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

Latest revision as of 20:36, 25 May 2020

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.

Players can redraw a pair of cards up to two times which enables them to increase the drop rate of desired cards (e. g. engines) by rejecting all others.

Caution: This renders the statistical results for this box biased. See →Statistics 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 Compact Shuffle Box 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:

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 %

Daily Tasks rewards Apr 10, 2019 – Apr 27, 2020

1 Optimal Shuffle Box	32	2.78 %
1 Optimal Split Box	37	3.21 %
Credits	1083	94.01 %

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 common Engines, for example, as valuable they may be for upgrading a vehicle, only give 500 when fused:

Fused Card					Fusion Coins
Vehicle Kit	Blueprint	Engine	Tech	Part	Fusion Coins
	Common	Common	Early, Common	Class D	500
			Initial	Class C	750
	Rare	Rare	Rare	Class B	1,000
			Mid	Class A	1,250
	Legendary	Legendary	Advanced, Pro	Class S	1,500
Extra					2,000
Prime					2,500
Superb					3,000
Festival					3,500

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 0.66 % = 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 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 0.66 %.
For comparison: As of the 2019 Spring Update, the Random Box 2 has a drop rate of legendary items of 2.61 % 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 ≈ 0.07 % which is still less than the 0.66 % 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 1 : 44 ⋅ 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 : 44 ≈ 2.27 %.
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 (43 : 44) times the chance of getting it from the remaining cards minus the one taken out with the first draw (1 : 43): (43 : 44) ⋅ (1 : 43) ≈ 2.27 %.
Analogously, the chance of getting the pair with the third draw is (43 : 44) ⋅ (42 : 43) ⋅ (1 : 42) ≈ 2.27 %.

As the player has three draws to get the pair, the probabilities of each draw add up to

2.27 % + 2.27 % + 2.27 % = 6.81 %

This is much higher than the chance of 2.27 % 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, rare and legendary cards will be higher than predicted by the official drop rates.

Engines

Name	Engines	D Parts	C Parts	B Parts	A Parts	S Parts
Champion Kit Box	12.22	11.85	13.33	8.06	18.10	15.60
Daily Kit Box †	10.00	16.83	16.41	17.02	15.54	14.20
Engine Box 1-5	100.00	0.00	0.00	0.00	0.00	0.00
Extra Fusion Box †	6.40	15.70	16.67	8.94	16.91	14.98
Finish Line Box	45.07	8.26	9.28	9.23	9.76	9.42
Multiplayer Pro Box	9.89	15.05	15.81	7.96	17.53	17.20
Optimal Shuffle Box	8.01	19.92	21.48	26.56	2.15	4.30
Optimal Split Box	3.76	22.78	21.73	20.52	1.78	2.26
Parts Box 1-5	0.00	21.08	20.57	20.57	21.85	15.94
Random Box 1-5	7.31	21.99	21.28	12.79	5.91	4.99
Specialist Kit Box	9.26	19.63	11.48	8.52	18.52	12.22
Starter Fusion Box †	8.40	21.60	21.36	12.22	6.05	3.95
Tech Box 1-5	0.00	0.00	0.00	0.00	0.00	0.00
Ultra Fusion Box †	8.17	5.53	5.78	3.27	34.67	36.43

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 common 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 common Class D, C and B parts. It is not recommended for rare Class A or S parts.

Previous versions

Optimal Shuffle Box (pre 4.2.0) †

@@ Line 1: / Line 1: @@
 {{Optimal Shuffle Box|style=infobox}}
 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]].
+Players can redraw a pair of cards up to two times which enables them to increase the [[drop rate]] of desired cards ({{nobr|e. g.}} engines) by rejecting all others.
+'''Caution:''' This renders the statistical results for this box '''biased'''. See {{→|Statistics}} 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 {{Compact Shuffle Box}} which grants only common cards.
 == '''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 Tasks|daily task]].
+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 Tasks|daily task]].
+[[Relative frequency|Relative frequencies]]:
+{{Daily ads rewards}}
+{{Daily tasks rewards}}
-== '''Hidden rules''' ==
+== Hidden rules ==
 The box always grants 2 equal cards. It is not possible to obtain 2 different cards.
-== '''Wrong description''' ==
+== 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 {{co|common}} Engines, for example, as valuable they may be for upgrading a vehicle, only give {{a8fusioncoins|500}} when fused:
-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.
+{{Cards to fusion coins table (pre 5.0.0) a8}}
 == '''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 value]]s in the {{A8BoxInfo}} box info. Especially for engines, players can increase the drop rate by rejecting all other cards.
+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 rate]]s in the [[box info]].
 ==== '''Card pairs''' ====
-As of the Fast Lane Update, the expected value of legendary cards in an Optimal Shuffle Box is {{nobr|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.
+As of the [[2019 Spring Update]], the drop rate of legendary cards in an Optimal Shuffle Box is {{nobr|0.66 %}} = 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 0.0064<sup>2</sup> = 0.00004096 which is less than {{nobr|0.01 %}}.
+* In normal boxes, the chance of getting two legendary items (not necessarily the same, but both legendary) would be their probablity multiplied twice, thus 0.0066<sup>2</sup> = 0.00004356 which is less than {{nobr|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'' {{nobr|0.64 %}}.
+* 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'' {{nobr|0.66 %}}.
-* For comparison: The {{Random Box 2}} currently has a drop rate of legendary items of {{nobr|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 0.0322<sup>2</sup> = 0,00103684 ≈ {{nobr|0.10 %}} which is still less than the {{nobr|0.64 %}} of the Optimal Shuffle Box.
+* For comparison: As of the 2019 Spring Update, the {{Random Box 2}} has a drop rate of legendary items of {{nobr|2.61 %}} 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 0.0261<sup>2</sup> = 0.00068121 ≈ {{nobr|0.07 %}} which is still less than the {{nobr|0.66 %}} 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.
-===== '''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 {{nobr|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.
+Thus, the chance of getting a specific pair of cards from an Optimal Shuffle Box with the first draw is {{nobr|1 : 44 ⋅ ''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 {{nobr|1 : 112}} = {{nobr|0.89 %}}.
+* The chance of getting the desired pair with the first draw is {{nobr|1 : 44}} ≈ {{nobr|2.27 %}}.
-* 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 {{nobr|1 : 111}} = {{nobr|0.90 %}}.
+* 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 ({{nobr|43 : 44}}) times the chance of getting it from the remaining cards minus the one taken out with the first draw ({{nobr|1 : 43}}): {{nobr|(43 : 44) ⋅ (1 : 43)}} ≈ {{nobr|2.27 %}}.
-* Analogously, the chance of getting the pair with the third draw is {{nobr|1 : 110}} = {{nobr|0.91 %}}.
+* Analogously, the chance of getting the pair with the third draw is {{nobr|(43 : 44) ⋅ (42 : 43) ⋅ (1 : 42)}} ≈ {{nobr|2.27 %}}.
-As the player can get the pair three times in a row, the probabilities of each draw add up to
+As the player has three draws to get the pair, the probabilities of each draw add up to
-: {{nobr|0.89 %}} + {{nobr|0.90 %}} + {{nobr|0.91 %}} = {{nobr|2.7 %}}
+: {{nobr|2.27 %}} + {{nobr|2.27 %}} + {{nobr|2.27 %}} = {{nobr|6.81 %}}
-This is much higher than the chance of {{nobr|0.89 %}} that the player would have with only one draw.
+This is much higher than the chance of {{nobr|2.27 %}} that the player would have with only one draw.
-===== '''Weighted probability''' =====
-It is also possible to calculate the factor ''w<sub>L</sub>'' 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 {{nobr|23 : 112}} = {{nobr|20.54 %}}.
-* According to the official drop rates of the box, however, the chance of getting a legendary card is {{nobr|0.64 %}},
-* thus ''w<sub>L</sub>'' = 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 {{nobr|2.7 % ⋅ 0.03117}} = {{nobr|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 {{nobr|(1 : 112)<sup>2</sup>}} = {{nobr|0.008 %}}.
-* The official drop rate of legendary items in a Random Box currently is {{nobr|3.22 %}}, so ''w<sub>L</sub>'' = 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 {{nobr|0.008 % ⋅ 0.1568}} = {{nobr|0.001 %}}, which is much less than the {{nobr|0.08 %}} of the Optimal Shuffle Box.
 ==== '''Conclusion''' ====
@@ Line 51: / Line 50: @@
 === '''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.
+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
+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:
-* 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.
+* All Part cards (including rare ones) are rejected in favour of possibly following engines.
-Therefore it can be predicted that the statistical values will generally show a bias towards the above-mentioned cards.
+* All Engine, Advanced and Mid-Tech cards are kept without further draw.
+As a consequence, the average [[relative frequency|relative frequencies]] of Engine, Tech, {{ra|rare}} and {{le|legendary}} cards will be higher than predicted by the official drop rates.
-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 {{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 rigght. 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}}
+{{Pro kit box statistics mini table
+  |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.
+  |main = e
-{{clear}}
+  |class = abcds
+}}
+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 {{co|common}} engines due to the high drop rate of common cards.
 ==== '''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).
+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 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).
+The Optimal Shuffle Box has a high drop rate of {{co|common}} Class D, C and B parts. It is not recommended for {{ra|rare}} Class A or S parts.
+{{clear}}
+== '''Previous versions''' ==
+* {{Optimal Shuffle Box (pre 4.2.0)}}
 == '''See also''' ==
+* {{Optimal Split Box}}
 * [[Pro Kit Boxes with hidden rules]]