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.
Players can redraw a pair of cards up to two times which enables them to increase the drop rate of desired cards ( engines) by rejecting all others.
Caution: This renders the statistical results for this box biased. See below.
== 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.
== Availability ==
The Optimal Shuffle Box can be obtained as a random reward from daily ads. Since the Fast Lane Update it is also rewarded for completing a single daily task.
Relative frequencies:
== Hidden rules ==
The box always grants 2 equal cards. It is not possible to obtain 2 different cards.
== Opening strategy ==
Players who only open Optimal Shuffle Boxes to get Fusion Coins should redraw and try their luck according to the able below. The box does not grant Vehicle Kit cards or blueprints, but Engines, for example, as valuable they may be for upgrading a vehicle, only give when fused:
== Analysis ==
=== 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 drop rates in the box info.
==== Card pairs ====
As of the 2019 Spring Update, the drop rate of legendary cards in an Optimal Shuffle Box is = 0.0066. In random boxes without guaranteed items, drop rate equals probability, so the chance of getting a legendary card from the box is also 0.0066.
* In normal boxes, the chance of getting two legendary items (not necessarily the same, but both legendary) would be their probablity multiplied twice, thus 0.00662 = 0.00004356 which is less than .
* 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 .
* For comparison: As of the 2019 Spring Update, the has a drop rate of legendary items of 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 0.02612 = 0.00068121 ≈ which is still less than the of the Optimal Shuffle Box.
If players are looking for several cards of the same kind, it can therefore be useful to open Optimal Shuffle Boxes before Random Boxes.
==== Redrawing ====
Since the Fast Lane Update, there are 136 different cards in the game. The 2019 Spring Update took away blueprints (63) and bike-specific parts (26) from the box, and it also does not grant i3, V12 MPI and Hot Wheels Engines, so the number of obtainable cards is 44. 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 , with w being the weight. As w is only a factor that doesn't change during the draws, it can be neglected for now.
* The chance of getting the desired pair with the first draw is ≈ .
* 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 the chance of not getting it with the first draw () times the chance of getting it from the remaining cards minus the one taken out with the first draw (): ≈ .
* Analogously, the chance of getting the pair with the third draw is ≈ .
As the player has three draws to get the pair, the probabilities of each draw add up to
: + + = 
This is much higher than the chance of that the player would have with only one draw.
==== 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 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.
Assuming a consensus among players that Engine, Advanced and Mid-Tech cards are more valuable than others, the drawing strategy of this experiment follows strict rules:
* All Part cards (including rare ones) are rejected in favour of possibly following engines.
* All Engine, Advanced and Mid-Tech cards are kept without further draw.
As a consequence, the average relative frequencies of Engine, Tech, and cards will be higher than predicted by the official drop rates.
==== Engines ====
If a player rejects all cards but engines, it is possible to increase their total drop rate significantly. This strategy makes the Optimal Shuffle Box one of the boxes with the highest engine drop rates. Players should be aware that these are mostly engines due to the high drop rate of common cards.
==== Tech ====
For the same reason, the Optimal Shuffle Box is a good choice for Early or Initial Tech, but not for Advanced or Mid-Tech (see Tech cards by type in infobox).
==== Parts ====
The Optimal Shuffle Box has a high drop rate of Class D, C and B parts. It is not recommended for Class A or S parts.
== Previous versions ==
* 
== See also ==
* 
* Pro Kit Boxes with hidden rules