The statistics of opening lockboxes has been discussed in detail by Wearingglasses and Titeuf24. In both cases, you'll see that the 50% mark (which is the middle of the distribution) for getting all 8 covers is somewhere between 180 and 190 lockboxes.
Here's basically what you need to know from the two blog posts above: It will take the average person approximately 185 lockboxes to obtain all eight covers when you open lockboxes 10 at a time.
The statistics are based on the behavior of the Bonus Bar. However, even with the blog posts and the Bonus Bar description there seems to continue to be some confusion about may many lockboxes it takes to get all 8 covers. Here's how the bonus bar works:
- The "length" of the Bonus Bar is equal to the number of the cover you are attempting to obtain. For instance, the Bonus Bar has a length of 1 segment if you have no covers are are attempting to open your first cover. Similarly, the Bonus Bar has a length of 7 segments if you have 6 covers and are attempting to obtain your 7th cover.
- One segment of the Bonus Bar is filled if you obtain a duplicate cover from a lockbox.
- If you are about to fill the bonus bar with the next duplicate cover you obtain, you are guaranteed to get a new cover. That new cover is the direct result of "filling" the Bonus Bar. Some people curse their luck when they obtain a "new" cover just as they're about to fill their Bonus Bar, but the fact that there is only one segment left on the Bonus Bar guarantees that the next cover that they get will be a new cover.
- Finally, the Bonus Bar resets to empty and grows in length by one segment when you obtain a new cover.
The behavior that everyone observes is that they are always one or two covers away from obtaining the hero at the end of the Special Ops or PvP Season. There is an obvious reason for this observation. The following table shows the the chance of obtaining each cover:
|Cover that you're attempting to obtain||Number of attempts at opening 10 lockboxes as dictated by Bonus Bar||Chance of getting a "New" Cover|
|First||1||8 in 8 = 100%|
|Second||2||7 in 8 = 87.5%|
|Third||3||6 in 8 = 75%|
|Fourth||4||5 in 8 = 62.5%|
|Fifth||5||4 in 8 = 50%|
|Sixth||6||3 in 8 = 37.5%|
|Seventh||7||2 in 8 = 25%|
|Eigth||8||1 in 8 = 12.5%|
You'll see from the above table that by the time you're trying to get your fifth cover, you're looking at a 50/50 chance of getting a new cover versus a duplicate cover, and at worst case, the Bonus Bar will force you to make five attempts. That's a 50/50 chance for each attempt.
By the time you're trying to get your seventh or eight cover, you're looking at 25% or 12.5% chance at getting the cover you want, respectively, while simultaneously the Bonus Bar requires you to try seven or eight times, also respectively.
So the odds are stacked against you such that there is a high likelihood that you need to fill the entire Bonus Bar for your last couple of covers. On the other hand, at least the Bonus Bar prevents you from never getting the last couple of covers you need. Wearingglasses and Titeuf24 have demonstrated that 50% of the time when their simulations are opening the 18th or 19th set of 10 lockboxes that's for the 8th and final cover.
What does all this mean for you?
- Always open 10 lockboxes at a time if you are trying to get a cover. You want to guarantee you get some cover, even if it is a duplicate. Titeuf24 discussed in another blog post the reason why you want to open 10 at a time. If you open boxes one at a time, you have a 15% chance of getting more than one cover, a 36% chance of getting one cover (same as if you opened 10 at a time) and a 48% chance of getting no covers(!!!). The overwhelming likelihood (more than 3 times) that you will get no covers is why you should just open them 10 at a time.
- Half of the people should be getting their 8th cover by the time they are opening their 19th set of 10 lockboxes (190 lockboxes). But this is the "statistical half". It's possible that everyone could have "average luck" and everyone could be getting their 8th cover when opening their 19th set of lockboxes. It may take more or less lockboxes, but don't assume that you're cursed if you don't get your 8th cover before you've opened your 19th set of 10 lockboxes.
- It may take you more or less than 190 lockboxes to get all 8 covers. That's the random chance part of this whole process. In a worst case scenario, it may take you all 360 lockboxes to get all 8 covers but Titeuf24's table shows that it's a one-in-a-thousand chance that you'll be the guy for which it takes 310 lockboxes to get all 8 covers. Don't start griping if you haven't gotten all 8 covers at 190 lockboxes. Sometimes it's just bad luck.
- There are only about 160 or so lockboxes to be had from PvP rewards or Spec Ops tasks and Group Bosses. 160 is a rough estimate, and doesn't take into account lockboxes obtained from helping allies defeat their Group Bosses during Special Ops, but you'll notice that the maximum number of free lockboxes to be obtained falls short of the average needed to obtain 8 covers.
- Expect to be filling the Bonus Bar to get your last couple of covers. This is normal and it's how the Bonus Bar is supposed to work. There is also a psychological aspect to why the bonus bar works this way. You are much more likely to buy lockboxes to complete a comic cover collection if you are only one or two covers away than if you are six or seven covers away from getting the hero, but at the same time the chance of your getting the last new cover you want is very low.
These observations are from a iOS player, but I believe that the behavior is the same for FB. Yes, this is another way that the game is trying to squeeze gold out of you. Make peace with that and you'll enjoy lockboxes a lot more.