Dice Probability & Expected Value
📋 What it is
Each die outcome has a probability; "expected value" is the average result you'd get over many rolls.
🗣️ Coach says
Dice are the math heart of many games. One six-sided die has six equally-likely outcomes, so each has a 1-in-6 chance. The "expected value" is the long-run average — for a fair d6 it's 3.5. Designers use expected value to balance how strong a dice-driven move should be.
🧠 Memory hook
Each face = 1-in-6. Expected value = the average over many rolls (3.5 for a d6).
😂 Giggle
Why did the six-sided die go to school?
It wanted to roll with a smarter crowd!
😲 Whoa!
The expected value of a fair six-sided die is 3.5 — a number you can never actually ROLL, yet it's exactly the average of all your rolls over time.
✅ Quick check: What is the expected value (average) of a single fair six-sided die?
Say your answer out loud first — then reveal.
3.5 — the average of 1,2,3,4,5,6; over many rolls your results centre on 3.5 even though you can never roll it.
Expected value is the mean of all equally-likely outcomes: (1+2+3+4+5+6)/6 = 3.5.
🪄 Trick question: If you roll one die, is a 6 more likely than a 1?
Careful — think it through, then reveal.
No — on a fair die all six faces are equally likely (1-in-6 each); no single number is more likely than another.
A fair die gives every face the same probability.
🧪 Try it! (2 minutes)
Roll a die 20 times, average your results, and compare to the expected 3.5. They should be close.