Multi-Sided Dice — Changing the Odds (Without Cheating)
If you’ve ever rolled a die and thought, “I need the universe to be slightly more on my side,” then congratulations — you’re already thinking like a game designer, a statistician, or a student five minutes before an exam.
Most people meet probability via the humble six-sided die (d6). Lovely. Familiar. Comforting. Like a mug of tea that can also disappoint you on a 1.
But the moment you introduce multi-sided dice — d4, d8, d10, d12, d20 (and their more exotic cousins) — you’re no longer just rolling… you’re tuning the odds.
Let’s have a rummage in the maths toolbox.
1) What changes when you change the number of sides?
A fair die with n sides gives a uniform distribution:
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Every number has probability 1/n
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The average (expected) roll is (n + 1) / 2
So:
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d6 average = (6+1)/2 = 3.5
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d20 average = (20+1)/2 = 10.5
That means swapping a d6 for a d20 doesn’t just “add variety” — it shifts the whole centre of gravity of outcomes.
Bigger die = bigger spread.
More dramatic highs… and more tragic lows (because maths enjoys balance).
2) “I need at least a 5” — how the odds change fast
Suppose your game / experiment / teacher says:
“Success if you roll 5 or more.”
Let’s compare:
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d6: outcomes 5–6 → 2/6 = 1/3 ≈ 33%
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d8: outcomes 5–8 → 4/8 = 1/2 = 50%
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d10: outcomes 5–10 → 6/10 = 60%
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d12: outcomes 5–12 → 8/12 = 66.7%
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d20: outcomes 5–20 → 16/20 = 80%
Same “target”, totally different reality.
So multi-sided dice let you keep the rules looking the same while changing how generous the universe is being behind the scenes. (This is also how some board games feel “kind” without admitting it.)
3) One big die vs lots of smaller dice (this is the really useful bit)
Here’s the twist: one die is uniform.
But adding dice changes the shape of the distribution.
Compare these:
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d12 → results 1–12, each equally likely (flat distribution)
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2d6 → results 2–12, but not equally likely (peaked distribution)
With 2d6, totals in the middle happen far more often:
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7 is common
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2 and 12 are rare
So:
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If you want outcomes to cluster around “typical” values: use multiple dice
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If you want outcomes to feel swingy and unpredictable: use one bigger die
Game design translation:
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Multiple dice = consistent characters, predictable systems
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One big die = chaos goblin energy
4) “Make it exciting” vs “Make it fair”
People often say they want a game to be “fair”, but what they usually mean is:
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“I want to feel I had a chance”
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“I don’t want to fail five times in a row”
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“I want the results to match skill… most of the time”
Multi-sided dice give you dials to turn:
To reduce random drama:
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Use more dice (e.g., 3d6 instead of 1d20)
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Or narrow the range (d6 instead of d20)
To increase drama:
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Use a bigger single die (d20 gives epic swings)
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Add “critical” rules (e.g., max roll = bonus event)
5) A quick classroom / home experiment (no lab coat required)
Try this with students (or willing family members who haven’t realised what’s happening yet):
Task: Roll each option 50 times, record totals, and plot a simple bar chart.
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Option A: 1d12
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Option B: 2d6
Prediction:
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1d12 will be flatter
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2d6 will build a hill in the middle
Extension:
Turn it into GCSE/A-Level discussion:
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mean, median, mode
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range and spread
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why distributions matter (hello, real life)
If you want to go full “data-nerd”, stick it in a spreadsheet and let the bar chart do the storytelling.
6) Why this matters beyond board games
Multi-sided dice are really just simple models for random events:
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choosing random samples
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simulating “chance” in experiments
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designing scoring systems
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understanding risk and reliability
They’re also brilliant for explaining the difference between:
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uniform probability (one die)
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combined outcomes (multiple dice)
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and why “more rolls” doesn’t always mean “more randomness” — it can mean more predictability.
7) The takeaway (before the d4 destroys your bare foot)
Multi-sided dice don’t just change the numbers.
They change:
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how often you succeed
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how swingy outcomes feel
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whether results cluster or scatter
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and whether your game/lesson feels “fair”, “brutal”, or “suspiciously generous”
So next time you’re tempted to say, “It’s just a different die”…
No.
It’s a probability settings menu — in physical form.
And unlike most settings menus, this one can be launched across the room when someone rolls a 1.
