Tuesday, December 7, 2010

Fortune Cards

Cold has a guest post from Wukam up today about fortune cards.

TL;DR – Even though the cards, when you use them, will vendor for different 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 are above X, then you’re taking a risk.

Now, as a math and game theory geek who got into poker a few years back, and who then spent a while analyzing the variance of various tournament scenarios, deals and prop bets, I have a pretty good handle on this, and am poised to be the guy who takes the gold from a lot of unsuspecting statistically naive players.

But since I am a gnome and not a goblin, I will be posting the best explanations I can here of how to analyze this situation, and not be taken in.

I suspect that Wutan here is making a mistake primarily in wording, but this: "If mats are below X, you can buy absolutely risk free. If mats are above X, then you’re taking a risk.", is just plain wrong.

I've read and heard a million poker players say essentially the same thing. "Playing this game isn't a risk -- I'm a winning player."

Also wrong.

Every time you put money on the line in a game with chance involved, you are taking a risk, even when you will profit on average.

What's going on is that Wutan (and many poker players) are confusing positive expected value (a good bet) with a 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 Wutan chooses, a craft has a 1/1000 chance of producing a 5kg vendor item, and a 999/1000 chance of producing nothing, or some unsellable trash. So, if the mats for a craft cost 4g, then you essentially make 1g per crafted card on average. A lot of people think this means that you can craft 1000 cards and be guaranteed a profit.

But it doesn't work like that. 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. Of course there is also a chance that you will get 2, or 3 or even more 5kg cards, and make a huge profit. On *average* you will make 1k profit, but random numbers are random -- on any given crafting of 1000 cards, over 1/3 of the time you end up with nothing, so it would be stupid to do this with all your working capital, even though it is a big positive expected value. Even crafting 2000 cards leaves a 13.5% chance of getting back nothing (for minus 8k), and around a 27% chance of getting only 1 card, leaving you 3k in the hole for a 40% chance of taking a big loss.

This will only be anything like printing money for those who can stockpile so many mats that the chance of ending up a loser is negligible. But in Wutan's example that would be a *huge* amount of cards. Probably in the neighborhood of 100,000 craftings. And even then, you will still lose some of the time, just not very often.

Now, in the actual game, the variance won't be anywhere near that high, since there will be lots of cards that go for in between 0 and 5kg, so your chances of ending up with nothing after 1000 crafts will be infinitesimal. You will probably do worse than break-even fairly often on 1000 crafts, but when you do, you'll normally keep at least 1/2 of your investment and most of the time your losses will be in the 5-10% range.

Look at guys who play +EV Video poker for a good sense of what the payoffs on a +EV lottery look like. Generally, if your actual hits of royal/quads over some long stretch are significantly worse than expected, you will be losing over that stretch, because the chance at one is a fairly significant portion of your equity, and your EV is usually very very thin (max 1-2%).

The basic payoff structure and variance will probably be similar for these cards. The chance at rare cards like 5k/1k etc. will be a big portion of the value of an unknown card, so any run that is very low on those cards, is likely to be a run that loses, unless the EV is enormous by real-money gambling standards.

Now, the EV of this probably *will* be enormous if these cards are the main driver of demand for their mats. I judge this by the general profitability of other items with a random component such as ore prospecting and disenchanting. Generally, the cost of saronite tended by bottomed not by it's average value for prospecting and shuffling, but by the absolute baseline value of the most likely path: getting green gems, making rings/necks and vendoring them (or de-ing and getting all infinite dust). Now any given prospect could result in a good blue gem worth more, or a de could result in cosmic essence, worth more, but generally this was all profit. Generally goblins bought up saronite for this process only when we were almost certain to profit.

Once we start seeing what the percentages are for the various cards, we can do some statistical analysis to see when it makes sense to craft them given various risk tolerances and bankrolls. I will definitely be watching this market like a hawk, as there's a decent chance this will be hugely profitable. If I can figure out how to get blogspot to put up docs for download, I'll put up a spreadsheet in a future post that shows how to analyze this craft based on the chances of various cards, and your bankroll and risk tolerance.

With the big 5k reward possible, it's also quite possible that the unopened cards will, like scratch tickets, sell for significantly more than their expected value. And just as in real life, it will generally be some of the people with the least gold and the most difficulty making it, who are most willing to give it away in small probabilistic increments to those of us who understand expected value.

My next post will be about risk tolerance in general and how to talk about it mathematically.

Friday, December 3, 2010

How to get your mining on

I decided I wanted to have a miner for early cataclysm when gathering tends to actually be worth as much or more than crafting.

I kinda bolloxed it up by not having enough time to level him to 80 before release, but I'm figuring a good shot at lots of player and lag free zones in outland and northrend come Dec. 7th, and I might catch up in time to still make it worthwhile. I do have 2 80s on my current main server. I could, I suppose, transfer another, but I am massively averse to transferring characters for goldmaking purposes. It feels like paying real money for gold.

In any case, one thing that I've found when leveling with a gathering profession is that it's a royal pain in the arse because unless you go out of your way to gather, you level past the things you can pick really quickly. One thing I love about mining is that you can come pretty close to powerleveling it with smelting, and it only requires actually going out and mining stuff in two spots (340-350 and 375-450/425 in cata).

Even more surprising, it turns out you can do most of this powerleveling for profit. Obviously every server is different, but so far I've done it a bunch of times and it always has been somewhere between cheap and profitable all told to get to 290ish.

This latest was surprisingly good. Here are the prices I dealt with:

copper ore 10s-25s
tin ore 20s-40s
tin bar 8s-20s
bronze bar 34s-75s
silver ore 5-10g ea.
silver bar 1g ea.
iron ore 50s-75s
iron bar 75-80s
gold ore 2g
gold bar 2g
mithril ore 75s-1g
mithril bar 75s-1g
thorium ore 75s-1g50s
thorium bar 2g50s-3g

So I smelted copper bars until I pegged. smelted the tin that was 20s, then smelted a huge pile of bronze with all the copper and tin, which I promptly sold *all* of at 50s ea that evening (along with the 3 stacks worth I had to buy out because it was below 50s). That all made me about 200g while skilling to 115. Silver was the kicker. I had to eat 12 silver ores to get to iron, costing me almost half what I made on the bronze. Iron will probably turn out to be profitable also, but it didn't sell as fast as the bronze so I don't know yet. Gold and Mithril will be basically breakeven if I can sell it all at current prices or close. Thorium is where I made my killing. I smelted about 800 bars for an average profit of 1g75s/bar. That's 1.5k gold for pulling a pile of crap off the ah and going afk for 10 minutes of smelting. Oh, and 80% of my thorium sold overnight at 2g69s, so that profit is pretty much locked in.

So I'm sitting at 290 mining after less than an hour in sw, and I made 1/2 of what I'd normally make in that time spent crafting and ah-ing.

PS: after discovering the new dwarven district for my forge-using activities, I think I am almost willing to forgive blizzard for ruining my mb/ah fun. This would have taken at least another 10 minutes of running around if I'd done it in old stormwind. Even IF wouldn't have been all that exciting. The only city pre-shattering that was convenient for a blacksmith/miner was thunder bluff. I'm guessing Org is now better also, but I haven't logged a horde since the 23rd.

Wednesday, November 24, 2010

The perils of making your money on the buy side*

*Everything you always wanted to know about opportunity cost but were afraid to ask.

Markco has an article today reposting a letter from one of his readers which contains an important truth about playing the gold game:
"It is at the time of buying when you set yourself up for future profits. But the profit potential that you control is 100% related to your buying decision."

But there is one thing that bothers me when many gold bloggers talk about this, and Dale, the letter writer, repeats the possible fallacy when he says:
"That person that is selling below "your" cost is very likely still making a profit if you are basing cost on auction house prices. This means they are getting their materials cheaper than you."

Perhaps they are making a profit. But they might not be making a profit on *crafting*.

One thing Gevlon consistently harps on that is crucial to understanding how to play this game is opportunity cost. The appropriate cost of an item is not what you paid for it. It's what you could get for that item if you sold it, or used it another way.

Ignoring the market for an item is the basic fallacy behind "I farmed it, so it was free". Leather is not free. Ore is not free. Herbs are not free. You may not have paid any gold for them, or you may have bought them for much lower than market price, but if you post current high-demand trade goods at 70-80% of the standard market price, they are going to sell and sell fast. Probably no matter how many you have, they will all sell, and if you have a moderate amount, you should be able to get 90-110% of standard market within a few days.

Let's suppose some fool just sold me a few bags full of borean leather for 1g/stack. (market range on my server runs 50-90s per leather, or 10-18g/stack).

I look at the auction house and see that borean armor kits are selling for 1g. Here's the crucial question: Am I making a profit if I craft some and sell them for 99s? NO, I am not. Making those destroys value. I know that leather will sell in quantity for 50s a piece minimum and often up to 75s ea, so somewhere in that range is how I should count the cost when deciding whether to craft something with it.

Remember the crucial line about buying: I made my money when I bought the item. That's absolutely true. As soon as that leather came into my hands, my net worth increased by at least 9g per stack that I bought.

Now, when I craft, I am making a separate decision about what to do with my leather. And in this step, I can either add value, or destroy it. If I craft borean armor kits for only 99s value, I am destroying value. If I craft heavy leather, I'm probably adding value (usually sells for at least 4.50-5g ea.), and I may add even more value converting to furs and crafting leg armors (currently 150-175g) or by crafting some of the leveling or basic pvp pieces

If someone else is consistently selling at or below my cost and the components are items with a strong high-volume market -- I don't need to wrack my brain about how to buy the stuff cheaper to get back in that market. I don't need to craft that item, they can have their zero/negative-profit market, and if I find the mats cheaply, I will sell the raw materials instead.

The only time it makes sense to ignore auction house price for materials is when the raw material market is too low-volume to compete with the crafted market as an opportunity to sell my stuff.

A good example would be snowfall inks versus runescrolls or off-hands during wrath. I spent some time in the ink business -- I'd mill craploads of herbs for ink of the sea, and creating snowfall ink at the same time. Now, there was a sweet spot with people going for insane before the shattering that let me sell piles of snowfall ink, but go back to the summer -- a typical ah price for snowfall ink was 8-10g ea. And people would buy it, but rarely in huge quantities. I would post 5 singles and a couple 5 stacks every 2 days, and sometimes they'd all come back to me, only rarely did they all get bought, most of the time I'd sell a few. I was generating far more than I could sell at that price. But the problem wasn't a high price. If I listed my snowfall for 5g, I would sell a little more, but still not enough to get rid of it all.

So it made sense to craft scrolls and offhands instead. And even if the price of those dropped to where costing snowfall at 8g ea (standard market price at which I sold it) made them break even or a small loss, it still made sense to craft them, as long as they were profitable with a minimal/zero cost for snowfall, because I would never get rid of all the snowfall otherwise.

So the crucial rule is:

  1. if you can reliably move the raw material on the auction house for market price, then the cost of using that item is the market price, no matter how you acquired it, or for what price.

  2. If you cannot reliably move the raw material in quantity for market price, then cost is whatever profit you could make from some alternate use of the item that would let you get rid of it all. If runescrolls are flying off the shelves at prices making you 5g per snowfall after other items are accounted, then you probably shouldn't craft offhands unless you can get at least 5g per snowfall from those as well. It's legitimate to treat your snowfall ink as a waste product and consider it as "free" only if every feasible way to get some value out of it won't use it all up.

I've seen a lot of glyph sellers boast about how they could make a profit selling glyphs for some very low amount (like 1.5g before glyphmas), because they had a connection to get their herbs for very very cheap. But this is a mistake if between your herb market and your ink market, you can support big sales at levels significantly higher than 1.5g/ink or 10g/stack of herbs. Even if you buy your herbs for 5g a stack, you should just sell herbs or ink rather than go to all the trouble of making and posting glyphs that you can't sell for more than 1.5g ea.

This is the #1 basic economic fallacy: a failure to understand opportunity cost. It's the same thing you see with the many people who will equip, rather than sell, an expensive twink item if they get a lucky drop or find it on the ah cheap, but would *never* dream of paying something near market price for it. Somehow gold in their bag seems more valuable than gold they could get for something -- even if the sale really is a sure thing.

I've seen it with poker players as well. I used to read rec.gambling.poker regularly. A number of posters would always play satellites in an effort to win a seat in the WSOP main event. They would treat it as getting to play in the WSOP if they won a satellite. They would *never* pay the 10k to play if they didn't win a satellite. But even though you could sell those entries for 95-99c on the dollar, they never even considered doing that if they won a seat.

But this is the same principle. Cashing that event ticket costs you the same 10k whether you won it in a satellite or pay it out of your own pocket. Either it's worth wagering 10k to play the event or it isn't. If it isn't, then you should sell your ticket when you win it as long as you can get fair value. If it *is* then you should be willing to play whether or not you win a satellite.

The general take is this: judge your crafting profit by the opportunity cost of the items you use, not by your actual cost.

Tuesday, July 6, 2010

The Monopolist Strategy -- How it Really Works

So Gevlon has another good post on markets in the world of warcraft today, but I would say he's still missing some key pieces to how other people play the auction house game.

Here's Gevlon from his best selling glyphs post
But there is a better reason why you should never buy a glyph for resale (unless it's below ink price of course). To have the mentioned profit, the glyph must sell. The reason for no sale can be undercut or simply low demand. Most people already have their glyphs and the summer decreases player activity. Imagine that you have monopoly (no other campers), but only 3 glyphs are bought by users a day of a type. I post 2, 2 times a day. So you must buy 4. You paid 80G for it, and get 150G income instead of 200. Also, when I'm collecting mail and crafting, I notice that my glyphs are sold. I will assume that players are buying it and increase my craft/post quota. If I sell 2 x 3 a day, you have to spend 120G to buy me out, but you still just have 150G income, 30G profit/day while I have 16*6 = 96G. I guess you can figure out the next step: believing that users buying my stuff, I increase my crafting even more, selling 2 x 4, that would cost you 160G to buy out. Of course on a high population server the numbers are higher, but the problem is the same. As deep undercutter I'm happy to work for the price I set. So if you buy me out, I'm happy and encouraged to work more, crafting and selling more, finally reaching the point where you can't buy out the legions of glyphs I'm pouring into the AH (cluelessly believing they are sold to users).

The mistake made here is that the putative monopolist is as automatic as using a streamlined QA3 or auctioneer strategy.

But it isn't. For exactly the reasons Gevlon gives, there doesn't seem to be a simple algorithm that works for the monopolist strategy. That's the big advantage of the deep undercut strategy. You can program a deep uncercut strategy into QA3 and put little or no further thinking into your strategy, while making gold.

As a monopolist, you do not have to to camp the ah to win, but you do have to put a bit more thought into when and how you buy and list.

The example I quote here shows the *danger* of buying glyphs for more than they cost to craft, but it does not demonstrate that you should never do it, only that buying every glyph that comes in order to prop the price up indefinitely is a long run bad strategy. If you want to be a monopolist, you must understand the market better than your competitors (or their algorithms) do.

Let's assume the consistent market sellers of some Glyph consist solely of X (potential monopolist) and Y (deep undercut crafter following your automatic strategy), X can use the following strategy and win (Y doesn't really lose, btw, X just makes gold from trading alone if he judges the market enough better than Y, Y still does quite well, just not as well as s/he could have):

Y lists 2 of a glyph twice a day at 20g fallback, X believes that the market supports selling 4 glyphs per day at 50g ea, so s/he figures out Y's posting schedule, and arranges to buy out those glyphs and repost them for 50g as soon as Y is offline.

All glyphs sell for 200g ea. day, for 120g/day profit.

After a few days, Y needs to craft, notices quick sales, so decides to post 3 of that glyph. X buys out all 6, sells 4 for 200g, 80g profit for a few days.

Now Y decides to craft and sell 8/day. X buys them out, and sells 4 for a 40g profit. Y ups again and goes for 5/half-day. Now X would make zero direct profit, buy 10, sell 4 leaves 0g. But there is still *some* profit, in that X now has 6 glyphs. So x does this also to build up a nice stock.

Now Y is listing 6 glyphs twice a day and that actually *loses* gold in the short term, plus X already has a whole pile of unsold glyphs stored up. So here's where the strategy changes up:

X stops buying the glyphs now, and doesn't try to control the price. Let's see what happens.

So for a while, X goes to a standard or deep undercut strategy with a nice low threshold. If Y updates listing and crafting behaviors every 5 days, X now has a nice stock of 60 glyphs that he has effectively paid nothing for (other than the time spent with zero resell profit to accumulate 30 glyphs while Y was posting 5/day), so he no longer needs to buy Y's to sell them. So he goes ahead and undercuts Y, selling them all for somewhere between 6g99s and 19g99s, given Y's 7-20g price range. Suddenly Y is selling fewer than 4/day, possibly none, while X is getting rid of the excess stock. If X has done this right, X is already in the black, so s/he can sell those glyphs at any price: sell them all at 6g, under Y's threshold, and that's another 360g. Meanwhile Y hasn't been selling much, so Y goes back to maintenance posting only thinking "hm, weird, market was really hot, now it's crashed", and once X's glyph stock gets low and Y has gone back to posting/crafting smaller amounts, X can start the strategy all over again.

So here's the deal -- this strategy makes money, but it requires more effort. Y is rolling along automatically, making however much g/day without having to think about the market. X is doing pure AH pvp, not the stupid kind where you give up your own profit in order to make the other guy lose, but a smart kind, where you look at markets carefully and decide that you can make some gold that the other guy is leaving on the table.

If there are multiple goblins keeping an eye your market, it doesn't work as well (because as soon as you raise the price for a few days, they come in, so you can't run the full course). Too many other monopolists, especially if one or more are campers, also spoil the fun rather quickly.

Further, in markets where there really is massive price elasticity (i.e. if a pair of glyphs are reasonable to use as a consumables for raiders at low prices, but will have relatively little takeup at high prices), there may be more money in crafting 10-15/day for 8-12g than in trying to push the price to 50g.

Now, one can easily argue that the undercutter could alter strategy as well, and ultimately keep the monopolist from making any gold. And this is true. But it would require understanding the market as well as the monopolist, and making the same sort of time commitment to that market as the monopolist is prepared to. Basically, you find the optimum monopoly price and listing strategy and change your settings to react appropriately to what the monopolist does, and it becomes very difficult for the monopolist to make any money short of camping you 24/7. But it may be more work than it's worth compared to simply playing the standard low fallback game and letting the monopolist make their gold.

In general the big disadvantage to the monopolist strategy is that it takes more work if you want to do it well. And honestly isn't generally worth it in the glyph market where your best case is getting profits of 20-30g per glyph for a few sales a day and that is quite rare. Where it makes sense to use, is in middle to big ticket markets (where profits of at least 40-50g per item are possible), and markets that move a lot of stock with relatively few big providers. It's also very helpful if you have a way to control the mat markets along with the finished markets.

I did *very* well with enchant mats in burning crusade, propping up prices on shards and essences and riding the wave back down, buying up cheap supply to reset the price -- ended up getting half way to cap without really having cap as a goal.

Lately, I'm more likely to do industry than try to control markets, because with more goblins around today, the inefficiencies are rarer and smaller.

-- The Gnome of Zurich