Dev Diary #2: The Underlying Mathematics of Loot the World

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Introduction

Hi everyone, Chris here, Lead Game Designer at Foxhole Games. Like Lloyd, this is my first Dev Diary entry for Loot the World, and my first post ever! Being a self-proclaimed maths nerd, I wanted to have my first post go into a little detail behind the decisions behind the economy of Loot the World. 

In Loot the World there are 5 types of hex tiles (2s, 4s, 6s, 8s, 10s) that make up a 5x5 hex tile map (that’s 25 hex tiles in total). This forms the basis of the game, where ownership of these tiles produces what we called “yield”, i.e. gold, which is the main driver of the economy. The end goals for everyone are the same: either connect one side of the board to the other, like in tic-tac-toe, or be the first player to amass 40 gold in total wealth. Below is a diagram of one of our hex tiles (note: designs are still WIP):

The Gold Economy

Let’s start things off with a simple investigation into the game’s Yield mechanics. At a very high level, things make some sense and seem quite balanced. Lower cost tiles yield less but also occur with a higher likelihood. The 4 Tile, for example, only yields 1 but you get said yield on any roll 2 or higher. Compared to the 10 Tile, which yields 9 but you get said yield only on a 5 or a 6, you might question why buying more expensive tiles would be worth it. And, at a glance, it seems like going cheaper would almost certainly be better. But let’s look at the actual probabilities that are going on here:

The maths is quite simple to explain. The Expected Yield column simply takes your yield and is multiplied by the probability of said roll. The efficiency is your expected yield divided by your cost. In other words, looking at this table, we can see that higher costing tiles actually yield you a higher return and should return said initial investment faster! If we plot these values we get an interesting curve.

The Actions Economy

Now, it’s all well and good to balance an economy in terms of gold or cash, but what makes Loot the World interesting, at least from my perspective, is that there is another hidden economy: Actions. All players get 2 actions per round. Unlike other games, where you are limited only by what resources you have, it was important to me that Loot the World took into account just how difficult it is to conduct several major simultaneous actions during the Victorian Era (especially as a mere trading company). One couldn’t just very well build hundreds of railroads all at once overseas; planning, manpower and resources were needed. To accomplish this, we decided to limit how many unique actions a player could make in a round.

Let’s look at Settlers of Catan, a game that we consistently thought about when making Loot the World (mainly because we know people are going to compare our game to Catan and we think it’s an okay-ish game). Hypothetically, if a player had 10 Sheep, 10 Ore and 10 Wheat, then they could very well purchase 10 Development Cards in one go! So if you had, let’s say, 2 Cities and 3 Settlements and then happened to draw 3 VP cards with that one move, the game would be over. For me, that experience means that as the game goes on, the Rich only get Richer and a player who is lagging has no means of recovering or even making a mark on the game. It feels bad.

So, with that in mind, we had a thought. What if you could only make one unique action of each type in each round? What if you could only deploy one Infantry, buy one tile, attack with one cavalry? Then, regardless of how much gold you have, you are just as limited as someone in last place! In fact, with Plot Twist Cards and the Rare Resources Expansion, players can easily change what leaderboard position they are in simply because all players have only 2 unique actions in each round! Effectively, even though we have a gold-based victory condition in Loot the World, a player with more gold is not necessarily in a significantly better position than someone with less.

Closing Thoughts

At the end of the day, who am I to really dictate what makes a good or bad economy in a game? There are many board games that have very simple and yet fun ideas behind an Economy (I’m looking at you Machi Koro 2!) and some board games with a significantly more complex system. One does not mean a game is better than the other, it simply comes down to your philosophy and how you like to play a game. For me, being a big old maths nerd and someone who obsesses over the underlying probabilities and theories behind a decision, designing Loot the World the way we have was a no brainer. If you are interested in some of the discussions behind the nuts and bolts of Loot the World or any other game we will design, feel free to sign up to our newsletter via the homepage.

If you made it this far, well done! We can't wait for you to try Loot the World when we launch in 2026.

Thanks for following along,
Chris