FAQ - Frequently Asked Questions

Our community members often discuss the same questions, so we decided to come together to compile this list of common answers, in the hope that it can help old and new members alike! But don’t be shy. If you have any further questions or suggestions, or think anything here should be changed, please enquire through our Discord page, and we will reply ASAP!

Are the bots on RoyalUr.net fair?

Yes. The probabilities of you and the AI rolling each number is the exact same! Each dice roll is independent, and has no influence based upon what would benefit the AI. The dice rolls are modelled based upon the roll of 4 fair tetrahedral dice, as in the physical game. In fact, Potherca from the Discord community created a CodePen to test the fairness of the RoyalUr.net dice, which you can find here.

Why then does it feel like the AI is cheating when its doing well? There are two psychological factors that we believe contribute to this: the Law of Small Numbers and the Gamblers Fallacy. The Law of Small Numbers states that the inferences we make about data is unreliable when the sample size is small, but people often consider these inferences to be reliable. For example, consider that while you are playing you observe a long sequence of five 0’s in a row. The probability of this happening is very small, only 0.00009%. Therefore, you may be inclined to believe that the game is unfair, with incorrect odds. However, this would be an example of the Law of Small Numbers! To gather meaningful inferences about the distribution of dice rolls you would need to look at rolls over the course of many games, not just your five unlucky rolls in a row.

Hopefully you are now convinced that the distribution of dice rolls is fair. However, you may also make another mistake in predicting future dice rolls based upon the rolls you’ve just made. This would be an example of the Gambler’s Fallacy! The Gambler’s Fallacy states that future random dice rolls are not affected by previous dice rolls, but people often believe that their dice rolls will be affected by the past. For example, if you have rolled five 0’s in a row, you may believe that it is less likely that you will roll another 0. In fact, this is false! The chance that you will roll another 0 is actually the exact same as before! These dice rolls are statistically independent.

Humans are hardwired to find patterns. In fact, we are so inclined to this behavior that we find patterns where there are none! In particular, evaluating the fairness of dice rolls can feel very unintuitive to people. Gambling has often exploited these quirks of human intuition to promote fun. However, unfortunately, casinos also often use them to exploit money from people. This can be avoided though, using mathematics and statistics! We hope that you will turn to these tools if you wish to evaluate random variables.

How complex (or hard) is the Royal Game of Ur?

Our own experience has shown that the Royal Game of Ur is easy to learn, but hard to master! We have some players that find good challenge from the Medium bot, and others who often beat the hardest Panda agent! However, these observations are quite subjective. Can we be a bit more scientific? In fact, we can! There are several mathematical definitions for complexity that we can use to compare the “hardness” of the Royal Game of Ur (RGU) to other games. Two definitions that are often used for this purpose are the State-Space Complexity (SSC) and the Game-Tree Complexity (GTC).

State-Space Complexity measures the number of possible valid game states (i.e., how many positions are there?). Alternatively, Game-Tree Complexity measures the number of possible games that can be played, including all dice rolls and chosen moves. Additional information about these measures of complexity can be found here and here. Diego Raposo found that The Royal Game of Ur has a low State-Space Complexity, but a medium Game-Tree Complexity, in his paper with Padraig Lamont that is yet to be published. A graphical comparison between the Royal Game of Ur (using the simplified rules used by Finkel in the YouTube video) and other popular games is shown below:

What is the primary source of the rules of The Royal Game of Ur?

Irving's paper on his translation of the special cuneiform tablet and its relationship to the zodiac and the Game of Twenty Squares was published in 2007 in his book “Ancient Board Games in Perspective”. This book is an assembly of information presented at the first Board Games Studies Colloquium in 1990 in London. It took them some time between first presentation and first publication!

The rules used by RoyalUr.net and in the Tom Scott v. Finkel video were included with a Royal Game of Ur replica board that has been sold by the British Museum since 1991 (if you know of any earlier publication of these rules, let us know!). This product also included a second, more complex, set of rules with a gambling element, which was based on the cuneiform tablet deciphered by Irving Finkel. However, there is no evidence that directly links these rules to the Royal Game of Ur board.

There are many other proposed rules for the Royal Game of Ur, including those from famous games historians R.C. Bell (Board and Table Games from many Civilisations, 1979) and H. J. R. Murray (Board Games other than Chess, 1952).

Are the default rules on RoyalUr.net the same as those presented by Finkel in “On the Rules for the Royal Game of Ur”?

No. The Royal Game of Ur is dated around 2500 years earlier and is played with different equipment to that identified from the tablet. The rules for the Game of Twenty Squares as played in 177BC were proposed by Irving Finkel primarily based on his interpretation of a cuneiform tablet held at the British Museum. The rules for the game played on the Ur board as explained in the video are also proposed by Irving, but are simpler. Irving simply concocted some straight-forward rules for a race game that play well using the equipment found at the Ur site. There are some reasonable basic similarities between the two games such as the path taken by the pieces and the very fact that it is a race game.

Is the Game of Twenty Squares the same as the Royal Game of Ur?

The Game of Twenty Squares is the term generally used for the game played on a board with a rectangle of twelve squares and a tail of eight squares, whereas The Royal Game of Ur is synonymous with the distinctively shaped board shown at the top of this page. The two games are not the same because not only are the boards different shapes, but the pieces and dice were also not identical. However, it was assumed by Finkel and other academics that the earlier Royal Game of Ur boards are probably the ancestor of the Game of Twenty Squares, and therefore that the two games had similar basic traits.

Was the Royal Game of Ur only played in Mesopotamia?

One other board exists with the same distinctive layout, and this was found at Shahr-e Sukhteh in ancient Persia (now Iran). However, any rosettes or other features on this board, if they once existed, are no longer visible. Therefore, it is possible that the game played on this board was different. For example, Draughts (Checkers) and Chess are a modern example of two different games played on the same board.

Ongoing Questions

There are still several questions that we are still investigating. If you have any opinions or work on these questions, we'd love to hear about it in our Discord!

• A simple and useful notation for the Royal Game of Ur
• Quantification of the amount of luck and skill in the game
• Ways to quantify, rank and analyze the progress of players
• How to best apply neural network algorithms to the Royal Game of Ur
• Analysis of the mathematics of the game