Changes: Optimal Shuffle Box

Optimal Shuffle Box
	"Redraw cards up to 2 times! Grants 2 Cards!"
Official info
Last checked	Apr 26, 2020
Description	✘ Wrong
Sample space	✘ Wrong
Drop rates	? Incomplete
Price	-
Drop rates	Common: 94.77 %; Rare: 4.57 %; Legendary: 0.66 %
Availability	Daily Tasks; Daily ads
Statistics
Period	Apr 16, 2019 – May 18, 2020
Sample size	1,024 trials (512 boxes); Excellent: Sample size >= 1,000
Mean value	790 per card
Dispersion per box
82 Engine cards by name
180 Tech cards by name
762 Part cards by type
762 Part cards by class
762 Part cards by vehicle type

Revision as of 23:52, 15 May 2019

The Optimal Shuffle Box is a Pro Kit Box in Asphalt 8: Airborne. Together with the Optimal Split Box it has replaced the Free Box 1 † and Free Box 2 † 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 rewarded for completing a single daily task.

Daily ads rewards May 30, 2019 – Mar 4, 2020

1 Double Credits	0	0.00 %
1 Nitro Starter	302	13.25 %
1 Tuning Kit	328	14.39 %
1 Extra Tank	0	0.00 %
1 Optimal Shuffle Box	263	11.54 %
1 Optimal Split Box	301	13.20 %
Tokens	474	20.79 %
Credits	612	26.84 %
1 Asterion or 150,000	0	0.00 %

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 Compact Shuffle Box which grants only common cards.

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 expected values in the box info. Especially for engines, players can increase the drop rate by rejecting all other cards.

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.

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 Random Box 2 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.

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

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.

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 %.

As the player can get the pair three times in a row, the probabilities of each draw add up to

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 w_L for legendary items:

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 w_L = 0.0064 ⋅ 112 : 23 = 0.03117.

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.

Comparison

The player could have opened a Random Box 2 instead.

The chance of getting 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 w_L = 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 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.

The data set serving as a base for this statistical analysis was built when the blueprint restrictions were active (the game didn't grant certain blueprints). Therefore

all blueprints were rejected and
all Part cards (including most rare ones) were rejected in favour of possibly following engines.
However, all Engine cards as well as all rare and legendary Tech cards were kept without further draw.

As a consequence, the outcome of rare items is lower and that of legendary items is higher than predicted by the official drop rates.

Engines

Enginges by box type Dec 11, 2018 – Mar 18, 2019

Finish Line Box		31.56 %
Optimal Shuffle Box		12.97 %
Champion Kit Box		12.33 %
Daily Kit Box †		10.00 %
Random Box 1-5		7.01 %
Ultra Fusion Box †		6.65 %
Starter Fusion Box †		6.51 %
Super Racer Kit Box †		6.13 %
Extra Fusion Box †		5.49 %
Specialist Kit Box		5.33 %

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.

Tech

Due to the high percentage of common items in the box, it is generally not advised to open the Optimal Shuffle Box if players are looking for Tech cards. They will most probably get only Early or Initial Tech (see Tech cards by type in infobox).

Parts

The Optimal Shuffle Box mostly grants common Class D, C or B parts. It is not recommended to open it for rare Class A or S parts (see Part cards by class in infobox).

Previous versions

Optimal Shuffle Box (pre 4.2.0) †

@@ Line 68: / Line 68: @@
 * However, all Engine cards as well as all rare and legendary Tech cards were kept without further draw.
 As a consequence, the outcome of {{ra|rare}} items is lower and that of {{le|legendary}} items is higher than predicted by the official drop rates.
-==== '''Blueprints''' ====
-{{Blueprints by box type|float=right}}
-The results for blueprints are not representative because they were only taken when it was inevitable. Therefore the Optimal Shuffle Box is not included in the bar chart to the right. Besides, blueprints are generally quite rare in this box and are mostly {{co|common}} because of the high drop rate of common items. Players searching for rare and legendary blueprints are advised to open other boxes instead.
-{{clear}}
 ==== '''Engines''' ====
 {{Engines by box type|float=right}}
-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, including legendary engines like V12 or Forced-Induction V8.
+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.
 {{clear}}
 ==== '''Tech''' ====