Festival Coin Pack | |
---|---|

"Contains up to 12 Festival Coins!" | |

Official info | |

Last checked
| Sep 21, 2019 |

Price
| - |

Drop rates
| - |

Availability
| Festival |

The **Festival Coin Pack** is a Pro Kit Box in the larger sense introduced with the 6th Anniversary Festival in Asphalt 8: Airborne. It does not contain Pro Kit cards but **Festival Coins**.

## **Availability **

Festival Coin Packs can be obtained by accomplishing festival quests. They are opened by tapping the **Claim** button of the quest. The coins are then automatically added to the player's coin score.

## Analysis

### Sample space

The box says that the box grants “up to 12 Festival Coins”. In reality, the box only grants even numbers of Coins, so outcomes like **1**, **3**, **5**, ..., **11** are impossible. Obviously, the underlying random process can be compared to a simple roll of a six-sided die, with the outcomes multiplied by 2. The sample space is Ω = {2, 4, 6, 8, 10, 12}.

### Probabilities

If a die is fair, all outcomes have the same probability P = 1/6 of occurring. The law of large numbers asserts that in the long run, the relative frequency of all outcomes will be the same. This means that players can expect that the number of times they receive **2**, **4**, **6**, ..., **12** all make up 1/6 of the total amount of received Coins. If the process is fair, the expected value (the average number of Coins per box in the long run) is

- (2 + 4 + 6 + 8 + 10 + 12) / 6 = 7.

For any number of received Coins from a single trial (opened box), the outcomes are only *success* (getting it) or *failure* (not getting it). Therefore, opening Festival Coin Packs is a Bernoulli process whose random variables are binomially distributed.

### Statistics

#### Sample size

Sample size from September 18 to September 29, 2019:

- 265 trials (opened boxes), of which 53 with Premium Pass.

If the underlying process is fair, the relative frequencies of getting a certain amount of Coins will get closer to the expected values of 1/6 = 16.67 % as the number of trials increases.

#### Results

The following table shows the number of times **2**, **4**, **6**, ... were received, together with the real relative frequency compared with the expected value for each outcome. The last row shows the probability of the outcome defined by the binomial distribution if the process was fair.

According to player feedback^{[1]} and to the analysis of the 53 Coin Packs claimed with Premium Pass, upgrading to Premium does not influence the drop rates, so the Premium Pass data has been included.

Coins | 2 | 4 | 6 | 8 | 10 | 12 |
---|---|---|---|---|---|---|

Times received | 45 | 185 | 21 | 7 | 3 | 4 |

Relative frequency | 16.98 % | 69.81 % | 7.92 % | 2.64 % | 1.13 % | 1.51 % |

Expected value | 16.67 % | 16.67 % | 16.67 % | 16.67 % | 16.67 % | 16.67 % |

Probability if process was fair | 6.45 % | 0.00 % | 0.00 % | 0.00 % | 0.00 % | 0.00 % |

The outcomes show significant deviations from the expected values if the process was fair. For example, such a high amount of **4** outcomes would have a probability of less than 0.01 % which is close to impossible. Furthermore, the average number of Coins received per box is 4.11 instead of the above-mentioned 7.

Therefore it is probable that the outcomes have roughly the estimated drop rates given in the table below:

Coins | 2 | 4 | 6 | 8 | 10 | 12 |
---|---|---|---|---|---|---|

Times received | 45 | 185 | 21 | 7 | 3 | 4 |

Relative frequency | 16.98 % | 69.81 % | 7.92 % | 2.64 % | 1.13 % | 1.51 % |

Estimated real drop rate | 17.00 % | 70.00 % | 8.00 % | 3.00 % | 1.00 % | 1.00 % |

Probability based on drop rate | 6.51 % | 5.32 % | 9.03 % | 14.21 % | 22.03 % | 14.58 % |

### Conclusion

The number of Festival Coins granted by the box is not fair. The most likely outcome is **4**.

## References

- ↑ Koolmunki (2019-09-23). User comment. Asphalt Wiki. Retrieved on 2019-09-23.

The statistical data on this page is part of WikiProject Statistics. It contains original research which may be incomplete, incorrect or biased. |