Mystery Box Prizes: Catch ’em all!

//Mystery Box Prizes: Catch ’em all!

Mystery Box Prizes: Catch ’em all!

Introduction

As you all likely know, every day you have the chance to claim up to 10 Mystery Box prizes from the Victor’s Wheel in Versus (Theme, Standard, Expanded, Legacy, excluding Events/Tournament Wheels).

Each day at 8:00 PM EDT the prize wheel resets.

You get a chance to get a Mystery Box each time you win a match, but if the wheel spins on a spot where you’ve already claimed the day’s prize, you won’t get another one. You will; however, always get a small amount of trainer tokens.

Need more info? Check out the Getting Started guide: How to Earn Tokens, Tickets, and Boosters in Pokemon TCG Online, as well as the post: How to Spend Tokens on PTCGO.

What’s in a Mystery Box?


Mystery Boxes can contain the following:

These odds are likely to be a little off, as the sample size is low.

Please feel free to comment below some of your Mystery Box pulls to help this data be more accurate. (Preferably a list of your last 20+ prizes, excluding Tournament Mystery Boxes)

Current sample size: 272.

  • 25 Trainer Tokens ~39%
  • 50 Trainer Tokens ~15%
  • 100 Trainer Tokens ~5%
  • 375 Trainer Tokens ~3%
  • 1 Tournament Ticket ~26%
  • 2 Tournament Tickets ~7%
  • 4 Tournament Tickets ~<1%
  • 1 Random Booster Pack ~5%

Average Loot Earnings

  • 61% of the prizes contain Trainer Tokens, with an average of ~40 Trainer Tokens.
  • 33% of the prizes contain Tournament Tickets, with an average of ~1.27 Tickets.
  • 5% of the prizes contain a Random Booster pack (trade-locked, Standard)

If you open 10 Mystery Boxes, chances are 6 of them will contain tokens, 3 will contain tickets, and 1 will be a random booster pack, with a total average of about ~237 tokens, ~3.82 tickets, and ~1 Booster Pack.

If you open 20 Mystery Boxes, chances are 12 of them will contain tokens, 7 will contain tickets, and 1 will be a random booster pack, with a total average of about ~474 tokens, ~8.92 tickets, and ~1 Booster Pack.

If you open 100 Mystery Boxes, chances are 61 of them will contain tokens, 33 will contain tickets, and 5 will be random booster packs, with a total average of about ~2411 tokens, ~42 tickets, and ~5 Booster Packs.

Okay, now we know what’s in the Mystery Boxes, and roughly what to expect from them, but how long does it take to get all 10 each day?

Math Ahead!

How long should it take to get all 10 MBPs each day?

Maybe I’m a crazy nerd, but I was really interested to find out this simple problem.

To start, it obviously takes at least 10 wins and therefore wheel spins to get all 10 MB prizes each day. (The odds of it taking exactly 10 wins is 10!/10^10, or <0.036%.) But on average, how many wins should it take?

It turns out that in combinatorics and probability, this is considered to be an example of the “Coupon Collector’s Problem“.

That is, there is a set number of items, which are “replaced”, where each item is ideally earned once.

The equation to find the average or mean Estimated Time is asymptotically n ln(n) (or n log (n)). To find a more accurate estimate, use E(Tn) = n ln(n) + γn +1/2, where γ ~= 0.5772156641 (Euler’s constant).

For n=10, E(T10) = 10 * ln(10) + γ*10 +1/2 = 29.2980, or about 29 wins / wheel spins on average.

So, it should take roughly 29 wheel spins to get all 10 MB prizes! Wha!

It may seem like overkill, but pay attention to the prize wheel spins in the future, and you’ll see that:

  • the first spin of the day is of course always a new prize
  • the second spin has a 90% chance to be new, only 10% old.
  • if the second spin was new, the third spin has an 80% to be new, 20% old…
  • the more prizes you get the more likely it is that you’ll get a “repeat” and therefore no MB prize.

To get even more accurate, we can calculate the standard deviation of this distribution using a simple equation and generate confidence intervals.

σTn ~ 3πn/√(6)

For n=10, σT10 ~ 12.8255

68%: μ ± σ

  • 16.4725 < E < 42.1235

95%: μ ± 2σ, E >= 10

  • 10.000 < E < 54.949

99.7%: μ ± 3σ, E >= 10

  • 10.000 < E < 67.7745

In other words, it will always take at least 10 wins to get all 10 MB prizes. On average, it’ll take about 29 wins, but of course could be lower or much higher. The vast majority of the time it will take between 10 and 55 wins. It will virtually always take between 10 and 68 wins.

(If it takes more than 68 wins to get all 10 prizes, Congratulations–you’re an outlier of more 3 standard deviations from the mean! Welcome to the 0.3%!)

How many times should it take to get p Prizes?

If you’re not up getting all 10 prizes (as it’ll take on average 29 wins) per day, here’s how you can find out how long it will take to get *p* prizes, where 1 <= p < n, n=10.

E(n,p) = n ln (n/(n-p), p!= n

Let’s plug in each relevant value, where n=10 and 1 <= p < 10.

  • E(10,1) ~ 1
  • E(10,2) ~ 2 (+1)
  • E(10,3) ~ 4 (+2)
  • E(10,4) ~ 5 (+1)
  • E(10,5) ~ 7 (+2)
  • E(10,6) ~ 9 (+2)
  • E(10,7) ~ 12 (+3)
  • E(10,8) ~ 16 (+4)
  • E(10,9) ~ 23 (+7)
  • and we know E(10) ~ 29 (+6)

This tells us that, on average the first two spins well net us the first 2 prizes without a repeat (the 1st prize is *always* new, second one has a 90% to be new). After 5 wins, we should have 4/10 prizes. After 9 wins we should have 6/10 prizes. 12 wins will net us 7/10 prizes, 16 wins will get us another for 8/10 prizes.

It was suggested that it may not be worth it to get the last few prizes each day to get to 10, and from here was can see that it only takes 1 or 2 spins per prize all the way up to the 6th one. The 7th prize takes another 3 spins, and the 8th another 4. The 9th and 10th prize take about 6-7 additional spins each.

I’d say it’s likely worth it to aim for the first 8 prizes a day, which should take about 16 wins on average. If that’s too much, aim for 7 prizes a day, which should take 12 wins on average.

Just a casual player? Odds are that if you win just twice a day, you’ll get 2 prizes. Just bring up your total to 5 wins and you should average 4 prizes a day.

In brief…

Average Prizes: 61% Tokens, ~ 40 Trainer Tokens, 33% Tournament Tickets, ~1.27, 5% Random Booster Pack.

It’ll take on average about 29 spins to get all 10 Mystery Box prizes each day. It can be as low as 10 spins (about 10!/10^10 chance, or <0.036%), and virtually always less than 68 times. Very unlikely to be more than 55 times.

By | 2016-10-09T06:59:24+00:00 October 4th, 2016|More Info|0 Comments

About the Author:

Lincoln is the creator of PTCGOhub.com and is an avid Pokemon fan. Lincoln has enjoyed the video game series starting with Pokemon Yellow, and a fan of the Pokemon Trading Card Game since the original Base Set.

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