As a former retailer for Magic: the Gathering (amongst many other games, comics, and everything else in orbit of that wonderful, geeky world), the concept of “Expected Value” (EV) was one that I dealt with a lot.

Every time a new Magic set came out (several times a year), the very savvy and financially-minded Magic collector market would deep dive into the available data to try and answer that most burning of questions: *what’s the EV of this set?*

After all, boxes of Magic wholesale in the low seventies, and had an MSRP (almost universally ignored) of around a little less than double that but were typically available around $100. A Magic player ready to drop a hundred dollars on a box of Magic certainly would like to know what they might be getting back, and EV was the universal unit of measurement for that.

For those unfamiliar with the concept, the idea behind EV is basically this: if the box of Magic costs $100, what is the value of the individual cards I’ll be opening? To derive that, you take market data on the value of all the possible cards (typically the rares and mythics, the cards that tend to have both the highest value and highest liquidity, and maybe uncommons). then factor that against the probability of getting each particular card in a box.

If the total EV was less than what you’d be spending on the box, then on the whole you’d be losing value. If it’s more, then you can expect a pretty good chance of coming out ahead. It’s worth noting that this is a guideline, not a flawless crystal ball. You could still luck out in a negative-EV set and get that “God-box” which happened to have all of the better rare cards, or some foil premium card, and come out well ahead. But then, you can’t judge success in a casino simply on that one time you win.

If that’s perhaps not clear, try this: you’re playing a game of coin flipping. Every time you lose, you have to pay $5. Every time you win, you get $3. Would you play this game? Of course not, you’re losing more than you’re winning. What if your prize for winning was instead $6, would that change your mind? *That’s* EV.

I’m not sure how it was obtained, but a list of possible payouts and odds of winning the War Robots Anniversary Event chests appeared on Reddit yesterday, posted by a user who has never posted anything else. Which means it’s either a leak, or a troll job. I won’t comment on the likelihood of either, except to say that the level of detail in the list is very high, and also easily disproven. If someone wins something not on the list, voila! List is bullshit.

So we’re going to operate on the assumption that the list is authentic. As we’ll see, there *is* a very logical and even compelling reason **Pixonic** might have to leak it themselves, though that’s no guarantee that the list is actually sanctioned. What the data elements in the list *do* mean is that unlike previous events, we can calculate an EV for the chests. Hallelujah!

Before we get into the numbers, a brief aside. I started playing **War Robots** towards the end of last year, so I missed the Halloween event but got to enjoy the **Christmas** one. And like any good degenerate, I gambled fairly heavily on snowflake chests. Now, when I say “fairly heavily,” I mean I probably bought about twenty dollars of currency to gamble with. It was fun and entertaining, and I had no regrets paying for the entertainment.

By the time the **Lunar New Year** event rolled around, I was much savvier. I spent the coins I’d accrued through gaming on the ol’ roulette wheel, reserving actual real money on the things I knew I wanted (**Doc** and **Jesse**). And now? I won’t even look at a chest. Like many, I feel they’re a suckers bet, and I have better uses for the **Gold**.

*That doesn’t mean they’re not entertaining*. You’re not an idiot if you like the experience of playing your luck out to see what you get. It’s fun to open them up and see if you got something good. Lots of people who don’t bother with a lottery ticket still fancy the occasional scratch-off game for much the same reason.

But when a clan member approached me earlier tonight and asked me if I thought it was worth it for 1,000**Au**, I didn’t just tell him no. It was *hell no.*

Now, the thing to bear in mind about EV is that it’s normalized across a spectrum of samples. As mentioned above, you can get a “God-box” that’s well in excess of it, or a box of crap that’s well below. But if you buy 100 boxes, you’ll start to sort of regress to the mean.

So let’s start by looking at the data on a single-chest basis, leading off with the data I worked with. The table below is simply what I ripped off of Reddit. I’ll be looking at Gold chests only today for two reasons. First, they’re simple to evaluate because they don’t require a Silver to Gold conversion. There are no Silver prizes here, unlike the cheaper chests. Second, this is the level of chest where EV really begins to apply. A 100**Au **chest is the equal of a dollar scratch-off ticket. You play for fun and a chance, not a real return. 1,000**Au** is, however, much more serious money.

Now, let’s say you have 1,000**Au** burning a hole in your pocket, and intend to play the ol’ roulette wheel one time. Wise? Maybe not. You have a 64.37% chance of coming out behind. That’s not very good, is it? I mean, if you’re in the market for a **Gekko** or **Aphid** already, then your odds of doing okay are more like 50/50, but for many players, getting one of those two weapons will feel like a loss. You could have simply bought them for less.

Next, you have a 4.03% chance of simply getting an immediate rebate. A thousand in, a thousand out. Thank you, come again.

That leaves just a 30% chance of coming out ahead. A lot of folks slagging the chests are really driving home your odds of losing. But here’s where seeing the data *really* helps. Look at your worst-case scenario: 500**Au**. That means that no matter what, you’re really only losing half of your initial outlay, right?

Now look at the other end of the spectrum. Your 1,000**Au** could get you a **Butch**, worth 14,000**Au**. Hell, “even” a **Lancelot** or **Fury** will *quintuple* your outlay. So while it’s accurate to say that most of the time you will “lose,” without the proper context that’s a misleading statement. And that context is simple: you will “lose” more often than you “win,” but when you win you will win so much more times your initial investment than when you lose.

*That,* folks, is Gold chest expected value in a nutshell. You may lose more than you win in terms of win/loss ratios, but overall, you’ll come out ahead *in terms of monetary value* with positive EV…and come out behind with negative EV.

So, we’ve covered your odds of winning. Now let’s open the envelope on that EV.

If you’re seeing what I’m seeing, then you’ll understand why I’ve been picking my jaw up off the floor for the past hour. The last column here is EV, which is simply value (column 2) times occurrence (column 3). And by Jove, **Pixonic’s** Gold chests have *positive* EV. And not just positive EV, but EV *in excess of twenty percent.*

A thousand **Gold** in, 1209.10 out.

I said above I came to this as a complete chest-skeptic. I’m afraid I’ve had to modify that position. Note that the EV here doesn’t even take into account the “bonus” treasure you’ll get from a superchest, which I believe you’ll get after opening seven Gold chests (**UPDATED**: confirmed to be eight, thanks NORSE PATRIARCH!). Here’s how those shake out:

First, I’d like to bring your attention to the anomalous superchest EV’s of the **Jesse** and **Butch**, we’ll be talking about that in a moment.

But let’s take a second to see what the EV is of opening seven Gold chests, which grants us a free superchest. We know the cost to be 7,000**Au**. What can we look to get back?

That equals (7 * 1209.1) + 3023.3, or 11,487. A difference of 4,487 or, put another way, a return on your investment of 64.1%. My 401K should be so lucky. (**CORRECTED**: Per NORSE PATRIARCH, it’s eight chests. A profit of 4696.1).

One thing I noticed with the data is how consistent it is with EV. It’s rather like whoever put this together knew the EV they wanted to return, then worked backwards to work out occurrence rate. Note the EV column in table 2. The lowest EV for a prize is 40.20, the highest 40.60. That’s extremely consistent, which simply means that **Pixonic** wasn’t “pushing” any prize over any other (or making a prize artificially scarce, on the other side of the coin).

This tells me that if indeed this was a troll job, the troll took their time to do it.

That’s why the superchest **Jesse** and **Butch** are so intriguing. The **Jesse** has an EV of 217.35, the **Butch** 184.8. **Jesse** got bumped up a little, **Butch** got bumped down the same amount. Average the two and what do you get? An EV of 201.08, right on par with everything else. Again, exceptional consistency.

So while your odds of winning a **Butch** in the superchest still exceed the odds of getting it in a Gold chest, **Pixonic** for whatever reason felt the need to hedge a bit and push the **Jesse** at the expense of the **Butch**. Curious.

Anyway, I hope this has been relatively clear and to the point. In a nutshell, if this data is accurate, it completely refutes the accusations of the higher-end chests being “scams” or “ripoffs.” There are a number making the claim (I was one), but the data simply supports the opposite hypothesis.

I can’t believe I’m saying this, but…the Gold chests are a good value. I imagine the dismay felt by **Pixonic** employees who have to endure the vitriol of the community, shaking silent fists saying, “no, you fools, don’t you get it?” Which is why I’m not ruling out that this data was a deliberate leak from Pixonic.

But if you’re going to go for chests, getting a superchest is absolutely the way to go.

One last caveat- I’ve been working with objective values in the data. A **Gareth**, for instance, is valued at 2,500**Au**. But to me, that’s a worthless prize- I don’t ever foresee needing more than the two I already own. So ultimately, if you have the time and inclination, this data will allow you to recalibrate based on your subjective valuation of each item.

In other words, as I always like to say…. *your mileage may vary. *

Well done. Spot on math and objective analysis. Thank you.

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Thanks, I appreciate it!

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I bought some gold for this one. From 21k gold I got back 160k in bots and weapons.

There are diminishing returns to be considered. I got 9 Galahads and 9 Gareths for example. As amazing as those are, there’s a ton of excess in there, obviously.

I did end up with enough good stuff to easily outweigh the initial cost though. Butch, Doc, 2 Jesse, 2 Lance, 3 Fury, etc. Just those 5 are enough to make the value very positive.

You need a decent amount of seed gold to start, to absorb a few downswings. For me, I kept getting enough gold to keep rolling and rolling for a long time. But I started with a lot of gold, so I could ride out bad runs until I’d land on a big gold re-infusion. If you have 1k gold and get an unfavorable roll you’re in a tough spot.

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… Dammit Dredd, my statistics teacher did not cover this far.

As interesting as this all is, I’m more infuriated at how I can’t follow the math.

Well, back to the topic at hand. Interesting story about my chest-drawing experience, I started out with 1.8k before drawing a 1k chest. Got 800 gold so drew again, drew 600 more gold, so I drew again…

And again…

And again…

Until I finally drew the superchest. And got a Fury. And lost only 200 gold in the end.

Uuuuuuuntil I drew again, got an Aphid.

Definitely the best chest event I’ve had yet.

Hoping everyone else is having similar luck.

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Since many of us do own some of the prizes given and in those cases, the prizes are worth their resale value. What would the EV chart look like if returned prizes were looked at with that in mind? I bring this up as most who will have the Au to spend on gold chests will be the same players who have most bots and weapons desired already.

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Since many of us do own some of the prizes given and in those cases, the prizes are worth their resale value. What would the EV chart look like if returned prizes were looked at with that in mind? I bring this up as most who will have the Au to spend on gold chests will be the same players who have most bots and weapons desired already.

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Nice computation Dredd. I didn’t know how legit those posted probabilities were though. For tomorrow’s entry, you should do the same analysis, but without the inflated costs for the Wild West bots, but instead, use the “normal” cost structure for premium bots. This would be:

Jesse = 1250

Doc = 2500

Butch = 5000

At a quick glance, it still looks like EV would be positive.

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Thanks, mate! I appreciate the suggestion, I was intending to work that out as you’re not the first person to ask that question. Indeed, it was the first thing I’d thought of when I ran the table data out. 😀

Today’s article addresses that, let me know what you think!

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Great explanation. I am confounded by some of the forum posts that complain about this event. It is far better than previous ones because you can use gold, rather than a special currency and can reinvest gold won, obviously. If you have 4,500 Au or more, you are guaranteed a superchest and 500 Au left. That is literally the worst case scenario. I started with about 2,000 Au, and ended up with a superchest (haven’t redeemed yet), an orkan, and a lancelot. Though my gold is almost all gone (including some gold won during the event).

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As i opened my superchest it evolved into a fury 2 orkans 2 gepard and a gareth, a snowball becomes avalanche..

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