Boxes with visible chances: an economy that cannot be exploited

Every game with a currency sooner or later runs into the same problem that the makers of online worlds also know: the currency piles up faster than it is spent. In Audamir this happened very quickly. The Golden Dice that the player gets for games, minigames and achievements could be spent in only one place, the gallery of looks, and the whole gallery was bought early. It followed that another thing to spend the currency on was needed, and even one that never ends.

This article is about the decisions that came out of it and which of them are deliberately non-commercial.

The first idea: a casino

The first proposal was a well-known one: a casino with dice poker. Five dice, two re-rolls, a payout table. The dice are in the game, the player has collected gold, so let them bet it.

A lot could be learned from the proposal, and it did not make it into the game. A value judgement decided it: poker was not considered a suitable way to spend the currency (the decision of the author: too contentious a topic). A value decision cannot be replaced by a table, but the measurement supported it. An exact calculation (dynamic programming over all the re-rolls) found that the simple strategy "keep the most frequent value" reaches 98% of the optimum (on a trial payout table 250% against 254% for ideal play). With no re-rolling only 34%. After an hour of play there is nothing to discover in it.

A note from the documentation remained: if such a casino were ever introduced, the payout table must give optimal play a negative expected value (a return of about 92 to 96%), with a bet limit and a daily limit. That is exactly what real casinos do, and the game decided to rather avoid it.

(Where dice poker is played in games and why is the subject of a separate article.)

The second idea: the player's die

The answer is the player's own die, today the Avatar^[1]. In this proposal it was at the same time the character of the player in the story of the campaign (the hero from the east), the narrator of the game (it comments on the game in a bubble) and the place where the three currencies of the game are spent:

• Golden Dice (Principalities^[2], minigames, the daily challenge) buy the boxes of the Golden world,
• Stone Dice (the campaign) the boxes of the Stone world,
• Iron Dice (the Iron Run) the boxes of the Iron world.

A box gives three faces of the die. A face has a number from 1 to 6 and a tier (in the Golden world: wood, bronze, silver, gold, diamond and star; the Stone and Iron worlds have four tiers). Three equal faces can be merged into one face of a higher tier, and two faces of one tier can be swapped for one with a number that the player chooses. The die is "at tier T" when it has a face of tier T or better for every number. Completing a tier unlocks looks: emblems, sets of dice, board themes.

The player gets looks, not power.

What is forbidden in this design

The design document has, before all the technical matters, a list of what must not be done. It is the most valuable part:

1. Looks are bought with the currency, never power. Power in the game (talents, trophies, bonuses) arises only from play, and the currency does not buy it.
2. Nothing is sold for real money. The currency cannot be bought.
3. No timers and no streak pressure. A box never expires.
4. The chances are always visible. In the confirmation window before a purchase and on the card after it.
5. The purchase is saved before it is shown. If the player logged out while a box was opening or the browser crashed, the find is already in stock and is not re-rolled. If saving fails, everything is rolled back in memory and the game says so.

To this belongs a sixth point, which turned out to be important in the design: in a game with several human players (later) a game will have no effect on progress.

The chances and what each tier costs

A box costs 150 Golden Dice. Each face comes from one draw: bronze 5%, silver 0.5%, everything else wood. The chances are absolute, they do not depend on what the player owns. The reason: relative chances would make the price of the next tier roughly constant and the "bottomless well" would disappear.

How many boxes each tier costs came out of an exact simulation (node tools/dice.js, 1,000 trials per row, today):

Tier 5 (diamond) is the real goal and requires about 195 wins in Principalities. Tier 6 is prestige, around 574 wins. The proposal also counted tiers 7 and 8 in the simulation (they would cost thousands of wins); they are not in the game, and the data would allow adding them later. Swapping faces shortens mainly the low tiers: without it tier 1 costs five boxes instead of three and tier 2 eleven instead of seven. The hard tiers hardly change with swapping; there the number of faces itself decides (6 × 3^(T−1)).

The table was not written by a human. A tool computed it from the data of the world (js/data/worlds.js), and if the world breaks (for example changes the chances so that the third tier comes after five hours), the tool fails. The number in the proposal and the number in the tool agreed to within one percent, so the proposal did not have to be corrected.

Free boxes and their table

Besides purchase, boxes drop for playing: a win in Principalities, the first win of the daily challenge and the first solution of the puzzle of the day. This is not a gift without rules. The table of chances is always visible in the game and for Principalities it looks like this:

The daily challenge and the puzzle of the day give a box for sure, at most three free boxes a day in all. Free boxes are a supplement: with a typical mix of games they make up about 21% of all boxes.

The original proposal was more generous for 6 to 8 players (28, 31 and 35%). The tool showed that with eight players the free boxes would make up 29% of the boxes, so the chances were lowered.

The decision about a box is made from the fingerprint of the game (seed, salt, mode) in the same operation that writes the game. It therefore cannot be re-drawn by reloading the page or by a second write, and no random stream of the game is used. A test substitutes a counter for Math.random and verifies that it was not called even once.

Where the pressure is in this, and where it is not

An honest question: is this not a box all the same? It is. The mechanism is the same as in the mobile market: a random reward, a collection, merging. The difference is in the values, not in the mechanics.

Let us look at what the mobile market does. A study of the 40 top Korean mobile games of 2025 (a preprint) found boxes with a random reward in 37 of them and a daily login in 38. In 2018 the Belgian Gambling Commission ruled that the loot boxes in Overwatch, FIFA 18 and CS:GO violate the local gambling rules, regardless of whether the reward is a look or an advantage. The Dutch authority claimed something similar a week earlier. Three criteria decided: a game, a stake that can lead to a gain or a loss, and a random outcome.

Audamir deliberately does not meet the second criterion (the stake): the currency can be earned only by playing and cannot be bought for money. This is a design decision, not a legal opinion. Platforms have their own rules, and so the design document counts on a flag at build time that would hide the boxes (so far only in the plan; nothing else depends on them).

One open compromise remains. The puzzle of the day has a streak of days with a bonus, which is a soft form of streak pressure, which the design otherwise avoids. Whether to keep it remains to be considered.

What I take from it

• The piling up of currency is a design problem. If a player has something to spend on in only one place, they will spend it quickly. A way to spend the currency is needed (in online worlds a "money sink") that cannot be exhausted.
• The chances must not depend on progress. Otherwise the well runs dry.
• Forbid things in advance. A list of "what must not be done" is more durable than a list of "what may be done".
• Write the economy with a tool, not by hand. When a number changes, the table rewrites itself.
• Also measure the depth of a game that you do not want. The casino had 98% of the optimum and after an hour there was nothing to discover. The reason not to introduce it was one of values, but the measurement supported it.

Sources and notes

• The proposal and decisions: docs/HERO-DICE.md §2 (decisions), §5 to §7 (worlds, boxes, economy); the casino: docs/ROADMAP.md, chapter 12; implementation and numbers: docs/DESIGN.md §24 and §27. Numbers from the tool: node tools/dice.js --world gold (20 Oct 2026, 1,000 trials).
• Belgian Gambling Commission 2018 (Overwatch, FIFA 18, CS:GO): PC Gamer and The Sixth Axis of April 2018; a week earlier a similar conclusion of the Dutch authority. The penalties differ between the sources, so they are not given.
• Korean mobile games: arXiv 2504.10714 (a preprint, a qualitative study of 40 games).