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Tuesday, December 7, 2010

Reader Submission On Fortune Cards by Wukam

Hi Cold, First off, huge fan of your blog. It has definitely helped me out a lot.

Second, I wanted to post a comment on your blog post about Fortune Cookies and Fortune Cards, but ended up getting carried away with the statistical analysis and vastly exceeded the character limit. Instead, I humbly submit it directly to you for you to use at your discretion:

WARNING! Excessively long comment ahead!

TL;DR – Even though the cards, when you use them, will vendor fordifferent prices, they all have the exact same statistical worth of X,where X is the potential value times the chance of getting that value.If mats are below X, you can buy absolutely risk free. If mats areabove X, then you’re taking a risk.

This has me quite worried, and I wouldn't be surprised if Blizz endsup removing the cards.

First, you're mixing gambling with the already addictive WoW. Second, it's going to be crazy easy for players with a littleknowledge of statistics to exploit those that don't. This is WoW lottotickets.

Let me try to illustrate using real life lotto tickets as an example.  Let’s say you buy a lotto ticket for $1 that has a 1/500 chance of youwinning $500. In the long run, you will never do better than breakeven: for every $500 you spend, you win $500. Of course, you couldalways get lucky. What’s more important to look at is the SELLER ofthe lotto tickets. If they’re selling $1 scratch offs with a 1/500chance that they’ll have to PAY $500, they’ll never make money! For every $500 they get (500 tickets sold), they have to pay $500! So thesmarter thing to do is change the odds. Make it a $1 ticket that has a1/500 chance of winning $400. So for every $500 in sales, they pay out$400, netting $100. But now look at it from the buyer’s side! You’regiving away money! In the long run, you’re paying $500 to win $400! Of course, you could always get lucky, which is what you’re hoping for and which is the exact faulty logic the sellers are banking on!

The same statistical analysis will apply to pricing these cards,though it’ll be more convoluted because of the varying possible winnings. Though scribes aren’t directly “paying” the buyers, theyessentially are through the cost of mats, and this is where things aregoing to get interesting. Scribes are going to need to keep a VERYclose eye on the price of mats to make sure they aren’t buying themfor more than they could ever hope to get from the cards. Just to keep things simple, I’m going to assume there’s a 1/1000 chance of the cardvendoring for 5k, and that the other options don’t exist (the analysis will essentially be the same, there’s just going to be a lot more math involved). Let’s say those mats cost 5k. You now have two options:sell on the AH, or use the cards. Statistically, you’re just going to break even if you use them. And anyone who buys them for more than thecost of mats is stupid, because they’re taking a risk that will(statistically) never pay off. But that’s what you want, and whatyou’re hoping for and what will probably happen; “6g for a chance at5k!?” your uninformed customer thinks, “How can I not!”

Where things are going to get interesting are when mats are above orbelow the statistical chance; e.g. 4k for 1000 when there’s a 1/1000chance at 5k, or 6k for 1000 when there’s a 1/1000 chance at 5k. Inexample number one, you’re better off crafting and using them foryourself, because statistically you’re guaranteed 1k! (or at least, inthe long run you will profit) You are literally printing gold. But inthe second example, you are taking a huge risk unless you can turnaround and sell them for more. You’re spending 6k for something that’sonly literally worth 5k. Let me try to simplify to clarify. Withobjects like these where chance is the only factor, they are worthwhat you stand to gain multiplied by the chance at getting that. Sosomething with a 1/1000 chance of winning you 5k gold is only worth 5g(5000g/1000). If you are paying less than this amount (e.g. 4g peritem), you are going to come out on top in the long run. If you arepaying more (e.g. 6g per item), you are throwing away money. Unless,of course, you can make some other sucker pay even more! (e.g. 7g per)

As soon as statistics are reached, this market is going to becomepainfully simple for anyone with an understanding of how the marketworks to make money. As soon as mats are below what the cards areACTUALLY worth (potential winnings multiplied by chance of winningthem), you buy them all and either use them on yourself for no risk(that is important to realize: though you may have “blown” that moneyand flipped nothing, in the long run you are statistically guaranteedto make it back and then some!) or attempt to sell for moreinstantaneous profit. (But make sure you’re selling for above what they’re worth!) If mats are more than what they’re actually worth, youcan take the risk and attempt to sell them but you should never everever ever ever use them on yourself!

I know that this sounds exactly like what we do every day anyway –mats are below what we can sell for, we buy and craft, if they’reabove, we ignore (or sell the mats ourselves) – but why it’s sointeresting to me is that there is always going to be a baseline forwhat the cards are worth, unlike Glyphs, for example, which are onlyworth what people will pay, and that can fluctuate. They are alwaysgoing to be worth X, if mats are below X, you buy, simple as that. Why this might be confusing is because what they’ll actually vendor for,“Y,” will fluctuate depending on the card. But, in the long run, allthose Ys will average out to X. And I think that’s the TL;DR of thispost.

- Wukam (aka Vince)

Altar of Storms

Thanks for the submission Vince. 
Anyone else care to weigh in?


  1. Some of what you are saying here confuses positive expected value with lack of risk. Even when the value of mats is less than the expected value of the fortune card and it is mathematically correct to gamble (assuming you have sufficient bankroll for your risk tolerance curve), there is still a great deal of risk.

    In the example you choose, crafting 1000 cards does not guarantee a 5k card. In fact, there is a ~36% chance that you will end up with absolutely nothing, having spent your 4k or whatever for mats. I had enough to say about this, that I put up a full post at my blog.

  2. This all assumes we can get accurate statistical data on the card distribution. I'm not convinced we can. I think Bliz will have no problem with tweaking this behind the scenes, which would invalidate our test data w/o actually letting us know they did it. Wouldn't be the first time.

  3. You're exactly right, Mr. GoZ, and I'm sorry if I wasn't clear. The only "guarantee" in my example will be over ridiculously large amounts of attempts; you won't notice real profit every 1000, but closer to, as you pointed out, every 100,000.

    Though I am curious, where does the ~36% chance you mention come from?

  4. Wakum,

    My calculator is out of batteries but the algebra works out to (999/1000)^1000 - that's the chance of not winning in 1000 draws when the odds are 1 in 1,000.

  5. Sorry I was so brief, Wakum - the biggest distinction with these cards is that they all have the same chance of winning, regardless of if the others are winners or not.

    This is different from drawing cards from a poker deck until you find an ace. If you draw a card that's not an ace and set it to the side, then you have a better chance of drawing an ace next time, as you've eliminated a losing card.

    Now imagine that you drew that card which wasn't an ace, but then returned it to the deck before drawing again.

    You could go ten minutes or longer without ever drawing an ace like that. That's how these cards are working (whic you seem to know, but this is another way of looking at it). Over a very large number (think hundreds, if not thousands) of draws, you'll average an ace roughly every 13 times (4 aces in a 52 card deck = 1/13 chance of an ace).

  6. I think the key to whether a scribe should make cards will have nothing to do with the math of the expected value. Only relevant fact will be the margin between the average selling price and the mats value.

    Wakum's absolutely correct that mathematically, the expected value should drive the sales price. But it won't. Like in RL, only the perception of the expected value will. People would rather take a one in a billion shot at a $100,000,000 than keep their dollar (that's a 1000% markup there for those of you counting zeros). And there's a million different lotteries and casinos and slots and versions and combinations, for exactly the reason that there's no good formula to predict what the perception of value will be. The successful games convince people it's worth it - the unsuccessful ones don't. In RL, the math isn't a dominant factor--if it was, no one would ever do slots.

    I'm a math guy. But I say, forget the equasions and expected value. It's enough to blindly (and I believe safely) assume that the expected value will be too low to be worth my time to just mass produce and flip for myself. And then I will decide to mass produce or not based exclusively on the current AH sales price of the mats and the cards.

    My personal bet - cards won't be worth touching for at least another 6 months because of mat prices, and then they will be. But either way, only thing I need to make the call is an AH scan, not a calculator.


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