Guest Posts
265
General Discussion / Best rare win story
« on: December 15, 2009, 10:10:04 pm »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.
