source key concepts: probability, randomness in game systems, designing with luck in mind
context: for 2 or more (scales up easily) in a room; 30-40 minutes
This is a tabletop exercise about probability. You and your partner each design a 6-sided die to beat each other in a simple game. By using tactile objects and visual graphing, it offers an intuitive path into understanding systems of randomness and luck.
This exercise is a version of Dice Wars by Stone Librande, a game designer whose brilliant and elegant design activities have been one of the primary inspirations for the exercises in this book. You can download Stone’s talks and exercises at Stonetronix.com.
Setup
The best way to run Die vs Die is with blank dice - they look just like normal six-sided dice, but with blank faces instead of the usual pips showing numbers 1 through 6. You can find blank dice in hobby stores and teaching supply websites, but in a pinch regular dice and masking tape work just fine.
- one blank 6-sided die for each designer
- one regular 6-sided die for each designer
- whiteboard markers for marking the sides of the dice
- a printout of the DIEvsDIE.PDF sheet - one for each pair of designers
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For remote teaching, we have prepared this spreadsheet instead. Make your own copy, then make copies for each student (or have your TA do it, or students do it themselves). Each pair of students will need their own copy.
- 25-30 small tokens in one color for each designer (each designer should have their own color)
I often use Die vs Die as part of a unit on probability and game design. It’s also a good way to warm up system thinking, as it looks at a very narrow problem in a generous amount of detail.
The simple version
To begin, make sure each designer has a regular 6-sided die and ask them to play a simple game. In pairs, each player rolls a die and the higher roll wins. On a tie roll, nobody wins. (I said it was simple!) A couple of practice duels should suffice to get the main idea across.
To start tracking what happens across several rounds, have them use the exercise printout and the small tokens. One player uses the red die numbers across the top, and the other uses the blue die numbers along the side. Follow this procedure:
- Roll their dice. For example the player using black rolls a 1 and the player using red rolls a 4.
- Find the square on the chart that corresponds to the roll - a blue 1 + red 4 means the square on the top row of the grid underneath the 4. ![[Pasted image 20250130142902.png]]
- Put a marker there depending on who won - since the red player won, put their color token in the spot. If nobody wins, leave it blank.
After a few rolls, a pattern should start emerging. The grid is split along a diagonal axis. You can tell everyone to stop rolling and just use their tokens to fill in the blanks. The resulting grid shows you which die wins in each possible combination of rolls - the universe of every possible match that might ever happen. And because the two dice are the same, each one wins an equal number of times. ![[Pasted image 20250130142946.png]] Yes, this is incredibly elementary probability statistics. But the point of this exercise is not to dive into advanced mathematics. It it is to use tactile and visual means to develop a gut sense for feeling probability.
The real game starts
The actual game of Die vs Die requires custom dice. You can pass out the blank dice (or the masking tape). Each designer is going to create their own unique battling die. The six faces of the die need to add up to 21, just like a regular die (1+2+3+4+5+6 = 21).
The designers can work out the distribution of values for their dice and write them on the faces of their own die. The numbers of on each side:
- must be positive whole numbers (no fractions, decimals, or negative numbers)
- can repeat (the numbers don’t need to be unique)
- can be zero
So 0/2/3/4/5/7 is a valid die. So is 0/0/0/7/7/7. Or 1/1/1/3/3/12.
Have players pair up with each other and battle ten times. Keep track of who wins each of the ten rolls. Then ask the group if there is a way to see which die is actually better than the other one - at least in terms of which is more likely to win a random die roll. The answer is - to use the chart, of course! You can cross out the 1/2/3/4/4/6 along the top and side and replace those numbers with the numbers of the two dice. Then there’s no need to roll - you can use the tokens to mark which die would win which combinations. Fill out the chart with tokens. It might look something like this: ![[Pasted image 20250130143126.png]] Which die beats which die? In this case, blue beats red, because you can count the blue tokens vs the red tokens.
Then - ask the students to compare the record of their 10 random battles to the results in the chart. Likely some pairs had results that mirrored the probabilities in their chart. But others almost certainly did not - because of the small sample size of only 10 battles. With a higher number of matches (100, or 1000 or more), the overall average of the outcomes would approach the ratio on the chart.
Best of the best
Likely there are one or two in the group that had a particularly strong die against their opponent and thinks they have the perfect Die vs Die die. It’s time to burst their bubbles!
Get the die numbers from two of these overconfident designers and chart their outcomes on a whiteboard or on a tabletop with tokens so that everyone can see which die actually has a better shot at beating the other. But… can we tweak things so that the losing die beats the winning die? What numbers can be changed in order to turn the tables?
In the example above, if the red die’s zeroes were turned into 1s or 2s, they would get the edge on the blue die’s lower numbers. And as long as the 6 and 7 stayed above 3, the red die can probably eke out a win over blue. It’s all about changing the numbers to use them efficiently against your opponent - there’s no need to beat numbers by more than one point.
The question comes up: is there a single die that is better (on average) than any other? Is there in fact one die to rule them all? There may be a die design that has better chances against more other dice. If you can solve that math problem, let me know how it turns out!
But the value of a die in Die vs Die is not whether it mathematically averages out better than other dice given millions of theoretical games. The value of a die is how it does at this particular moment, against the opponent right in front of you. Evolving your die design to adjust for different opponents is a simple analog for the many kinds of customizable systems we see today - from deck-building CCGs to character-drafting MOBAs to the strategic jockeying of the stock market or social media stats.
To go deeper into Die vs. Die, visit Stone Librande’s website stonetronix.com. He adds an additional twist, which is to replace the “renewable resource” of a die with a “depleting resource” of a deck of cards numbered 1 through 6. It’s mind-expanding!