Path of Exile - Crunching the Numbers on 20000 Stacked Decks
157Thanks to Twitch streamer Xalxixinha for letting me use their data! You can check out their stream at http://twitch.tv/xalxixinha
I have a maths background (albeit not in stats) and thought I'd rip into Xalxixinha's pulls from 20000 stacked decks, from which they looted divination cards worth about 63000 chaos. In the sort of silly coincidence that only I care about, this is almost exactly equal to Pi chaos orbs per Stacked Deck.
Note that of that 63000 chaos, 46000 - almost 75% - came from merely 360 divination cards. The remaining 92.2% of cards awarded only 17000c in loot.
Even more extreme, the 'best' 59 cards looted contained over 58% of the total value. With Stacked Decks, you are chasing the jackpots, not the 5c and 10c cards. These 59 cards were worth more than an exalt each.
From calculating estimates based upon Poission distributions with 10% tails at each end (for all cards over 15c) and 2.5% tails at each end (for cards under 15c), I can only conclude that the expected value of a Stacked Deck in the Delirium economy is more than 1.6c and less than 6.1c.
I hypothesise that the formula for stacked decks considers the weighting of the divination cards, but raised to the 0.8th power. This would mean that if the Doctor divination card was a hundred thousand times rarer than the Rain of Chaos card in normal play, it would be ten thousand times rarer from a stacked deck, as 10000 = 100000^0.8 . (The actual number is probably closer to 1000 than 100000).
Xalxixinha's raw data is online: https://docs.google.com/spreadsheets/d/1aXVY0U9Azk_SMUHNsuW-5HoITRcr2-35kB5kVX1jtik/edit#gid=1466797463
The out of date (but still maybe mostly accurate) datamined currency drop rates are here: https://www.pathofexile.com/forum/view-thread/997165
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