Modified Regular Dice for the Royal Game of UR

After seeing this great video [https://www.youtube.com/watch?v=WZskjLq040I] about the millennia-old boardgame The Royal Game of UR, I wanted to build one myself. There are already some great Instructables about this game as you can see here [https://www.instructables.com/howto/royal+game+of+ur].

The design of the board is very simple, it consist of just 20 connected squares. As the other Instructables show you can create one out of any flat material. There are many designs to be found online that you can print and use. Or you can just draw it on a piece of paper (that's what I started with). Besides that you also need 14 player pieces in two different colors, any kind of boardgame piece will do.

However, the dice used in this game are very uncommon so I decided to see if I could modify regular dice to get the same results.

Step 1: Analyzing the Original Dice

There are four dice in this game. They have triangular-based pyramid shapes, also known as tetrahedrons. Two of the corners of each die have a dot on it. When a die is rolled it will always land with one of its four corners pointing upwards. When this corner contains a dot it counts as 1 point, else as 0 points. With four dice you can roll a total value between 0 and 4.

All dice have a 50% change of each value (0 or 1), with four dice this gives us 16 different combinations of die values. The probabilities of rolling the possible values are as follows:

• Value 0 -> 1 out of 16 = 6,25%
• Value 1 -> 4 out of 16 = 25%
• Value 2 -> 6 out of 16 = 37,5%
• Value 3 -> 4 out of 16 = 25%
• Value 4 -> 1 out of 16 = 6,25%

Step 2: Using Four Regular Dice

The easiest way to get the same results is to use four regular dice. Each die should have a 50% change of each value (0 or 1) so all you need to do is change three sides to have one dot and the other three sides to be blank. I will show you how this can be done in step 5.

But first I will try to get the same result with just two regular dice!

Step 3: Using Two Regular Dice

Using two dice needs some more calculations. With 6 sides each there are 36 combinations of values. Since we want the total value to be between 0 and 4, each die should be able to produce a value between 0 and 2, not just 0 or 1.

The closest probabilities that are possible are as follows (values rounded for readability):

• Value 0 -> 2 out of 36 = 5,6% -> difference of 0,7%
• Value 1 -> 9 out of 36 = 25%
• Value 2 -> 14 out of 36 = 38,9% -> difference of 1,4%
• Value 3 -> 9 out of 36 = 25%
• Value 4 -> 2 out of 36 = 5,6% -> difference of 0,7%

These small differences mean that once every 72 throws the resulting value will be 2 instead of 0 or 4. That's close enough, such a small difference will not really influence the game.

To get these results we need two dice as follows:

• To get two possibilities of value 0, one die should have one side with value 0 and the other die two sides with value 0
• To get two possibilities of value 4, one die should have one side with value 2 and the other die two sides with value 2
• All other sides should have value 1
• To get the correct probabilities the die with two sides with value 0 should not also have two sides of value 2

So to sum it up:

• Die 1 -> two sides value 0 + three sides value 1 + one side value 2
• Die 2 -> one side value 0 + three sides value 1 + two sides value 2

When using regular dice you could change them as follows:

• Leave the 1-sides and 2-sides as they are
• Change the 3-sides to have 1 dot
• Remove all dots on the 4-side of one die
• Change the 4-side on the other die to have 2 dots
• Change the 5-sides to have 1 dot
• Remove all dots from the 6-sides

See the picture for more information.

Step 4: Modifying the Dice

There are several ways to change regular dice to have new values. The easiest way may be to put stickers on the sides and draw dots on them. If you have dice without cavities for the dots you could try to remove the dots with sandpaper or a hobby knife.

The first thing I tried was a paintmarker. I don't really like the result, the edges of the dots are still visible and the somewhat glossy and brighter white paint still shows the original values.

I then decided to use my Dremel to remove the paint out of the dot cavities. I first used a small round bit to remove most of the paint and then a bigger one to smooth the edges of the cavities. This last step really helps to let the remaining dots stand out. The rounded edges also match the overall roundness of these dice.

Step 5: Conclusion

I am very satisfied with the result! The resulting probabilites are very close to the original dice, close enough to not really influence the game. The dice also look good and the values can be easily read without being distracted by the original values.

The next thing for me to do is to create a better-looking board and some custom player pieces. And then play the game over and over again!