calculate drop rates for all the FGs and whether or not it'd have an impact on FG grinder deck selection.

Here's (http://elementscommunity.org/forum/index.php/topic,495.msg6904#msg6904) a post by chriskang detailing drop rates for 11 FGs.  It's so old there's no way of knowing what the FGs looked like at the time or even whether the spin methodology was changed after chris wrote it.  But check it:

Rainbow	46.9%	19.0%	661
Fire Queen	43.3%	17.2%	599
Gemini	41.6%	16.4%	571
Incarnate	40.2%	15.8%	548
Graviton	39.3%	15.3%	533
Seism	36.8%	14.2%	493
Hermes	35.1%	13.4%	467
Chaos Lord	34.8%	13.3%	462
Miracle	33.0%	12.5%	435
Morte	32.6%	12.3%	428
Scorpio	31.8%	12.0%	416

The first percentage is chance of getting 1+ cards (from the chriskang thread), second percentage is chance per spin (I derived), third is how much you'd net from selling the cards you won (assumes rares sell for 1159).

Theoretically one could take the decks of each FG found here (http://elementscommunity.org/forum/index.php/topic,7919.0.html), the spin likelihood calculation found here (http://elementscommunity.org/forum/index.php/topic,1091.msg107605#msg107605), and calculate current numbers for each FG.  I don't have the mad math skillz required and it doesn't look like anyone around anymore does either, but I strongly suspect FGs like Decay (6 pests, 6 fractals, and 6 siphons in 30 cards) might have a higher droprate than any of the old FGs.  Maybe some are worse.  And if beating FG(A) is on average worth 400 electrum more than beating FG(B), I'd want my deck to have a high winrate against FG(A).

This obviously isn't worth building a deck around.  All of the math in this thread is potentially outdated, time to play and normalized winrate are both far greater considerations, and one doesn't really know his winrate against each FG until a large number of games has been played against the current AI for each FG.  Just food for thought. 

[Falcon4415]

I think that these stats took the chance of winning a tower in consideration, like those in the wiki.

PS: dibs on calculating current drop rate.

[Newbiecake]

I happen to be pretty good at math, so here's the formula I derived for the chance of getting 1+ cards: Take the total amount of each TYPE, then -1, followed by dividing that number by the number of cards the FG has. Follow that by calculating the average percentage (to calculate average you add the percentage of every type of cards Divide Glory then divide by x different cards there are).

Example) Divide Glory has 10 Explosions, out of a total of 80 cards. I would take that number, -1, then divide it by 80 to find out the chance of drawing 1+ Explosion. The result is 11.3% of drawing 1+ cards. If I want to calculate the chance of 2+ Explosions, I would -2 then divide by 80. The result is 10%. You get the idea.
Now to calculate the TOTAL percentage of drawing more than +1 of ANY type, I would have to calculate all the chances of drawing more than 1+ card for every type of cards Divide Glory has, with the formula given in the above example. Then I insert those numbers into the formula for calculating average, given in the first paragraph. If I want to calculate the chance of drawing 2+ of ANY type, I would have to calculate all the chances of drawing 2+ cards for every type of cards Divine Glory has, etc.

[jmizzle7]

The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.

[Falcon4415]

Decks of each FG found here (http://elementscommunity.org/forum/index.php/topic,7919.0.html)

After a quick investigation, those calculations are all good except for Rainbow's (there was a bug with the recognition of QTs as towers by the algorithm). Only 15 FGs to go .

EDIT on jmizzle7's comment: if the algorithm has been changed and nobody has yet made it public, the only chance of this project is empirical testing, and I lack the skills to do that.

[teffy]

The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.

How do you know ?.

[BluePriest]

The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.

How do you know ?.

better question, what is it?

[kev]

The stats provided by chriskang are far out of date. The algorithm has changed since those were released, iirc.

In my opening post I linked quotes from zanz, chriskang, and Evil Hamster.  Together they describe an algorithm, and I think it's the "new" algorithm you're referring to.  Am I wrong, mizz?

As I said in the opening post I'm not sure whether chriskang's table above or the change in the algorithm came first because they're all timestamped with the new forum.  Doesn't matter, though.  I just showed the numbers to illustrate the point.  As long as we have the current algorithm we can recreate the numbers.

After a quick investigation, those calculations are all good except for Rainbow's (there was a bug with the recognition of QTs as towers by the algorithm). Only 15 FGs to go .

Errr... out of curiosity did you recreate the algorithm and test the original 11 FGs using the current decklists?

[QuantumT]

Falcon, I will join you on the math side of this little project. I'm going to start by finding the chance of winning depending on each combination of the 5 cards chosen.

EDIT: Well that wasn't too hard. Here are the chances for all the possible combinations of the 5 cards chosen

11111=4%
2111=8.8%
221=13.2%
311=23.2%
32=28%
41=52%
5=100%

So before I do much more, is the formula still the same as to old one? It tries for non pillar cards 5 times before it takes pillars, and that's for the whole set of 5 cards.

Note: Chaos Lord will also be wrong.

[Falcon4415]

According to the last algorithm posted by chriskang:
- Cards are chosen ate random.
- If the card chosen is a tower, then you choose again, up to 10 times. Then the tower is kept.
- Only 4 variables are used in the spinning wheel.

However, if that is not the current algorithm, I'll say it again: this has no future unless somebody is able to hack the game and unveil its darkest secrets.

Assuming we are using the correct one:
-Chaos Lord is also wrong, my bad (thanks QuantumT).
-I there is somebody who can actually recreate the algorithm, probably using some matrix knowledge and a little programming language, he can save me the time using raw, hardcore math is going to take me (I'll end up using some Excel-like program, but still). I can't recreate that algorithm because I know 0 about programming language. The best I can do is following it in my head.

[BluePriest]

heads up, please forgive me for being very newbish on this. I looked at the links, and I got a question. After it determines the 5 cards, is it 5 different cards for each spin, or 5 different cards used for all 3 spins (spins, not slots)? I didnt think it was quite clear on that?

edit

if it checks for towers 10 times before actually deciding to use the tower, is it even worth calculating them into it? If I did my math right then you have a approcimate 99.808138195768508416% chance of not getting a tower in the spin. Seems wrong since i remember getting several towers though Such a neglegible amount, is it even worth calculating? If I did my math right...

edit, I think I completely misunderstood, no time to post why now though...

[jmizzle7]

The latest patch possible from chriskang's statistics is v1.14. The drop rate during this patch held more bias regarding the recognition of pillars/towers in spins. Since then, Zanzarino has altered the algorithm so that towers don't drop as much. This makes farming Rainbow less profitable than it once was, but it evens out due to the non-pillar redundancy in other false god decks.

I don't know what the current algorithm is, so I can't give any hard stats. I do know that the drop rates are different than what is shown in the original post.