Designing Balanced Dice

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The “broken” dice algorithm is a highly debated topic. So we researched this comprehensively and we were surprised by the results!<br>“The odds are way too low to roll a 6 three times in a row!”<br>“Look at this distribution, it’s nuts, what are the odds of rolling 4 three times more than 5?”<br>“Wow, I just played a game and the 7 almost didn’t roll!”<br>Does this sound like you? We heard you!<br>Read more about our random dice algorithm.<br>Are the dice broken?

The “broken” dice algorithm is a highly debated topic. So we researched this comprehensively and we were surprised by the results!<br>2 Common issues players run into:<br>Roll Streaks (Example: rolling 4 multiple times in a row)<br>Skewed distribution (Example: 3 rolling way more than 5)<br>“If there are 50 rolls in a game, the chances any number is rolled 3 times consecutively at any points in the game is 3.8%. However, it seems like it happens every other game.”- Source<br>At your request, we revisited our algorithm and this is what we’ve found...<br>57% chance to roll the same number three times in a row...

To properly address why this is the case we need to consider the probability of rolling a 2 three times in a row OR a 3 three times in a row… OR a 12 three times in a row then sum all the probabilities together. After running the numbers, for a 50 turn game the chance to roll a number three times in a row is 57%.<br>Yeah, we were surprised too! The statement "happens every other game" was quite correct.<br>If you’re curious on how we got to this answer, we broke it down.<br>Does Colonist dice match expected results?

Next we compared 1 million Colonist.io simulations to the expected results. This is what we found:

The Colonist.io dice actually has a ~1-2% lower total probability of rolling triples than expected. This is close enough to mimic real dice.<br>Try it yourself<br>Want to see how dice rolls play out in practice?

We’ve created an open tool for simulating dice rolls, available at this link. You can input the number of rolls and instantly see a chart showing how often sums from 2 to 12 appear. This helps understand how randomness works in the game Colonist.<br>How to Use<br>The tool is easy to use. After visiting this link, you’ll see an interface in the fourth block with a field to enter the number of rolls and a "Generate" button.<br>This process helps visualize why, for example, the chance of rolling the same number three times in a row seems high (57% in a 50-roll game), though it’s normal for random events.<br>We recommend starting with 50 rolls to see a typical distribution for a standard game, then increasing to 200 or 1000 to notice how the distribution becomes more even.<br>We hope this tool helps you better understand the mechanics of dice rolls in Colonist and dispels doubts about "broken" dice. Use it to experiment with different numbers of rolls and see how randomness works in practice.<br>Technical Details<br>The code is available for review, showing how it generates random rolls (1 to 6 for each die) and sums them to produce results from 2 to 12. CSS styles the interface, including buttons and charts, while JavaScript handles the simulation logic.<br>61% chance of rolling non-ideal distributions

To measure the probability of rolling non-ideal distributions, we used a statistical value called Goodness of Fit. The values span a range from 0 to 1 where a perfect distribution approaches a value of 1. There are more complex explanations but this is a concept more easily visualized. Note below the increasing normality as we increase the Goodness of Fit:<br>So what is the average Goodness of Fit for a standard game?<br>This means 61% of the games have an awful dice graph. Surely we must fix this.<br>It takes >200 turns to get a good fit

More competitive Colonist players are often quoted saying “This is randomness, games on Colonist aren’t long enough to get an even distribution.” After crunching the numbers, we’ve worked out that games would only be expected to be evenly distributed after 200 turns! That is roughly the length of 4 games!

Implementing the Balanced Dice

While some of the most competitive among you argue that random dice are at the core of the game, this doesn’t change the fact that a large subset of you are frustrated by what can easily be perceived as a lack of randomness. So, as game developers, it was important to us to provide a new optional dice algorithm, Balance Dice, that more closely matches expectations. Don’t worry though, the original Random Dice remains untouched!<br>Using Dice Deck to control distribution

Dice Deck is a card deck with all 36 combinations found in a 2 dice system. Instead of rolling the dice you draw a card. After the card is drawn it is discarded. This provides an easy way to create a balanced distribution. The problem with a Dice Deck is that it creates a system that is easily countable. To lower the predictability (Goodness of Fit) it is possible to change the point at which the deck is...