Best rare win story

[CB!]

I was grinding the fake gods to upgrade my last tower for my darkness deck.  I had like 1502 quanta and decided to upgrade then play level 1 and 2 to get the cash to start grinding the fake gods again.  After the upgrade, I took my measly 2 quanta and started a level 1 match.  The win was easy, obviously.  But then came 1 spinner roll: Pulverizer, Pulverizer, PULVERIZER.... off of a lvl 1.... woot....

[CB!]

Today's your lucky day

Level 1 deck is composed of about 13/14 pillars of various types and 47/48 other cards chosen randomly between all non upgraded cards (including rares).
So basically, the chances for a pulv to be in this deck are about 35%.
Then, as it is a very mixed build, your chances to win something during the (unique) spin must be somewhere near 10%
And the chances for this card to be a pulv (and not another one from its deck) are clearly far below 1%.

Do the math, you've seen something that happens far less than 1 time out of 3000.
This is your very lucky day.

Where did you find the level 1 deck build information?  Just curious.... and I guess I should've bought a lottery ticket, too....

[CB!]

It's called Electrum, and congratz!

Yeah, electrum... that's what I meant....

[chriskang]

Today's your lucky day

Level 1 deck is composed of about 13/14 pillars of various types and 47/48 other cards chosen randomly between all non upgraded cards (including rares).
So basically, the chances for a pulv to be in this deck are about 35%.
Then, as it is a very mixed build, your chances to win something during the (unique) spin must be somewhere near 10%
And the chances for this card to be a pulv (and not another one from its deck) are clearly far below 1%.

Do the math, you've seen something that happens far less than 1 time out of 3000.
This is your very lucky day.

[Evil Hamster]

Today's your lucky day

[oaky180]

Dang, lucky you
 

[Uncle Jellyfish]

It's called Electrum, and congratz!

[chriskang]

This is the general algorithm for all card spins: level 1, 2, 3, 6, pvp and t50. There is no special treatment for level 1.
It just confirms what we already know:
- chances to win a card from a 50 cards deck are actually much higher than 1/2500 thanks to the "4 card shortlisting" mechanism described above (if would be 1/2500 if every pick was random)
- chances to win a card increase a lot for cards that are present multiple times in the deck

As level 1 deck is mostly composed of unique cards (just 1 or 2 copies of each card is present inside the deck), then the chances to actually win something are far lower than, say, a fake god.
If you compare the first table on those 2 pages:
http://elementsthegame.wikia.com/wiki/Scorpio
http://elementsthegame.wikia.com/wiki/Fire_Queen
You'll see that Scorpio, who has a wide range of different cards (16), lets you win only 32% of the times. Whereas with Fire Queen, who has 8 different cards, your chances to win are much higher (46%).

My second percentage (10%) was an estimation of what the win rate would be for a deck composed of about 35 different cards. This is not the result of a real simulation, just a guess from me, seeing the progression of the 2 fake gods above:
8 different cards --> 46% chance to win
16 different cards --> 32% chance to win
25 different cards --> probably something around 20%
35 different cards --> probably something around 10%

Now the third percentage (1%) comes from the fact that cards present in multiple copies have much higher chances to be present in the "4 card shortlist" and therefore to be finally chosen. Look at scorpio again:
- cards that are present 1 time inside the deck have a 1.9% chance to be won
- cards that are present 2 times have a 4.7% chance to be won which is more than twice the previous number (4.7 = 1.9 + 2.8)
- cards that are present 3 times have a 8.5% chance to be won which represents an even bigger increase than above (8.5 = 1.9 + 2.8 + 3.8)
and so on, till the end.

On a typical level 1 deck, most cards will be present just 1 time but some will probably be more present than that (because, well, random is random). And those are the ones that will make the chances to get a pulv go down drastically.
My guess is that the table for a level 1 deck will look something like this :
- random card present 3 times inside the deck --> 25%
- other card with 3 copies --> 25%
- card present 2 times --> 6%
- other card with 2 copies --> 6%
- other card with 2 copies --> 6%
- other card with 2 copies --> 6%
- unique card --> 0.7%
- and so on for the 33 other unique cards --> 0.7%

Your next argument will probably be "ok, but what if the pulv is the card that has 2 or 3 copies". And I'll answer that this case is so rare that it won't actually change the overall statistics. After an infinite number of fight against level 1, the percentages will be equally distributed between all existing cards (about 136), not just the 47 of a single given deck.

[chriskang]

Why below 1%? If there's about 50 eligible cards to chose from, shouldn't there be about a 2% chance for any one of them? That should make it about 1 in 1500, if the first two numbers are accurate.

If it worked that way, the chances to win would be far too low, as you suspect.
The real algorithm is a bit more complex:
1. Pick a random card in your opponent's deck
2. If it's a pillar, go back to 1
3. Security mechanism (for builds that are composed of pillars only) : if, after 10 random picks, you still get a pillar then keep it
4. Store card in variable card1.
5. Repeat steps 1 to 4, until you have filled 4 variables
6. Now the spinning starts for 3 rounds but you only pick cards in [card1, card2, card3, card4]. This ways, the chances to pick 3 times the same one are much higher.

[chriskang]

Assuming there's no special treatment of any cards at deck selection, and likewise when selecting cards for the spinners (except for pillars), then the chance of a successful spin yielding any particular card should be exactly the same for every eligible card.

Yes

If this is true, the chance of getting a particular card would be 1 in 122 (if I've counted right, and assuming the shards are excluded, ignoring the pillars as they should be rare enough not to matter).

Exactly. That's where my "less than 1%" comes from. The "far less" was a bit exaggerated

The chance of getting a card after a win is a bit trickier to figure out, but the worst case scenario (no duplicates selected) would be 1 in 16 (1/4²), or 1 in 25 if there's five cards in the spinner.

Agree too. There are 4 cards in the shortlist so the worst case is 1/16 (6.2 %). On average, my figure of 10% shouldn't be too far from truth.

If this is all correct, the chance of getting a (non-specific) rare isn't all that bad, really, at better than 1 in 140. Compared to the about 1 in 12 for Fire Queen it's not all that impressive, but only EE, Fahrenheit and shard are available there.

That seems pretty correct too. By taking 10% win rate at spinning, the calculus gives 1 rare for 90 victory with level 1 (instead of your 1/140).
This is indeed 7 times lower than Firefly Queen and AI3 (whose drop rates are very similar to FG).
IMHO, your best bet is still hoping for a rare farm deck in t50.

I don't know if this is well known or not but the best rare farm deck is undoubtedly something like this:
24 x useless pillar
6 x eternity

This has probably near 100% chance to give you the rare (on average, after 3 spins). And the changes for the player to get it are actually much much higher than, say:
18 x pillar
4 x pulv
4 x eternity
4 x eagle's eye

[Delreich]

Errm, what I meant was, assuming you win a card and there's a pulverizer in the deck, wouldn't the chance of getting a pulverizer be exactly the same as getting any particular other card?
Going one step further, if rares aren't treated differently from non-rares in deck or spin selection, wouldn't the chance of a card won from AI1 being rare be <number of rares> in <number of non-pillar cards>?

[Delreich]

It's a shame I'm so utterly useless with words, or I might even make myself understood sometimes...

By "50 cards to chose from", I meant for the shortlist (which I thought was five cards, but if you say four then that's probably what it is). But nevermind that, I think we're overthinking this a bit.

Assuming there's no special treatment of any cards at deck selection, and likewise when selecting cards for the spinners (except for pillars), then the chance of a successful spin yielding any particular card should be exactly the same for every eligible card. If this is true, the chance of getting a particular card would be 1 in 122 (if I've counted right, and assuming the shards are excluded, ignoring the pillars as they should be rare enough not to matter).

The chance of getting a card after a win is a bit trickier to figure out, but the worst case scenario (no duplicates selected) would be 1 in 16 (1/4²), or 1 in 25 if there's five cards in the spinner.

If this is all correct, the chance of getting a (non-specific) rare isn't all that bad, really, at better than 1 in 140. Compared to the about 1 in 12 for Fire Queen it's not all that impressive, but only EE, Fahrenheit and shard are available there.