Dungeon Dice

Rolling dice, digging tunnels, and avoiding guards in Dungeon Dice

After a series of interviews, we are back to tabletop games and Python simulations. This week we are taking a look at Dungeon Dice (Gruen, 1977)!

Dungeon Dice

Dungeon Dice - Be first out of the dungeon in Parker Brothers escape game

Dungeon Dice was designed by Paul J. Gruen, who also designed Pay Day (1975), Bonkers! (1978), and the perhaps less well known Barney Miller board game (1977).

Here’s the description from the back of the box:

Escape is all you can think about when you live in a cold, dark dungeon.

It’s impossible to not comment on the art of this game! It’s steeped in the 1970s cartoon style. Unfortunately no artist is listed on the BGG page. If you have any idea who the artist was, please comment below!

Digging out of the dungeon

The game includes six wooden dice, 4 prisoner cards, 28 tunnel cards, game board, and a plastic “dungeon pit” that fits into the board.

Be the first to dig your way out of the dungeon by rolling matching sets of dice!

You roll the dice to acquire Tunnel Cards that are added to your Escape Path on the board. The card art fits together to look like one continuous tunnel.

Get eight Tunnel Cards in your Escape Path and you win!

Pushing your luck vs. guards

The general turn sequence looks like this:

1. Roll all six dice in the dungeon pit.

2. Remove any matches of two or more dice, placing them on the wall.

3. Take Tunnel Cards based on the size of the sets.

4. Choose to either stop and keep your cards or continue and try for more cards.

5. During each subsequent roll of the remaining dice, matches are added to the wall.

Even if no matches are made, you need to remove at least one die to the wall each turn. So the dice pool is ever shrinking.

The push your luck mechanism comes in the form of the Guard dice (i.e. helmets with the side-eye):

Pairs or sets of Guards are moved to the wall just like any other dice, but also force you to keep rolling until all six dice are on the wall.

If you ever end up with three or more Guards on the wall, all Tunnel Cards gained that turn are returned and you lose a card already played to your Escape Path!

Chance of getting matches

Getting pairs of dice (i.e. two matching dice) doesn’t earn any Tunnel Cards. You need at least three or more:

Tunnel Cards for matches of Escape Tools

I was curious what the chances are of getting at least three of a kind (earning one Tunnel Card) on your first roll.

So what are the chances of getting at least a pair on your first roll? What are the chances of getting at least three matching dice or more?

There are certainly ways of calculating this using statistics, which can be more complicated than one might imagine. You need to consider the balls into bins problem, the pigeonhole principle, and the birthday problem.

Instead, I wrote some Python to just roll the dice a million times and see how often I got at least X matching dice:

The chance of getting at least 2 matching dice is over 98%, which is probably why simple pairs of dice aren’t rewarded with Tunnel Cards. Getting at least 3 matching dice on your first roll is significantly less likely, at about 37%. From there it drops off fast, with just about a 5% chance of getting at least 4 matching dice.

Note that this is only for the very first roll, not subsequent rolls. Most of the game is deciding if you should should keep rolling or not.

Challenging other players

There is a take that mechanism in the the game as well. You can “challenge” other players instead of taking your regular turn:

1. Announce who you are challenging.

2. Roll up to three times, moving any guards to the wall.

3. You succeed if you end with at least three (3) guards on the wall.

If successful, you steal one card from the other person’s Escape Path and immediately add it to your own. Challenges can continue as long as each is successful. When one fails, all cards are returned to the original owner.

So what is the chance of winning a single challenge?

Simulating this in Python (N=1,000,000) shows that there’s an almost exactly 50% chance of success on each challenge.

Basically no different than a coin flip! That means we can use a coin toss streak calculator to estimate the successful challenge streaks: 1 = 50%, 2 = 25%, 3 = 12.5%, and so on. Half as much each time.

Conclusion

Dungeon Dice, dice and dungeon pit

Some things to think about:

• Equivalent probability mechanisms: The challenge mechanism is an interesting example of how obscuring the underlying probability can change the feel of the game. Imagine if each challenge was resolved with coin flip? It might seem more arbitrary than multiple dice rolls. It would also be less thematic without using the Guard dice. Exact same result, but a significantly different player experience!

• Micro games vs. custom production: The One-Page RPG Jam recently ended, so I’ve been thinking about micro games quite a bit. The rules for Dungeon Dice could easily fit onto a single page. If the components were abstracted, it could be a print and play game. It’s interesting to think about how games can be stripped down and abstracted, or expanded and enhanced with custom components.

• Custom dice can have a significant impact: With six unique faces, there’s no reason this game couldn’t be played with standard d6 dice. You could just define a 6 as being a Guard. It would be the same game, but would have much less visual and thematic appeal.

Have you ever played Dungeon Dice, Pay Day, Bonkers!, or the Barney Miller board game? If so, please leave a comment about your experience!

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See you next week!

— E.P. 💀

P.S. I just released a new solo monster hunting game called Eleventh Beast. You should try it.