War Robots WR Data and Analysis

By the Numbers: Know When to Walk Away

The Gold chests are a lot of fun...but when do they stop being a good investment? Jay breaks it down!

Many years ago, I was a moderator on a Forum of a very different sort than the Wiki Forum, one that catered to members of the greatest sporting rivalry in the world. While that latter claim is certainly debatable, there’s no denying that the animosity between Glasgow Celtic and Glasgow Rangers fans is fierce and impassioned, encompassing the best- and worst- of sporting fandom, history, politics, religion, and culture.

It was toxic, it was bilous, it was horrendous- and it was wonderful. I genuinely enjoyed the chance to banter with the ‘enemies across the aisle,’ the Bears, the Bluenoses, and yes, the Huns. I was somewhat useful as a moderator because I was a Celtic fan abroad, and somewhat detached from the day to day steeping effect of the Old Firm.

Although undeniably partisan, I nevertheless strove to keep a certain detachment and even-mindedness when it came to matters of the board, and it’s perhaps telling that the handful of genuine friendships that endure to this day are all with Rangers supporters. I may not agree with their choice of team or politics, but at the end of the day we can certainly share a pint- even a virtual one.

It’s not so very different with War Robots. The divide between “exploit players”- those that club, tank, and do other me-first sorts of things- and anti-exploit players is probably the closest thing we’ve got to the Old Firm divide I moderated through all those years ago. I can’t condone the conduct, but it doesn’t mean that some of them aren’t otherwise enjoyable people to converse with and get to know.

A friend of mine from the Forum, Golden Sabre, reached out to me recently. Golden Sabre is the leader of Nitro Squad, an Android clan whose most recent recruiting drive is “Tankers- Nitro Wants You!” I sort of envision the direction of his clan as becoming the Mos Eisley cantina of the Forum- a wretched hive of scum and villainy if you’re not into tanking… but probably a whole lot of fun if you are.

“Hey Dredd,” he asked, messaging me on the Forum. “Is this you?”

9stzLwe.png

“The 59% win rate might be,” I quipped in my best Oscar Wilde, “but you wouldn’t catch me dead in an Orkanless Thunder Boa.” Or maybe I didn’t, but I should have. In truth, I was a little taken aback that someone felt it important enough to bother parodying me with what could be seen to be a tanking hangar.

The timing, however, was uncanny. It happened the exact same day I’d dusted off my old Android account (platform being another divide which has its share of rabid partisans!)

HEDR

I have an Android account I started awhile back after the matchmaker rollout on a tablet I own (same name, DREDD_77, note the critical underscore). At level 6, it’s done little more than provide me with data and insight on the new-player experience. While I hadn’t used it in awhile, I recently resolved to begin playing the account in earnest, to give me another take on the game to explore here.

Last week I wrote a piece examining the value of the Gold chests in the current event, with the endorsement that, in fact, they were worth it from an “expected value” (EV) perspective (if you’re not familiar with that term, I’d strongly suggest reading the previous column first, as this one revisits some of that). More than a few folks told me in various ways that my article nudged them past the tipping point they needed to buy Gold and participate in the Gold chest roulette.

Conventional wisdom has held that the less you already have, the more use you’re likely to get out of what the chests offer, so my Android account seemed like the perfect beneficiary.

I ponied up $100 for 14,000Au, and headed to the casino. Was I correct in my estimation of Gold chests, or would I pay a steep price for my folly?

I initially decided I was only going to do a few “cycles,” or Gold chest purchases up to a superchest. With my very first spin, I won 3,000Au. I laughed, so this is how they hook you! Of course, I don’t actually lend any credence to the theory of variable returns, but I got a chuckle out of it. Overall, the first cycle of eight chests returned 7,100Au and a Galahad. The superchest came through in a big way, refunding me 4,000Au and putting me well ahead. I’d eventually repeat the process another eleven times. Let’s go look at some numbers!

ChestChart1

Okay, so what are we looking at here? Let’s define a few terms. A cycle is the number of chests it takes to open a free superchest, and includes the results of the superchest. This actually varied between seven and eight, which accounts for some of the \confusion in the first Gold chest post. Since each Gold chest costs the princely sum of 1,000Au, Gold Out is the total cost of that cycle. In other words, how much did I spend?

By the same token, Gold In represents how much Gold I won off the chests in the cycle. Gross Gear represents the total Au value of all bots and weapons won in the cycle, while Net Gear is a subjective measure of value. Of the non-Gold things I won, how many of them did I actually want? To help understand the gear values, I also included a lit of all gear won below each cycle column. If the name is in bold, as they all are above, then it’s stuff I was happy to get.

Gross Profit is how much I “made” above how much I paid when you total up the Gold, bots, and weapons won in the cycle. Similarly, Net Profit totals up the Gold, as well as the bots and weapons I wanted. This is an important distinction, because if you win seven Gepards…what have you really won? At least two of them are redundant (at least), and don’t really offer you any value outside of the Silver you can sell them for.

Note that the above data does not take into account the sell-off value of anything I didn’t want. The Gold to Silver exchange rate doesn’t appear to be an accurate representation of the value of the two currencies, but is rather pegged artificially high (likely to deter/profit from over-rapid leveling).

HEDR

Here’s how each cycle broke down (Cycle 1 was covered above):

Cycle Two (seven chests): 6,700Au, with a superchest of 3,250Au.

Cycle Three (eight chests): 6,900Au, an Orkan, an Ancile, and a Galahad. Superchest Doc (sweet!)

Cycle Four (seven): 9,250Au (Holy Maloney!), a Gareth, and a Gepard. Superchest 4,000Au.

Cycle Five (seven): This one wasn’t great. Only 4,200Au returned, plus a Gekko. Superchest of a Zeus.

Cycle Six (eight): Another bad one. 4,200Au again, but with two Gekkos (huzzah, I can field a Geppo!). However, the superchest gave my my first Fury, so I was delighted overall.

At this point, I was sitting at just under 20,000Au, and entertained thoughts of quitting. I had a few premium weapons and bots, and could easily splash some Gold to round out the bench with things like a Lancelot. But heck, who knows when the next event is, so why not push my luck? I did go ahead and make the smart play, purchasing my fifth hangar slot.

ChestChart2

Cycle Seven (seven): Terrible return Gold-wise, just 3,450Au. But a Gareth and Aphid, so not a total disaster. Superchest gave me a Rogatka. I have one on my iOS account, and I don’t love it enough for this to feel like a win.

Cycle Eight (seven): An all-Gold run returned 5,300Au and another 3,000Au in the superchest.

Cycle Nine (eight): 5,950Au, not bad at all for a cycle that included two non-Gold prizes (a Gepard and Gareth). Superchest brought me another Galahad. All three off to the recyclery to be repurposed.

Cycle Ten (eight): 4,850Au and an Aphid. 3,000Au in the superchest. Right about here I was starting to look for the exit, down to around 7,000Au in the kitty. I decided to press my luck one last time.

Cycle Eleven (seven): 6,700Au means I only lose 300Au on the deal, which is repaid with interest when I hit 2,000Au in the superchest. I thought I was done, but then I decided to let my son Liam run out one more cycle.

Cycle Twelve (eight): Only 4,450Au this time, but two more Galahads and- huzzah!- a Jesse. Alas, the superchest is a somewhat disappointing Zeus, but this does mean I’m close to outfitting a Zeus Fury, so maybe it’s a blessing in disguise.

At that point, I tipped the dealer, finished my drink, and headed for the exit.

So now I’ve got a fifth hangar slot and a whole new remodel on the bots, and am delighted with the investment as I climbed up four levels with a hanger of pure brutality.

HEDR

As you probably noticed, in cycles 1-6 I was happy with all of the gear I won (names were all in bold). In cycles 7-12, however, I was pleased with less than half of my bots and weapons. This is a lesson in the principle of diminishing returns. I’m putting the same amount in, but getting less and less out. My average net profit for the first half was a mighty 5083.33Au. For the second half? Right into the toilet: 200.00Au. This underlines one of the most important aspects of the chest system, that conventional wisdom noted above: the less you have, the more you win. 

What if I wanted to get “lucky” with cycle #13? What’s the likelihood of me getting something I want? What’s the expected value (EV)? While my answer may not be the same as yours, here’s how you can calculate it.

Put plainly, here’s how you know when to quit. 

Remember that table in the Gold chest post where it listed the chance of winning all of the different possible prizes? I did ask out Pixonic contact to confirm or deny its authenticity and did not get a response, so draw your own conclusions there. Well, we’ll want to revisit that.

Girl watching the stars.

That 1209.1 represented the EV of a Gold chest. You spend 1000Au, you get back (on average) a hair over +20%.

But now, for each prize you don’t feel is valuable to you, you’ll want to zero that out. Bear in mind that everyone should zero out any Gold value less than 1,000Au, because that’s automatically a loss. Unless you like losing Gold, which you might. Your call. Here’s mine:

NewROI

I zeroed out all the Gold losers, as well as some of the gear. I have three Gekkos, the magic number I need for a Geppo and don’t want any more. I have all the Gepards I’ll ever want, same with Gareth (one of each is plenty). I’ll only ever want one Ancile, so that’s out, and so are the Rogtaka, Galahad (I’ve kept two), Jesse, and Fury.

Now what’s my EV? Oy, 524.55. That means on average, when I play the Gold chests I’ll be more or less cutting my money in half. Pass!

But Dredd, you may ask, what about the superchests? That’s all upside, right? Let’s revisit the rewards table for those:

Stats3

While it’s true that this is pure return- the superchests cost nothing to open, but rather are a reward for opening a number of Gold chests- they’re not entirely free. You still have to spend thousands of Gold to get the opportunity. And if the EV for my chests is only 524.55, that means after opening seven chests, I’ve gotten an estimated average return of 3671.85Au. Add to that the superchest EV of 3023.30, and you get 6695.15. That means that I’m still losing Gold on a seven-chest cycle. I lose another 524.55Au on an eight-chest cycle. And this is assuming that I’m happy with every reward on the superchest table. If I prune the superchest table the way I pruned the Gold chest one, my return looks much worse.

NewROI

So unless I “feel lucky,” I should keep what I’ve got and be happy with an Event well done and well won. Obviously your own mileage may vary, but I’d strongly encourage you to plan out your purchasing strategy in advance wherever possible.

HEDR

One last quick point before we conclude. I’ve had it put to me more than once that the values I used last week for the chest values were “inflated,” because of the “ridiculous” prices for the WIld Bunch bots. I’d like to take a closer look at that concern.

Let’s first isolate that data to give us something clean to look at.

NewROI

This is the bottom of the Gold chest payout list, where we find our Jesse, Doc, and Butch. The general concern here is if that if Pixonic’s valuation of the Wild Bunch were more realistic and in-line with player expectations, the EV on the chests wouldn’t look as good. Usually the suggestion is to price them in line with the BritBots– 5,000Au for Butch, 2500Au for Doc, and 1250Au for Jesse.

On the face it it, this seems absolutely correct. We’ve tanked the value of these robots compared to their inflated value, so we’d be expecting the EV to drop by a comparable proportion, right?

AdjWB

The above chart replaces the Gold chest values of the Wild Bunch with the equivalent BritBot values. A difference of only 78.04Au.

And the superchest table?

AdjData

A bigger hit here, with a difference of 388.13Au. Even taken together, it’s not the largest difference in the world, but it’s still significant, right?

Ehh, not exactly. This highlights the risks associated with looking at data elements in isolation rather than in their full context. The “reasonable EV” theory goes off the rails when you take into account Pixonic’s overall approach. Pixonic didn’t pull its numbers from a dartboard, but rather had a method for filling out their prize table. I remarked upon the very evident EV consistency in the original post, where all of the EV values for the Gold chest were somewhere between 40.2 and 40.6 or so.  What that means is that EV was the constant. If you devalue the Wild Bunch bots to their BritBot equivalents, then by necessity you must increase the frequency at which they appear.

Why, it’s almost like one of those memes!

LOK

The result? Same EV, and a lot more Wild Bunch running around. Probably not what Pixo had in mind for such an exclusive prize.

Thanks for reading! I hope I’ve caught you in time with this to help you make an informed decision about this event!

HEDR

And please, please, please enjoy this event responsibly. It shares a lot of characteristics with gambling. If you fear you might be getting too far in, please check out this article which has a helpful survey to assist you in determining whether or not there might be cause for concern.

7 comments on “By the Numbers: Know When to Walk Away

  1. Before this event my hangar was all silver with the exception of a carnage. Dropped 93$ so far. Came away with all the gunslingers, fury and all three zeus, galahad ×2, gareth ×4, 2 rots, 1 gep and enough gold to buy my first lance. For 93$ I received enough britts to compete at gold (still in silver) and the westies to play with later. I work hard and bust my ass everyday. Some would say never spend your money and ride for free. I love this game and the down time it gives me. Spending money was a way to support pixo and crazily I got an amazing hangar for it. Well worth every penny.

    Like

  2. Silentone2k

    Just wanted to say how much I enjoy this data driven economic analysis. I think a lot of games could be improved by people taking this sort of rigorous look at the underlying maths.

    Like

  3. Fascinating, but i do find it hard to reconcile the results with my own cycles, both of which have been out-and-out disasters. 2 x cycles netting me: 1 x galahad, 1 x gareth, 1 orkan, 1 x raijin (superchests: another galahad and 2250 gold) – the rest all silvers or say 600 gold from a 1k chest. Its drained about 7.5kgold – the idea of being able to just keep rolling to a superchest and then winning big enough to go again hasnt matched up to my experience at all. But then thats gambling, it has its winners and its losers, and it was at least exciting even if it did **** over my monies!

    Like

  4. Pingback: By the Numbers: The View from the Bottom – Gepard Diary

  5. Pingback: Russian Roulette: Dashes and the Black Market – Mech*Spectrum

  6. Deuteronomy 31:8

    Awesome article, looks like a lot of work and thought went into it.

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: