Death by Million Cubes

The year is not completely over yet but I already found my biggest disappointment in games of 2012: Peter Molyneux' Curiosity. In the unlikely case that you missed what the game is about: it's basically a huge cube floating in space that is made of millions of little cubelets that disappear when tapped upon. Everyone that downloaded the game taps on the same cube and together the players make the cube disappear and eventually the game self-destruct because there is nothing more to do. The person that taps on the last cube gets a reward.

My Expectations I was really looking forward to that game. Not because I find it an interesting game — far from it. I was looking forward to it because there are two things in life that I find more interesting than anything else: technology and human behavior. This game had the chance to showcase an excellent implementation on the technical side and tell is something new about how humans work. Instead what I got was a failure of monumental scale. The technology behind it is not very clever and because it barely works it won't be able to tell us anything about how humans work, at least as far as the game is concerned. In fact there is more to learn from discussions outside the game than behavior that people show in the game itself (if it even loads).

Scaling Problems So for the unlikely case that someone reads this blog who is not a programmer at heart, here is why Curiosity is an interesting technical challenge. Let's ignore Curiosity the final product for a moment because it actually does not at all behave like you think it should. I will come back to Curiosity a bit later. Let's say we would like to build our own Curiosity on the concept outlined previously. Let's assume our cube is made out of millions of cubelets: how large is it? Let's say one face on the top of the cube is set to 8001 by 8001. Since there are six sides and the cubes on the edge are shared with other sides the easiest way to count the cubes on the outside is to calculate the volume of the cube and subtract the volume of everything but the outer layer which leaves us with 8001^3 - 7999^3 (383.904.008) individual cubes on the outermost layer. That's three hundred eighty-four million two individual cubelets. The good news is that the cube gets smaller as we're going in. In fact the number of cubelets per layer is growing quadratically from the core outwards which also means that the time it takes to chip away layer after layer from the outside to the inside is quadratically. The more we're chipping to the core of the cube the faster it will get — quickly. Why is that interesting? It's interesting because it means as the cube gets smaller there will be higher contention as the same player count now operates on a much smaller surface. There are two areas where Curiosity needs scaling: on one hand you have the client which needs to render the cube. That part is not too complicated because of the restriction that you can always only operate on one layer. That makes drawing very simple. On the other hand however you have the server where you need to store and process the data. Let's say we go with the above dimensions for a cube. Next we're assuming 10.000 concurrent players and each player taps exactly two times per second. In that case it would take the players 5.3 hours to tap away all the cubelets on the top. But imagine how quickly those players would tap away lower layers. These players would tap away the last 200 layers of the cube in less than 15 minutes. Worse, the last 20 layers would disappear in less than a second. The simplification in Curiosity's design that you can only ever tap on the outermost layer does not only help with rendering. Thanks to that our storage requirements on both server and client will be predictable and manageable. The largest layer is the outermost one. For the largest version of the cube with a size of 8000 that would be a total of ~46MB of storage for the individual cubes assuming one bit per cubelet. On top of that we need one measly integer that tells us on which layer we are. That's definitely something the client could keep in memory on a modern mobile phone but the initial synchronization time would be killer. What complicates things is that with the amount of tapping that is expected from that game the whole thing would change rather dramatically until you finished downloading everything. The solution for this would be to have a general level of detail system. Here is where it gets annoying: our cube only have two states per cubelet: present or not present. It's just two extremes which is problematic to deal with if you want to build a lower resolution representation of the cube (LOD). Regular nearest neighbor will not work since it will pick a single pixel and that decides what to show. With a cube of the size of Curiosity you might want to zoom out quite far. With 8000 by 8000 pixels you will have to skip over more than 10 by 10 pixels if you zoom all the way out. The best result is probably achieved by counting the number of black pixels within each N by N quad and then write the LOD level. You then would have to load the higher resolution picture as quickly as possible on loading, definitely before the user can start issuing taps because otherwise the user might modify areas that are already cleared. The good news is that the game design does not allow to resurrect already removed cubelets which would allow some optimizations. The real issue however here is concurrency. On the top layer everything might be cool. The game once zoomed close enough would subscribe to the areas and all taps are immediately exchanged between the people participating there. Let's say the zoom level on which you tap is 20x20 cubelets. We could optimize the system by dividing the topmost layer of our cube into 20 by 20 large subscription areas. Clients subscribe to these areas to be informed about updates as they happen. Assuming you could always only fully zoom into the game the worst case would be subscribing to four of these areas which covers a total of 40x40 blocks. At the topmost level you would have approximately 240.000 such subscription areas. If you distribute 10.000 players among them each group has on average 0.05 players on it. As the cube grows smaller and smaller more players would subscribe to the same groups driving up the outgoing network traffic from the server. Where at the start most traffic on the server would be inbound only since barely anyone is in the same subscription group you run into troubles with smaller groups. If the cube is approximately 500x500 in size you're expecting 10 players in the same 40x40 block. At the end you would have every player in the same group since the cube is no longer big enough to distribute the players around.

Latency Issues Now obviously the whole game is self-terminating as designed. Someone will chip away the last block and then the experiment will be over. However what this means in terms of network traffic is ridiculous. Let's assume the game would be really popular because you have something special behind the last block which only one person in the world can get. Once the cube is smaller than the zoom level all players will have to get all network traffic. Let's assume 50.000 concurrent players which is not completely impossible and these players tap away quickly at a rate of 5 taps per second. That means that the server would have to process 250.000 requests per second and directly send back data to the clients. That's a lot! This becomes a problem because information on the internet travels at a certain speed. With the assumption that the average player has a latency of 150 milliseconds to the server (Which is already ludicrously optimistic since most people will play on mobile connections or connect from different parts of the world to the server) there is a high chance that the cube already disappeared by some other user before you had the chance. With 25.000 players tapping on the same screen the last tap will be absolutely random. Multiple players would see themselves as the last tapper and only a single one wins. A way to counter that would be to make it harder to tap on individual cubes as it goes on to rebalance the game somewhat.

Keeping the Secret The other problem you have with the game is how to keep the secret secret. Only one person can get it, how do you make the game not reveal its secret? This is actually not that hard. You just need a way to load code and assets on the fly from the central server for the one lucky guy.

Keeping Cheaters Out Now that's the hardest part: how do you keep cheaters out. How do you make sure people don't just use the network interface directly and bypass the tapping. This can't really be countered I think. I think there is really only one way to counter that problem: basic velocity testing on the server. That way you can ensure that a player doesn't tap faster than humanly possible. With that you can still bot the hell out of the game but you won't be faster than the fastest human tapper. That however gives people that cheat the game still a higher chance to win it than a human being. You could potentially make it harder by changing the API every couple of levels but at one point people will have that figured out as well. With a game that simple you will have a cheating problem on your hand sooner or later.

How Curiosity Does It Alright. Now that we know some of the problems, how does Curiosity solve it? The answer is: it does not. It saddens me but the game does not even appear to have realized what the problem with the design might be. The cleverness in the execution seems to stop after realizing that transmitting all the blocks at one time is a bad idea. Instead of looking at this as a form of interesting engineering problem nobody thought anything at any point as it seems: The server backend is a simplistic PHP application, I can only guess it actually uses some form of database for it, why otherwise would you use PHP …

the gold rewards in the game that are generated for tapping is apparently entirely client side — I did not even bother finding out how purchases are handled. I would not be surprised if that was not very secure.

the game only synchronizes with the server once per minute. You can tap in areas someone else is tapping without realizing it.

the LODding is incredibly basic and often lies about areas. You can even start tapping in unloaded content without the game giving an indication that this is happening. It seems to also only use a single pixel since some people managed to write a four letter swearword across the cube which disappears after you zoom in.

Not only does the game seem to LOD oddly, sometimes it seems like it does not even remember the individual cubes. If you zoom down even if you wait for minutes you will still see 8 by 8 blocks that are either present or completely chipped away. Never have I seen individual blocks sitting around except for my own ones in the same session.

the game does not appear to handle the edges of the cube properly. If you tap away one block at the edge of the cube and then rotate the cube you can't see the damage you did sideways. Understandable but also very boring. For a game that has DLC worth many thousand US dollar in the game this is a very disappointing execution. I would have spent some time figuring out if it reveals its secret but in all honesty I am already disappointed and considering how overloaded the severs are at the moment, it's not at all interesting playing around with the API to see how it works in detail and if it's exploitable.