Royal Game of Ur Dice Odds

The Royal Game of Ur doesn't use numbered cubes — it uses four small pyramid-shaped (tetrahedral) dice, each with two of its four corners marked. That unusual shape gives the game a very different, more predictable probability curve than a normal six-sided die, and knowing it well is most of what separates a beginner from a strong player.

How the dice actually work

Each of the four pyramid dice has exactly two of its four corners marked. Roll one, and a marked corner lands face-up 50% of the time — it's a coin flip, not a 1-in-4 or 1-in-6 chance. Your roll total is simply how many of the four dice show a marked corner, so it can only ever be 0, 1, 2, 3 or 4.

The full probability table

This is just Pascal's triangle at n=4 — the same shape as flipping four coins and counting the heads. A roll of 2 is by far your most common roll, at over a third of all turns; the extremes (0 and 4) are each rare, at 1 in 16.

What this means at the table

• Expect a 2 more than anything else. Plan your moves assuming a 2 is coming, not a 3 or 4.
• A 0 isn't a disaster, but it does happen. About 1 in 16 turns (6.25%) you'll roll nothing and lose the turn entirely — in the Masters rules a 0 instead counts as a 4, which is one of the reasons Masters plays faster. See the full breakdown on our rules comparison page.
• Rosettes are worth fighting for. Because a roll of exactly 4 is rare (6.25%), the rosette squares that are 4 steps apart are genuinely hard to land on by chance — all the more reason to grab one when the dice cooperate.
• The curve is symmetric. Rolling a 1 is exactly as likely as rolling a 3, and 0 exactly as likely as 4 — useful when you're estimating whether an opponent's piece is in capture range.