Define risk mathematically for each game. Understand why consequences make games exciting. Build a paper model of your game's risk system.

Before we do math, let's see how real game designers think about risk. Watch one or both of these together:

Video 1: Risk and Reward — Masahiro Sakurai (10 min)

The creator of Kirby and Super Smash Bros explains how risk and reward create the "push and pull" at the heart of fun games. Uses examples from games you've probably played.

Video 2: This Psychological Trick Makes Rewards Backfire — GMTK (11 min)

Game Maker's Toolkit on how reward systems can accidentally ruin the fun. Teaches why your reward/risk balance matters deeply.

Discussion after watching: What game from the videos had the best risk/reward system? Why did it work? Can you name a moment in a game you've played where you felt real tension about a choice?

Risk = Gain + Loss + Decision.

Every interesting game moment has three ingredients:

  • Gain — What you stand to win
  • Loss — What you stand to lose
  • Decision — The player chooses whether to take the gamble

Without real consequences, there is no tension. If failure doesn't cost anything, the "risk" is fake and the player knows it. But if failure costs everything, the player stops taking risks at all. The sweet spot is somewhere in between.

The Golden Rule: The player should feel nervous — not hopeless. If they're sweating a little, your risk system is working.

You need: One six-sided die (or use random.org/dice), a piece of paper, and a pencil.

Rules:

  1. You start with 0 points. Your goal is to reach 30 points.
  2. Each turn, roll the die. You earn that many points — but they're unbanked.
  3. After each roll, you choose: BANK (save your unbanked points safely) or ROLL AGAIN (keep your unbanked points at risk).
  4. If you roll a 1, you lose ALL unbanked points for this round. Your turn ends.
  5. First player to reach 30 banked points wins.

Play 3 rounds. After each round, write down:

  • How many points you had unbanked when you decided to bank
  • How many points you lost to rolling a 1
  • What your banking strategy was (bank early? push your luck?)

This IS your game. Ami's combat engine works exactly like this — XP is unbanked until you return to Camp. Ida's economy works the same way — karma is at risk from debt until you complete the build. The feeling you had when you decided to roll one more time? That's the feeling your players will have.
Ami — Combat Risk Engine

XP earned during exploration is "unbanked" — if the player dies, unbanked XP is lost. The longer you stay in the danger zone, the more XP you earn but the higher the chance of losing it all.

Calculate these 3 scenarios on paper:

Scenario Unbanked XP Enemy Power Win Chance If You Win If You Lose
Safe run 5 XP Low (5) ~80% +10 XP -5 XP
Medium push 25 XP Mid (12) ~55% +10 XP -25 XP
Greedy run 60 XP High (18) ~30% +10 XP -60 XP

Questions to answer on paper:

  1. At what point would YOU bank instead of fighting? 20 XP? 40? 60?
  2. What makes the "greedy run" tempting even though you'll probably lose?
  3. If a player always banks at 5 XP, is the game fun? Why or why not?
Ida — Economic Growth Engine

Players can take on debt to fund larger builds. Debt accrues interest over time. If debt exceeds −50 karma, the player goes bankrupt and progress resets.

Calculate these 3 scenarios on paper:

Scenario Job Cost Payout Profit Debt Risk Interest/sec
Small fence 5 karma 8 karma +3 None 0
Medium house 20 karma 35 karma +15 Maybe +1 if in debt
Big tower 45 karma 80 karma +35 High +1 if in debt

Questions to answer on paper:

  1. If you have 15 karma and the big tower costs 45, you'd need to borrow 30. With interest at +1 per second, how long before you go bankrupt (−50)?
  2. Is it smarter to do 3 small fences (+9 total) or 1 medium house (+15) with some debt?
  3. What makes the big tower tempting even though it could bankrupt you?

Now that you've done the math, compare the two games side by side:

Ami (Combat) Ida (Economy)
What you risk Unbanked XP Karma (via debt)
When risk happens Every encounter Every build decision
How to be safe Bank at Camp Take small jobs
Worst case Lose all unbanked XP Bankruptcy (full reset)
The feeling "One more fight..." "I can afford it..."

Key insight: Different surface, same structure. Both games are about greed vs. safety. Both punish the player for being too greedy. Both reward the player for taking smart risks.

If probability is new or needs a refresher, watch one of these:

Math Antics — Basic Probability (4.4M views, clear explanations)

Scratch Garden — Probability! (1.4M views, very kid-friendly)
  • Watch at least one game design video and discuss
  • Play the Risk Dice Game (3 rounds minimum)
  • Calculate gain/loss for all 3 scenarios in your game
  • Answer the 3 questions for your game on paper
  • Fill in the comparison table: your game vs the other game
  • Write down your "breaking point" — where risk becomes too high
  • Explain your risk system verbally to the instructor
    •
    Checkpoint

    Each child can explain their risk system with numbers. They can describe a scenario where risk pays off and one where it doesn't. They can point to the exact moment where the player makes the decision.

    Paper math only. No code. No game engine. Just numbers, dice, and decisions. The code comes on Day 3.

    Making risk too punishing — the player quits because failure is too harsh. If your "greedy run" scenario wipes out hours of progress, that's probably too much.

    Making risk too easy — the player never feels tension because failure barely matters. If losing costs 1 XP when you have 100, that's not real risk.

    Forgetting that risk needs a CHOICE — automatic loss isn't risk. The player must actively decide to take the gamble. If it just happens to them, it's unfair, not tense.

    The dice game is the most important part of this lesson. It gives both kids a visceral, first-person experience of the exact risk mechanic they're designing. After they play it, ask: "Remember when you had 12 points unbanked and you decided to roll again? That's what your player will feel." Connect the physical experience to their digital design.

    For the math tables, have them actually write numbers on paper. Don't let them skip the calculations. Ask follow-up questions: "If XP reward is 10 and risk of death is 20%, is that a good bet? What if the risk is 60%?" This is applied math — make it tangible.

    If one child finishes faster, have them play the dice game as the other child's game. Ami plays Ida's economy version (spend points to earn more), Ida plays Ami's combat version (roll to fight).