Free lean training game · Play online or print the card
The Dice Game: why a balanced line still misses its numbers.
The dice game is the classic lean exercise for teaching dependent events, variability, and throughput — four stations, one die each, and a line that never delivers what the averages promise. Run it right here with a facilitator mode built for projecting to a room, roll the line yourself, or print the free card and run it at a table.
- Time
- 20–25 min
- People
- 1 to a full room
- Teaches
- Variability · dependent events · WIP
- Cost
- Free, no signup
Projecting for a workshop? Choose “Run it for a room” — you click (or press Space) to roll each round and stop whenever the room needs to look at the piles, or flip on Auto to let the line roll itself at 1×, 2×, or 4×. The ⛶ button goes fullscreen.
What is the dice game?
The dice game is a hands-on lean training exercisemade famous by Eliyahu Goldratt's The Goal, where it appears as the match-and-dice game on a Boy Scout hike. Four to six people sit in a row — each person is a station with one die. A pile of about 40 tokens sits in front of Station 1 as raw material. Every round, everyone rolls at once: a roll is that station's capacity, and it moves that many tokens to the next station — but only what is actually in front of it. Whatever leaves the last station is finished output.
Here is the trap: every station averages 3.5 tokens a round, so ten rounds “should” deliver 35 — and every room writes 35 on the flip chart. Then the dice start rolling, piles form between stations, and ten rounds deliver 25–30, not 35. The line is perfectly balanced on paper and still misses its numbers — which is exactly the point, and why the game has anchored theory-of-constraints and lean workshops for decades.
How to run the dice game
What you need
- 4–6 people in a row at one table — each person is a station, with piles between people
- One die per station
- ~40 tokens — pennies, paper clips, or chips — piled as raw material in front of Station 1
- One scorekeeper who tallies output after every round
The rounds
- Everyone rolls at once.Your roll is your capacity: move that many tokens from your incoming pile to the next station. If you don't have that many, move what you have.
- The last station delivers. Its tokens are finished output — tally it every round.
- Play 20 rounds in two blocks of 10. Record output and the biggest pile after each block, then compare against the expected 35.
Before rolling, ask the room what ten rounds “should” deliver — the average roll is 3.5, so the math says 35. Write 35 on the flip chart. Then watch. The gap between the number on the chart and the number the line delivers is where the learning lives.
What will happen
| Rounds | Expected | Typical room | Piles | Shortfall |
|---|---|---|---|---|
| 1–10 | 35 | 25–30 | wander & grow | ~20–30% |
| 11–20 | 35 | 25–30 | wander & grow | ~20–30% |
The shortfall isn't bad luck, and it doesn't average out over the second block — the piles just wander to new stations and keep growing.
What the dice game teaches
- Dependent events plus variability beat averages. Every station averages 3.5, yet the line delivers 25–30 per ten rounds instead of 35. Averages describe stations; they do not describe lines.
- A station can never pass more than it received. A six is worthless behind a station that just rolled a one. Capacity you can't feed is capacity you don't have.
- Bad rolls compound; good rolls evaporate. A bad roll starves every station downstream for rounds to come. A good roll is gone the moment it happens — there is no banking it against tomorrow.
- Buffers cost something. Stock between stations steadies output, but you pay for that stability in work-in-process — inventory sitting in piles instead of flowing.
Variations worth running
- Elevate the constraint. Give one station two dice. Watch throughput follow the slowest station, not the average of all of them.
- Buffer stock. Start every station with 4 tokens already in its pile. Output steadies — and you paid for it in WIP.
Both variations are built into the simulation above as toggles on the start screen.
Debrief questions
- Where did the piles form — and did they stay in one place?
- Why can't today's good roll make up for yesterday's bad one?
- What would a small buffer between stations change — and what does it cost?
- Which of our own handoffs “rolls dice” — and how big is our die?
- Make it stick: where do we plan our line on averages — and what does variability actually do to those plans? Averages lie about lines.
Print it and run it at a table
The Dice Game — printable facilitator card
One page, print-and-go: setup diagram, the round tables with expected numbers, both variations, and the debrief script. Part of the free Kaizumi lean game library — one email unlocks all four cards.
Letter-size, print-ready, readable in black and white.
Dice game FAQ
What is the dice game?
The dice game is a classic lean training exercise from Eliyahu Goldratt’s The Goal. Four to six stations sit in a row, each with one die. Every round all stations roll at once; a roll is that station’s capacity, but it can only pass the tokens actually in front of it. Every station averages 3.5 per round, so ten rounds should deliver 35 — a typical room delivers 25–30. The gap is dependent events plus variability, not bad luck.
How long does the dice game take?
20–25 minutes including the debrief: a couple of minutes of setup, 20 quick rounds in two blocks of ten, and five to ten minutes of discussion.
How many people do you need?
Four to six: each person is a station in the row, plus a scorekeeper who tallies output after every round. With the online simulation, one facilitator can run it for a room of any size.
What does the dice game teach?
Dependent events and variability — the two effects that make a perfectly balanced line miss its numbers. A station can never pass more than it received, so bad rolls compound down the line while good rolls evaporate. It also shows what buffer stock buys, and what it costs in work-in-process.
Can I run the dice game remotely?
Yes — share the free online simulation on a video call. Facilitator mode rolls the line on screen with a prediction stop, a halftime pause at round 10, a running scoreboard, and debrief questions built in.
More free lean games
Lean game
The Penny Game
The classic batch-size exercise — four workers, twenty coins, and a stopwatch that does the arguing. Play it online or print the card.
Simulation
One-Piece Flow Simulator
A continuous flow simulation with factory, café, and office scenarios — explore what the games teach at production scale.
The library
All lean games & cards
Digital games plus printable facilitator cards for the penny game, paper airplane game, and 5S numbers game.