You're (Not) Going to be Rich!

Guest Post By Deepcut From Warcraft Gold Analysis
My name is Deepcut, and I currently play on the Eldre'Thalas realm. After seeing all the fuss about "Blizzard Sanctioned Gambling" in World of Warcraft, I decided to see if I could help the community by running an experiment of my own. I emailed Markco of Just My Two Copper with my idea, and with that decided to start with my first gold-making blog.

Statistically Speaking
I am a finance major here at the local university and I also enjoy spending my time in World of Warcraft making gold. I was recently inspired to see if I could successfully perform meaningful statistical analysis on Mysterious Fortune Card. I was inspired by the blog World of Warcraft Fortunes.

The House Always Wins

What was I setting out to do (besides lose a ton of money)? At the basic level, I wanted to be able to predict the expected value when flipping a Mysterious Fortune Card with reasonable accuracy. Originally I had estimated I could calculate within 70-75 silver, however, I didn't take into account what the 5,000 gold card (I actually got one!!!) would do to the analysis. I also wanted to see if I could figure out any rhyme or reason to the possible drop rates of any individual card.
 

So, over the course of a couple of weeks, I gathered up over 8,000 Mysterious Fortune Cards and then tried my luck.  Here's the statistics rendered from flipping the cards:


Crunching the Numbers
What does this data mean? Well, it means after flipping 8,062 cards, I am 95% confident (which is pretty good), the expected value of a Mysterious Fortune Card is 2g28s27c +/- 1g27s53c (1g0s74c to 3g55s8c). At a cost of roughly 11g each, there is hardly a profit to be made from flipping the cards.

Also it shows that I made back a paltry 18,402g on my nearly 90,000g investment. Here are the percentages of the flips:  -->

A Wild Guess
If I had to speculate on the possible percentages, given the fact that I am assuming Blizzard is using nice round numbers for their probabilities, I would break it down as follows (I incorporated the data from the World of Warcraft Fortunes blog as well):
        
10s = 53.5%
50s = 20.5%
1g = 16%
5g = 7.75%
20g = 1.75%
50g = .23%
200g = .2%
1000g = .05%
5000g = .02%

Since I know with a decent amount of confidence my expected value should be between 1g0s74c to 3g55s8c, these percentages give me an expected value of 3g6s85c, which falls well within my confidence interval while following a natural progression of lower percentages for the higher value cards.

Of course, there are 58 different Fortune Cards, and maybe the percentage is derived from a fraction of 58:

1s = 31/58 = 53.4483%
50s = 12/58 = 20.6897%
1g = 9.2/58 = 15.8621%
5g = 4.5/58 = 7.7586%
20g = 1/58 = 1.7241%
50g = .14/58 = 0.2414%
200g = .12/58 = 0.2069%
1000g = .03/58 = 0.0517%
5000g = .01/58 = 0.0172%

These percentages give an expected value of 2g96s21c, also within my confidence interval.
You can tweak the percentages and still easily fall within the confidence interval. So really it's anyone's guess. I would need many, many, many more flips to determine what the actual drop percentages are - roughly 32 million flips. (This is 95% confidence +/- 2 copper, with the assumption standard deviation won't change radically).

Now, these could be off by quite a bit, especially on the ones with much lower probability. I could have been very unlucky on the 1,000g card (like if they were 1/1000), or extremely lucky on the 5,000g card (like if they were 1/10000). However, I think we can all agree your chances of getting one of the rarer cards are extremely cost prohibitive, and not worth your time and effort.

Conclusion
TLDR: Don't bother flipping the cards - sell them or make Fortune Cookies, or just make glyphs from the ink. Of course, maybe you just want to see if you can get one of the 5,000g cards for bragging rights and to help peddle more cards!

Thanks for reading, and I hope you enjoyed my first foray into blogging about making gold in World of Warcraft!

21 comments: on "You're (Not) Going to be Rich!"

  1. Thanks for spending the time and money analysing the stats :) I though it would be low, but a <3% chance to profit from a flip is kinda scary.

    Oh well it's just good that there are ppl out there who care more about the thrill than the maths :D

  2. Incredible stuff! Thank you so much for taking the time and gold to do this, as you've more or less answered the question that's been plaguing goblins (or at least me) since we first learned about these!

  3. As a seller of MFCs I really don't care about the math at all. As long as there is ANY chance to win 5k gold from a 20g card, there will be buyers - lots of them.

    I'm up to over 200k sales from MFCs alone. How many have I flipped myself? 2 and those were by mistake.

  4. Makes me think that it's even more important to find those who win the 5k cards and brag about those people to keep the sales up then. With such a low chance for the 5k card we need to play it up so people don't get scared off from them.

  5. OH NO!!! The cat's out of the bag! Well, it was just a matter of time. :) Thanks for putting out the numbers!

  6. Deepcut - can you comment on the model you used to get your SE and CI? Was it a straightforward ANOVA?

  7. I plugged in all the values to Excel and ran the descriptive statistics, while selecting the 95% CI. From there I just added or subtracted from my mean to give the values I posted.

  8. Well, I think it's obvious that Blizzard would not create something with a high chance to actually make gold out of nothing.

    Anyway, I had assumed that the chance would be even lower, so thanks for doing the math.

  9. "Inspired by" is putting it mildly :)
    http://wowfortunes.blogspot.com/2011/02/data-keeps-flowing-in.html this guy have been at it for atleast 2 months, and he have reach a samplesize of 2400 atm. I admit, 8000 is much bigger samplesize, and I applaud you for doing that, but I would personally like to see wowfortunes.blogspot.com getting some more credit for this one.

  10. I've always wondered about this. Thank you for investing the time and more importantly gold so I didn't have to.

  11. Thank you for your efforts:

    A couple of points:

    1) the 5000g card is worth a bit more than 5000g. To a lesser extent the same applies for the 1000g. There are two reasons: someone hawking the cards could buy one to show/market (and can always trade it in later.) A US top 50 guild recently fell apart on my real, so there are a number of transfers. Anyone wanting to realm transfer will find 5000g vendor items quite convenient to transfer wealth considering there is iirc a 20k gold cap.

    2) You have actually calculated something new in Cata: a floor for blackfallow prices and thus herb prices.

    E.g., at the end of this expansion when nobody is buying anything, if the price of obsidium ore gets too much below 54g/stack someone will buy it, prospect it and expect to get 6 gems/stack that cut and vendor for 9g each.

    Cinderbloom is under 60g/stack on my realm. If due to a mature expansion, bots start winning or another mistake like the recent Uldum-herb spawn , Cinderbloom got to under 10g a stack, one could see the floor for herb prices being to use cheap herbs for cards.

  12. Maybe I'm wrong, I don't have a degree or anything, but does this mean that if you were buying cata herbs at somewhere between 4-10g a stack you could make profit from crafting these and flipping them yourself?

    I know you can't get herbs that cheap right now, but hypothetically speaking...

  13. Higher end herbs (Twilight Jasmine and Whiptail) yield about 6 ink per stack, and lower end herbs about 5 inks per stack.

    If we round the expected value of a Mysterious Fortune Card to 3g (which is pretty close to what I calculated), then the price floor is 18 for the high end herbs and 15 for the low end herbs, excluding any cost for inferno ink.

  14. Nice try
    "Also it shows that I made back a paltry 18,402g on my nearly 90,000g investment."

    You just deleted the Inferno Ink?
    11g per Blackfallow is a very high price.
    For sure - if you use the Blackfollow (Glyph, direct sell, by Inferno) the Blackfollow has a high value but this ist only Profit you dont get - it is not loss.
    I think by Inferno Ink you became a lot more paltry from your 90k investment. Much more then 18k..

    Hope your calculate better in your job ;->

  15. Thanks a lot 4 your work!

  16. Awesome work. The 8,000 cards flipped were definitely worth it...for my money anyway ;)

    Good to put some real numbers to what we all knew to be some pretty awful odds.

    Thanks to all the MFC hawkers out there. I can't be bothered, but love it when they're out there barking - people have to go through my cards to get to the higher priced ones.

    I haven't done a lot with this market...sometimes it's kind of stiff and there's little or a negative premium over Blackfallow...and still, almost three months into Cata, I can't believe I just sold close to 200 cards (mostly in stacks of 10) in the last 48 hours - at close to 20g a pop - with Blackfallow at 12g.

  17. A lotto is a lotto. Chances are bad and prizes are big.

  18. Not to step on anyone's toes, but since we are looking at a probability for the 5k card of well below 0.1%, a sample size of 8,000 is too small to make any statement about the 5k card. I think a valid sample size for that would be something like 50k, if not six digit numbers.

    It's nice to see how much somebody flipping 8,000 cards will earn 95% of the time, but that's about it.

  19. The guys asking about the inferno ink missed the point that Deepcut said he "gathered" 8k in cards. In other words he bought them from random sellers over a period of time when the price of the cards met his 11g per card price point. The problem is did he just get "unlucky" when he was buying his cards. I have sold about 5,000 cards. I am sure I have sold one 5k card and believe I sold another one. Think I am going to try this myself with 8k of sequential cards.

  20. My 90k investment took into consideration the inferno ink, which I valued at roughly 80g per ink.

    When all was said and done I had spent 11g per ink. Sometimes I bought cards outright, sometimes I bought inks to make cards, and sometimes I milled herbs into inks.

    @The Apprentice Trader: Read my post, I am making a LARGE assumption when guessing the drop rate of the higher value cards. As stated in my blog, you would need 32 MILLION flips to accurately gauge the true drop rate.

  21. The amusing thing I find it that Deepcut is actually on my server and we're usually playing off one anothers auctions and advertisement. I've seen him around so its nice to see him making some valuable comments about it. However, if at all possible, I'd prefer for him to bring the price back up to what I originally had it at between 30-40g a card >.> Instead of the 15g

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