How to Play

🎲 First Rolls: See Randomness in Action

Start with the default — two dice and 100 rolls. Press Play to send the dice tumbling. Each roll flashes the result in the tray and raises a bar in the histogram. Watch how the bars dance — uneven, jumpy, sometimes surprising. This is what small samples look like: randomness on full display.

Try pausing after ten or twenty rolls to make a quick prediction: which total will end up tallest? Then continue and see whether the trend holds. Even in short runs, you’ll notice that middle numbers like 6, 7, or 8 start winning more often — and that pattern only gets stronger over time.

⚙️ Experiment with the Controls

Use the Dice per roll slider (1–10) to change how many dice are rolled at once. With one die, results are spread evenly from 1 to 6. With two dice, totals range from 2 to 12 and the chart forms a small mountain around 7. Add more dice and that mountain becomes wider and smoother.

Next, use the Roll count slider to decide how many times to throw. Try short bursts of 10 or 20 rolls to see quick wiggles, or long runs of 500 or 1000 to watch the bars stabilize. Notice how increasing the number of trials reduces the “wiggle” and brings the shape closer to a gentle curve.

📈 Compare Data to the Expected Curve

Turn on the comparison overlay to see the predicted shape for your chosen number of dice. The game draws a smooth theoretical curve — a preview of what would happen if you rolled forever. As you gather more data, the live bars begin to match the curve almost perfectly. This side-by-side view helps you understand the power of sample size and why averages matter.

🔁 Reset, Predict, Repeat

When a run finishes, press Reset to clear the board and set up a new scenario. Try doubling the dice, halving the roll count, or switching back to a single die to see how the distribution changes. Before each run, make a prediction about which totals will appear most often — then test your guess. Each run feels like a mini experiment where randomness gradually gives way to predictability.

Study Notes

🎯 What You’re Really Seeing

Every bar in the histogram represents how often a specific total appears across all the dice. Each roll adds one count to a single bar — the one matching its total dots. This simple process, repeated many times, reveals the hidden structure behind randomness. You are watching a real accumulation of outcomes, not a pre-drawn animation.

🔢 Why the Middle Wins

There are many more ways to roll a middle total than an edge total. For example, when rolling two dice, seven can appear in six different combinations (1+6, 2+5, 3+4, etc.), while two or twelve can appear only one way each. That’s why the middle bars grow faster — and why the overall shape forms a smooth hill instead of staying flat.

📊 Randomness, Order, and the Law of Large Numbers

Early on, results bounce around wildly, but as the number of rolls increases, the average settles near a steady center. This is a real-life example of the law of large numbers: as sample size grows, the observed results approach the expected probabilities. The histogram is a living picture of that law at work.

💡 Classroom & Curiosity Tips

• Predict the tallest bar before each run and see how often you’re right.
• Compare short vs. long runs to see how data “smooths out.”
• Discuss how adding dice changes the shape from flat to bell-shaped.
• Overlay the theoretical curve to see how close your experiment gets to the ideal.

Each roll is simple, but together they form a deep lesson in probability, variation, and why data patterns emerge from randomness.