Castles of Burgundy Dice Odds: What a Worker Buys You

Welcome to Level 1. At Level 0 you learned what a die can do. Now you learn what a die is likely to do, and how much control the game really gives you. The answer surprises most new players: a lot. The Castles of Burgundy uses dice, but it hands you the tools to steer them, and a few plain numbers show how far those tools go.

Every figure here comes from counting the 36 ways two dice can land, using the rulebook’s worker rule: each worker changes a die by 1, up or down, and 1 and 6 wrap around.

Wrapping makes the die a circle

Because a 6 can become a 1 and a 1 a 6, the six faces sit in a ring. No number is ever more than 3 steps from another. That means:

• 0 workers: a die reaches 1 number, its own face.
• 1 worker: it reaches 3 numbers, its face and the two beside it.
• 2 workers: 5 numbers.
• 3 workers: all 6. Three workers can turn any die into anything.

The odds of hitting one number

Most turns, you need one specific number: the depot with the tile you want, or the space that tile goes on. You have two dice, so you need just one of them to get there.

Read the jump from the first row to the second. One worker more than doubles your chance. On average, hitting a single number costs just under one worker. That is why players who keep a worker or two in hand seem to roll well all game.

The odds of hitting two numbers

The best turns use both dice on a plan: take a tile from depot 4 and place it on a 2 space, say. Now you need both numbers, one on each die. That is much harder.

A two-number plan with no workers almost never happens. With two workers it is a coin flip or better. On average, landing two numbers next to each other costs about two and a half workers.

The lesson: do not build a turn around needing two exact numbers. Build around one, and let the other die do whatever it can.

How to make one number enough

Since one number is easy and two are hard, split your plans so each needs just one die:

• Take a tile this turn, place it next turn. Your storage holds three tiles. A tile waiting in storage turns next turn’s plan into a one-number problem.
• Keep tiles for several numbers in storage. A stored ship that fits a 2 space and a stored building that fits a 5 space give you two ways to use your dice.
• Use the free actions. Taking 2 workers works with any number. So does a black depot buy, which needs no die at all.

The rulebook warns that discarding from full storage is usually a bad idea, so this works best with one or two tiles waiting, not three.

Tools that change the math

Several monastery tiles bend these numbers further:

• Monastery 8: a worker may change a die by 2 instead of 1. The rulebook’s own example: a 3 becomes a 6 with 2 workers instead of 3. Your workers go a lot further.
• Monasteries 9 to 12: change a die by 1 for free when you place certain tile colors, or when you take a tile.
• Monastery 14: the take-workers action gives 4 workers instead of 2.

And a castle is the strongest tool of all. Once you place it, it gives an extra action with any number you choose, no worker needed. A castle waiting in storage is a turn that can grow when the dice line up.

Putting a price on a plan

Before you commit to a plan, price it in workers. If it needs one number and you hold a worker, it is very likely. If it needs two numbers and you hold none, it is a hope. Choose the plan you can pay for.

Our piece on luck and skill explains why dice with this much control reward planning. Here the control has a price, and now you know it.