Optimal Shuffle Box

The Optimal Shuffle Box is a Pro Kit Box in Asphalt 8: Airborne. Together with the it has replaced the  and  in the Fifth Anniversary Update.

Availability
The Optimal Shuffle Box can be obtained by watching daily ads. Since the Fast Lane Update it is also sometimes (but rarely) rewarded for completing a single daily task.

Hidden rules
The box always grants 2 equal cards. It is not possible to obtain 2 different cards.

Wrong description
The German description of the box reads "Enthält 2 gewöhnliche Karten!" (Contains 2 common cards!). This is wrong—the box does grant rare and legendary cards, like in all other language versions. It is probably a badly adapted copy of the description of the which grants only common cards.

Probabilities
As the Optimal Shuffle Box always grants 2 equal cards and players can redraw up to two times, the probability of getting desired items is actually higher than suggested by the expected values in the box info.

Card pairs
As of the Fast Lane Update, the expected value of legendary cards in an Optimal Shuffle Box is 0.64 % = 0.0064. In boxes without guaranteed items, the expected value equals the probability of getting an item, so the chance of getting a legendary card from the box is also 0.0064. If players are looking for several cards of the same kind, it can therefore be useful to open Optimal Shuffle Boxes before Random Boxes.
 * In normal boxes, the chance of getting two legendary items (not necessarily the same, but both legendary) would be their probablity multiplied twice, thus 0.00642 = 0.00004096 which is less than 0.01 %.
 * But as the Optimal Shuffle Box always grants a card twice, the multiplication of probabilities does not apply: the chance of getting two equal legendary cards already is 0.64 %.
 * For comparison: The currently has a drop rate of legendary items of 3.22 % which is significantly higher than that of the Optimal Shuffle Box. But the probability of obtaining two legendary cards from a Random Box 2 is 0.03222 = 0,00103684 ≈ 0.10 % which is still less than the 0.64 % of the Optimal Shuffle Box.

Probabilities for 3 draws
As of the Fast Lane Update, there are 136 different cards in the game. 24 of them are restricted blueprints, so the number of obtainable cards is 112. There are also specific weights assigned to each card, such as legendary cards appearing less often than common ones, or engines appearing less often than parts.

Thus, the chance of getting a specific pair of cards from an Optimal Shuffle Box with the first draw is 1 : 112 ⋅ w, with w being the weight. As w is only a factor that doesn't change during the draws, it can be neglected for now. As the player can get the pair three times in a row, the probabilities of each draw add up to
 * The chance of getting the desired pair with the first draw is 1 : 112 = 0.89 %.
 * If a player chooses to draw again, the card of the first draw will not be offered again, so the chance of getting the pair with the second draw is now 1 : 111 = 0.90 %.
 * Analogously, the chance of getting the pair with the third draw is 1 : 110 = 0.91 %.
 * 0.89 % + 0.90 % + 0.91 % = 2.7 %

This is much higher than the chance of 0.89 % that the player would have with only one draw.

Weighted probability
It is also possible to calculate the factor wL for legendary items: If the desired specific pair of cards from above is legendary, the weighted probability of getting it from an Optimal Shuffle Box is therefore 2.7 % ⋅ 0.03117 = 0.08 %. This result assumes that all legendary cards within the box have the same probability of appearing—which is almost certainly not the case, but this can only be verified with a statistical analysis.
 * Without the restricted blueprints, 23 of 112 cards in the game are currently legendary. So the chance of getting a legendary card should be 23 : 112 = 20.54 %.
 * According to the official drop rates of the box, however, the chance of getting a legendary card is 0.64 %,
 * thus wL = 0.0064 ⋅ 112 : 23 = 0.03117.

Comparison
The player could have opened a instead.
 * The chance of getting the a pair of the desired card is (1 : 112)2 = 0.008 %.
 * The official drop rate of legendary items in a Random Box currently is 3.22 %, so wL = 0.0322 ⋅ 112 : 23 = 0.1568.
 * If the desired pair of cards is legendary, the weighted probability of getting it from a Random Box 2 is therefore 0.008 % ⋅ 0.1568 = 0.001 %, which is much less than the 0.08 % of the Optimal Shuffle Box.

Conclusion
The official drop rates of the Optimal Shuffle Box only show the expected values for one draw and do not reflect the hidden rule that a card always appears twice and that a player can draw up to 3 times. The statistical outcome if a player is looking for several rare or legendary items of the same kind will therefore be higher than the numbers given in the box info. If players have both Optimal Shuffle Boxes and other boxes, they should consider opening the Optimal Shuffle Boxes first.

Statistics
The statistical analysis of the Optimal Shuffle Box highly depends on players' preferences as they can influence the outcome of the experiment by redrawing if they do not want the result of a previous draw. Therefore results for this box are always biased.

But it can be assumed that there is a certain consensus among players if they aren't looking for one specific card and reject all others: Players will ususually take a card and not redraw if
 * a legendary or rare card is offered,
 * an Engine card is offered,
 * a Tech card other than Early or Initial Tech is offered,
 * a blueprint is offered for a vehicle that the player doesn't have yet.

Therefore it can be predicted that the statistical values will generally show a bias towards the above-mentioned cards.

However, from January to February, 2019, the data set serving as a base for this statistical analysis was biased towards V8 Engines. Furthermore, the blueprint restrictions already applied and all desired blueprints were withheld by the game. Therefore As a consequence, the outcome of rare items would be lower than predicted by the official drop rates.
 * all blueprints were rejected and
 * all Part cards (including rare ones) were rejected in favour of possibly following V8 Engines.
 * However, all rare and legendary Tech cards as well as all Engine cards were kept without further draw.