I think there’s an issue with the new card percentages in the Deluxe EX pack. The results I’m getting are far from reality, and I believe the percentages are being calculated as if the Deluxe pack were a normal one, instead of having only 4 cards. Moreover, one card is guaranteed to be an EX, so the actual number of non-4-diamond cards in each pack is 3.
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Both of the things you are talking about are taken into the account, but there is an issue that we overestimate the probability for foil cards. I’ve added it to our backlog: #848
Anyway, if you apply “deck building mode” or filter out diamond rarities, the number should be correct.
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The website’s calculation for my probability of obtaining a new card for the Deluxe Pack: ex is 43.4%, which does not seem correct with how I understand the math for this pack.
In the Deluxe Pack: ex pack you pull 4 cards:
- the first card pull can only have ◆ (non-[Parallel foil]) cards.
- the second card pull can be ◆ (non-[Parallel foil]) cards or ◆◆ (non-[Parallel foil]) cards.
- the fourth card pull can only be ◆◆◆◆ cards.
The pull of the third card in a pack, is the only pull where you can get cards with the following rarity:
- ◆◆◆
- ★
- ★★
- ★★★
- ‘shiny’
- ‘crown’
- ◆, ◆◆ and ◆◆◆ [Parallel foil] cards
Currently the cards I am missing from the Deluxe Pack: ex pack is:
- 25 ◆ [Parallel foil] cards (0.359% each)
- 16 ◆◆ [Parallel foil] cards (0.359% each)
- 7 ◆◆◆ [Parallel foil] cards (0.359% each)
- 10 ★★ cards (0.156% each)
- 1 ‘2-shiny’ card (0.833% each)
- the ‘crown’ card (0.198%)
My calculation for my probability of obtaining a new card is the following (added extra parenthesis for clarity):
((25+16+7)·0.359)+(10·0.156)+(1·0.833)+(1·0.198)=19.823
My intuition for my calculation might be wrong, and I would very much like to be corrected. But the probability of obtaining a new card of 43.4% and of 19.823% is a large difference.
It makes sense if the websites code for calculating probability, is setup in a way that does not work for the Deluxe Pack: ex pack and/or it would be a very large task to recode the foundation of the website to work for the addition of the Deluxe Pack: ex pack.
That is understandable that if the website’s calculation of the probability of obtaining new cards is wrong, since the Deluxe Pack: ex pack was a curveball when it was announced to release the first time, and with the Deluxe Pack: ex pack containing a lot of the cards from the previous packs in the ‘A Series’ and the Deluxe Pack: ex pack contains ◆, ◆◆ and ◆◆◆ cards with and without [Parallel foil], and have differing probability rates while being within the same rarity.
Hopefully either my math will be corrected (please do!) or there will be implemented a change to the website’s calculation of the probability of obtaining new cards for Deluxe Pack: ex pack.
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As I said, the code currently overestimates the chance of getting a foil card (it thinks you can also get them at positions 1 and 2). That’s where the most of the difference comes from.
(But your formula is also incorrect, the probability for a new card is 1-(1-p1)(1-p2)(1-p3)*(1-p4), where p1…p4 are the probabilities to get a new card at a specific position. In other words, you should not add them, but multiply their negations. But that only makes the true number even smaller than your 19%)
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