Starting board has less skulls than other colors


More like question to developers, IDK really, maybe somebody else knows the inner workings. Now, I was running some explore with Elspeth and noticed that on the starting board, when you are casting on the first turn, number of skulls are on average lower than number of other colored gems. And no, I am not imagining things, I have a data set that confirms this. And the difference is quite substantial.

Is this intended?

Now, do subsequent skulls dropped during the match also have reduced frequency compared to other colors or is this a feature for board generation only?

Also, I’m getting a bit paranoid but I think I should run a few statistical tests to check whether the random in GoW is actually random. Obviously, running some Diehard tests is impossible (since they require raw continuous output) but I can generate random simulation with some other pRNG, check whether it is actually random, and compare simulated output to GoW output to see what is going on. It might even be possible to roughly estimate quality of pRNG output including skewness and kurtosis. Skewness can tell whether random is skewed and to what direction (plus or minus) and kurtosis is a rough indicator of how frequent is occurrence of low probability events.

I have a couple of hours free time, should be enough to collect the data and try to analyze.


Skulls have a lower drop rate.


Sometimes it can be hard to search these forums if you don’t know what you’re looking for and you don’t know if it’s even been asked before.

Fortunately, sometimes a forum old-timer like me can find it for you:

Tl;dr Sirrian confirms that it’s deliberate that there are fewer skulls on the starting board but it doesn’t affect subsequent drop rate.

Also the “combo breaker” referred to in this old post no longer exists in the same way as it did then.


Wow, I don’t think I ever saw that post.
Wonder if Sirrian will post the new Unity equivalent.


Thanks, I remember I’ve seen this, I did not remember whether it was clearly stated what is the percentage and then, how it goes further on. So, after the start it should be all at 14.29%. And certainly, it was not known whether Unity uses the same parameters. It seems like it does based on what I can see in the data.

No big deal for me, I just change the simulation frequencies.

I’ve collected the data and ran some preliminary tests. Can’t say anything definitively. But the pRNG does not pass a few primitive tests I tried. So far, I have been unable to figure out what specifically is wrong with it. I need to run probably MANOVA to compare with the simulation. Simulation by itself is OK, I used Excel 2010 that has Mersenne Twister and it passes all the pRNG and normality tests fine at least at P=0.05 and some at P=0.01.

Edit after trying some more tests and tweaking the simulation, it does work better now with corrected frequencies. So, no, not all hope is lost. :rofl:

I’ll continue tomorrow if I have nothing better to do.


Only on starting board, after that, it is all equal. :wink:


Speaking of the starting board calculation, I was just writing about empty game boards. If you don’t upgrade to 3.2 and your opponent uses the banner from the new kingdom (Merlantis), the starting board will be empty. This makes me wonder if the starting board algorithm does take the opponent banner into consideration. Otherwise, why would the board fail to spawn gems on startup? It’s quite curious from a programming perspective.


I generated data in Explore mode in Zaejin, so that the banner is apparently fixed. I did check correlation between colors of the opposing team and did not find anything meaningful or significant. Highest correlation was around 0.15 which basically means that there is no association between opponent colors and spawns for the board. To detect some correlation between banner of the opponent and spawning colors, another data set is needed in various kingdoms. I estimate, at least 100-150 data entries required, which might take about 1.5 hours. I can do 100 sets in about an hour. If anybody volunteers to collect the data, please pm me and I’ll tell how to do it and how to arrange it. There are certain rules that should minimize fluctuations and ensure consistency.

IMO, the banner is just something that is checked prior to the match and it must be loaded to resolve the moves. There is no team without a banner. If moves cannot be resolved, the board cannot be generated, it looks quite logical.


The data for the banner is at least partially in the game. The last time I encountered a Merlantis banner while running 3.1.5, it had the appropriate artwork for both the banner and the home kingdom. It seems odd that the rest of the data (mana bonuses, etc.) would be locked behind some gate that required version 3.2 to access.


That is actually easy to explain. The following is theoretical, but I’ve seen and written enough similar code to know it is a distinct possibility.

  1. As the board is set up, troop traits and other information are checked. The 3.1.5 world data had information about the new troops, but it was out of date and contained references to mechanics that may not have been fully coded.
  2. As those troops loaded in, something in the creation process failed, throwing an exception.
  3. The exception was subsequently caught, preventing the app from crashing, but in the process bypassing the rest of the startup sequence (dropping in the Gems). This left the game running but functionally broken.


Yes, the reason is probably mundane. I just found it interesting that you get a blank board when someone uses a banner from the new kingdom if you haven’t updated.


Just to pipe in on this: The code for gem spawning is the same in Unity as it was in AdobeAir.


Well, that analysis is certainly not some trivial task. The whole area of multivariate statistics is only emerging, so I think I need more time to make sure that everything is done carefully and there are no errors. I had resorted to converting the data to simplified formats as currently there is no good software apart from MANOVA plugins for r package or for Excel to analyze distributions within 7-dimensional vector space. :rofl:

But so far, it looks quite good. It seems that essentially all output during board generation is more or less random with minor deviations that do not significantly perturb the picture. I’ll post some report probably in a separate thread later.