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yeehaw

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AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg15976#msg15976
« on: January 07, 2010, 08:37:08 pm »
I find the chance of upgraded cards to be of a very low percentage of all cards, around 20%. Can others share their experience? Want to know if it is just bad luck or this is common.

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg16017#msg16017
« Reply #1 on: January 08, 2010, 02:45:25 am »
Winning Upgraded cards from the AI5 is supposed to be very low. Lower than 20% i know that.
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Offline Essence

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg16030#msg16030
« Reply #2 on: January 08, 2010, 05:22:15 am »
15% is the official number -- up from 10% when they were first introduced. :)
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zac80

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg17883#msg17883
« Reply #3 on: January 15, 2010, 11:28:31 am »
Isn't this 15% the ratio of upgraded cards in their decks? Winning any one of these cards (from 1 spin) then has a probability around:
p = Sumi((n(i)/60)3),
where i goes from 1..9 (i.e. 15% of 60) and n(i) is the number of copies of the ith upgraded card in the deck. For winning exactly k upgraded cards in 3 spins is:
q = Binomial(3, k) * pk * (1 - p)3-k,
where Binomial is the binomial coefficient.

We can assume that n(i) = 1 for any card i in the deck, as upgraded cards (if I understand it correctly) are assigned randomly during dynamic deck building, before each game. Therefore there's no bias for two cards of the same type to be upgraded. Of course the value of n(i) depends heavily on the redundacy of the actual deck, but to analytically calculate this would be quite hard. Thus - with our fair assumption - q gives a chance of:

0.012499% for winning exactly 1 upgraded card
5.20812*10-7% for winning exactly 2 upgraded cards
7.2338*10-12% for winning exactly 3 upgraded cards
("at least k" wins can be easily calculated by adding appropriate probabilities)

These are obviously lower than 15%. I can confirm on this. I've played around 100 games against AI5 winning around 80%, and got only one upgraded card at all. Values of course may be further modified by specific card checking algorithms of the spinner (i.e. pillar exclusion, etc.), which about I don't know much.

Please correct me if I'm wrong.

Delreich

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg17956#msg17956
« Reply #4 on: January 15, 2010, 04:13:50 pm »
I'm not following you there. Let's simplify a bit.

Assuming the upgrades are done randomly without preference, any given card would have a 15% chance of being upgraded, right?
If the spinner hasn't changed, worst case scenario is a 1 in 16 chance of card per spin. If spinner is using 5 cards these days, that's 1 in 25.
If the above is correct, a conservative estimate would be a 0.9% or 0.6% chance of an upgraded card per spin.
Still a lot less than 15%, obviously, but 1.8% for at least one upgrade is a lot higher than what your calcs get.

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg17971#msg17971
« Reply #5 on: January 15, 2010, 05:06:28 pm »
I have no idea how what I said got reinterpreted as "you will win an upgraded card from 15% of games."  What I actually said, referencing the OP, was simply that, of cards you win, 15% will be upgraded.

If the spinner math hasn't changed, you win at least one card in roughly 10% of AI5 games, which means you win an upgraded card in roughly 1.5% of AI5 games (15% of 10%). 

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zac80

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg17975#msg17975
« Reply #6 on: January 15, 2010, 05:18:49 pm »
Ok, sorry for the annoying math, I got a bit enthusiastic.

Perhaps I'm wrong, but I don't know much on the spinner algorithm. Doesn't it draw more or less randomly from the 60 cards (pillars excluded a priori, although I won much more pillars than anything else from halfbloods)? What do you mean, Delreich, by the spinner using 4 or 5 cards?

@Essence: So the spinner is deliberatly designed to give you a card with probability .15?

In that case of course my argument is useless, ignore it. My line of thought presumed completely random draws...

Offline jmizzle7

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg18006#msg18006
« Reply #7 on: January 15, 2010, 07:44:29 pm »

tmhopper

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg82746#msg82746
« Reply #8 on: June 05, 2010, 12:50:57 pm »
I got a lava destroyer in my first fight against a level 5

Offline eNeutrino

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg164575#msg164575
« Reply #9 on: September 25, 2010, 09:45:59 am »
@Essence: So the spinner is deliberatly designed to give you a card with probability .15?

Um... Definitely not.  At the best, according to your assumptions...  The chance would be 15%... times 15%....  times 15%.  Which means: not good.

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg164722#msg164722
« Reply #10 on: September 25, 2010, 04:57:14 pm »
I think sometimes, you can - if the topic is still actual, and the things you have to say are important enough.

To the probability 15%:

15% of the cards you win are upgraded, if the spinner chooses 5 4 (pairwise) different cards.
The probability to win a card in a spin is >= 4% as zanz said in the slot wheel mystery.

If there are 2 or more cards of a kind in the 5  4 cards, the chances to get a card increase, but the chance for an unupgraded card increases more than the chance for an upgraded card, because the chance is higher, that an unupgraded pair (3 of a kind and so on) is in the 5 4 cards than the chance for an upgraded one.

So less than 15% of the cards you win are upgraded.
Hope you can understand this.

Edit (2.1.2011):
Change of Patch 1.26: AI5 have 30% upgraded cards now, not 15%, as before.

Edit(8.8.2012) I have read, that there are 4 cards. See here.
« Last Edit: August 08, 2012, 02:58:56 pm by teffy »
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Offline Daytripper

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Re: AI5 drop rates https://elementscommunity.org/forum/index.php?topic=1840.msg165094#msg165094
« Reply #11 on: September 26, 2010, 08:11:19 am »
That makes sense to me. On a good run I would win an upped card from ai5 in about 12-15 times. I can't garantuee it happens always, but that puts it at 8% at best.

And yeah, if a topic is not locked and people think it is important, why not reply? It's better than a new thread.
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