Goldratt's Dice Game (Theory of Constraints)

Goldratt's Dice Game is a simulation inspired by the matchstick game described by Eliyahu Goldratt in the novel The Goal. Participants form a chain of interdependent workstations. In each round, a die determines the capacity of the workstation, but the workstation can only pass on what it actually has in progress. The game vividly illustrates the gap between theoretical average capacity and actual production, then opens the discussion on bottlenecks and the theory of constraints.

Walkthrough

1. 1

   Set up the chain and the framework

   5 min

   The facilitator arranges 5 to 30 participants in a line or arc: each person represents a workstation, from supplier to customer. They say: "You will simulate a production chain; what comes out of the last workstation is the actual delivered production." The first workstation has an unlimited supply of tokens or matchsticks. Between each workstation, provide a visible space to place the in-progress items so that accumulation can be observed.

   Tip — Place the last workstation near a board or score sheet: this reinforces attention on the actual output, not on the activity of each workstation.

2. 2

   Explain the capacity rule

   5 min

   The facilitator gives a die to each workstation and announces: "In each round, you will roll your die; the result is your capacity for the day." A 1 allows processing a maximum of 1 token, a 6 allows a maximum of 6 tokens. They immediately clarify the key constraint: "You can only pass on to the next workstation the tokens available in front of you." The first workstation can always draw from its unlimited stock.

   Tip — Emphasise the word 'maximum': the die does not create material, it only defines what the workstation could process if it has enough in progress.

3. 3

   Conduct a trial round

   5 min

   The facilitator guides a trial round without counting it in the results, to avoid confusion. Everyone rolls their die, then the first workstation moves to the second as many tokens as its capacity allows. Then the second workstation does the same to the third, within the limits of its capacity and the available tokens, and so on until the last workstation. The facilitator checks that no one passes more than their actual stock, as this is the core of the simulation.

   Tip — Have a simple case solved aloud: "You have 2 tokens in front of you and you rolled a 5, how many can you send?" The correct answer is 2.

4. 4

   Launch the simulation

   10 à 25 min

   The facilitator announces the number of rounds, between 10 and 20 depending on the available time, then starts round 1. In each round, all workstations roll their die: the theoretical average capacity of each workstation is 3.5. Movements occur in the order of the chain, from the first to the last, respecting the available in-progress items. At the end of each round, the facilitator only notes the production output from the last workstation, and possibly the visible in-progress items between workstations.

   Tip — Maintain a steady pace: announce 'roll', then 'transfer workstation by workstation'. If everyone moves in disorder, the dependencies become unreadable.

5. 5

   Make the results visible

   5 à 10 min

   At the end of the 10 to 20 rounds, the facilitator sums up the actual production output from the last workstation. They remind: "Each workstation had the same average capacity, 3.5 per round." They ask participants to observe the areas where tokens have accumulated and those where workstations have waited due to lack of material. The contrast between local activity, in-progress items, and overall output prepares for the debrief.

   Tip — Do not comment too early during the game: let participants notice the accumulation of in-progress items and waiting times themselves.

6. 6

   Debrief the mechanisms

   10 à 15 min

   The facilitator opens the discussion: "What did you feel when your die was high but you had nothing to process?" Then they ask participants to name the two observed phenomena: dependencies between workstations and statistical fluctuations in capacities. They link these phenomena to the result: despite an average of 3.5 at each workstation, the actual production is lower. They conclude that the apparent balancing of capacities does not guarantee flow.

   Tip — Encourage those at workstations just before an accumulation to speak first, then those just after: their opposing experiences make the bottleneck more concrete.

7. 7

   Anchor the teaching on the bottleneck

   5 à 10 min

   The facilitator formulates the lesson: "In a dependent chain, flow is driven by the constraint, not by the average of each workstation." They ask where the bottleneck seemed to appear and how the in-progress items revealed it. They highlight that producing more upstream of a bottleneck mainly increases the in-progress items, not necessarily the output. The discussion concludes with the idea: managing the bottleneck is more important than mechanically balancing all capacities.

   Tip — Avoid looking for a scapegoat: talk about the system, dependencies, and variability, otherwise participants will focus on the 'bad luck' of one player.

Variants

• Play a first round of 10 turns to discover the phenomenon, then a second round of 10 turns after asking the group to identify the bottleneck and propose a flow management rule.
• Have a few non-playing participants observe a game: their mission is to note the queues, starving workstations, and moments when a good roll cannot be used.
• Increase or decrease the number of workstations in the chain according to the size of the group, while keeping the same rule: one die per workstation, unlimited supply at the first workstation, output measured at the last.
• Large group variant in person: create several chains in parallel with the same rules, then compare the final productions and observed in-progress items to show that the phenomenon repeats despite different rolls.