Chapter 10 Quiz: Randomness, Probability, and the Art of Uncertainty

Multiple Choice

1. Input randomness in game design means:

a) The player's controller input is randomized
b) The random event resolves before the player makes a decision, creating a situation for the player to respond to
c) The player enters a random seed at the start of the game
d) Randomness is only applied to input devices like keyboards and controllers

2. Output randomness in game design means:

a) The game randomly outputs audio or visual effects
b) The player commits to an action first, and then randomness determines the result
c) The game's output resolution is randomly selected
d) Random numbers are displayed on the screen

3. A player has fought 40 enemies, each with a 5% drop rate for a rare item, without receiving it. The probability of the NEXT enemy dropping the item is:

a) 95%, because it is "due" after so many failures
b) 40%, because the probability accumulates
c) 5%, because each roll is independent
d) 100%, because the pity timer should have triggered

4. The gambler's fallacy is:

a) The belief that casino games can be beaten with skill
b) The belief that past independent random events influence future probabilities
c) The mathematical proof that gamblers always lose
d) A design technique used to make randomness feel fair

5. If an item has a 10% drop rate, approximately how many attempts does it take for 50% of players to receive the item (the median)?

a) 5 attempts
b) 7 attempts
c) 10 attempts
d) 20 attempts

6. Pseudo-Random Distribution (PRD), as used in DOTA 2, works by:

a) Using a truly random number generator instead of a pseudo-random one
b) Starting with a lower-than-stated probability and increasing it after each failure, resetting on success
c) Displaying a fake probability to the player while using a different one internally
d) Removing randomness entirely and using a fixed rotation

7. A pity timer in a loot system:

a) Tracks how long the player has been in the game and gives rewards based on playtime
b) Guarantees a specific outcome after a set number of unsuccessful attempts
c) Reduces enemy difficulty when the player is losing
d) Displays a countdown showing when the next rare item will drop

8. In a weighted loot table with entries: Sword (weight 10), Shield (weight 5), Potion (weight 25), Gold (weight 60), the probability of receiving a Sword is:

a) 10%
b) 25%
c) 40%
d) 50%

9. Spelunky's procedural level generation achieves playability by:

a) Using pure randomness and hoping for good results
b) Generating a guaranteed traversable path first, then filling remaining rooms from curated templates
c) Copying levels from other games and randomizing the textures
d) Letting players manually edit levels that feel unfair

10. Which of the following is the MOST ethical approach to monetized randomness?

a) Never publishing drop rates so players cannot calculate expected costs
b) Publishing drop rates, implementing a spending ceiling, and providing a non-random acquisition path
c) Making the randomized items purely cosmetic, which removes all ethical concerns
d) Using the word "surprise" instead of "loot box" in marketing materials

11. The key advantage of using a seed for random number generation is:

a) It makes the numbers truly random instead of pseudo-random
b) It allows exact reproduction of a random sequence, enabling shared worlds, bug reproduction, and replays
c) It prevents players from predicting random outcomes
d) It increases the speed of random number generation

12. Which game demonstrates the purest form of input randomness design?

a) XCOM (percentage-based hit chances resolved after the player shoots)
b) Slay the Spire (card draws resolve before the player decides which cards to play)
c) Roulette (place bets, spin the wheel, result is unknown)
d) Slot machines (pull lever, random result)

13. In the context of randomness design, "rubber-banding" refers to:

a) Using elastic physics in platforming games
b) A system that slows the leader or boosts the trailing player to keep competition close
c) The visual effect of stretching and squashing game objects
d) Connecting multiple random events together in a chain

14. A two-stage nested loot table first rolls for _, then rolls for _.

a) Player level; item name
b) Rarity tier; specific item within that tier
c) Weapon type; weapon damage
d) Drop or no drop; number of items

15. Belgium's 2018 ban on loot boxes classified them as:

a) Intellectual property violations
b) Gambling
c) False advertising
d) Age-restricted content

Short Answer

16. A designer creates an enemy with a 2% chance to drop a legendary weapon. Players must defeat this enemy to progress through the main story. The enemy takes approximately 15 minutes to fight each time.

Calculate the probability that a player still does not have the weapon after 50 kills. Then explain in 2-3 sentences why this design is problematic and propose two specific fixes.

17. Explain the difference between input randomness and output randomness using a specific example from a game you have played. Which type does the game use, and how does it affect the player's perception of fairness? (3-5 sentences)

18. A game has a 25% critical hit chance using flat probability. Describe in 3-4 sentences how Pseudo-Random Distribution would change the player's experience compared to flat probability, assuming the average critical hit rate remains 25%.

19. A free-to-play game offers a "character banner" where each pull costs $3 (equivalent) and the featured character has a 0.6% drop rate. The game has a pity timer at 90 pulls.

Calculate: (a) the expected number of pulls for the median player, (b) the expected cost for the median player, and (c) the maximum cost for any player (pity ceiling).

20. You are designing a roguelike. An early tester reports: "The game feels too random. I keep dying to things I could not have predicted." Using concepts from this chapter, propose three specific design changes that would make the game feel less random without removing randomness. Explain why each change works. (5-7 sentences)

Answer Key

1. b) The random event resolves before the player makes a decision, creating a situation for the player to respond to.

2. b) The player commits to an action first, and then randomness determines the result.

3. c) 5%, because each roll is independent. The gambler's fallacy is the belief that past independent events influence future probabilities. Each enemy is a separate 5% roll regardless of how many previous rolls failed.

4. b) The belief that past independent random events influence future probabilities.

5. b) 7 attempts. The median is ln(0.5) / ln(0.90) = 6.58, which rounds to approximately 7 attempts.

6. b) Starting with a lower-than-stated probability and increasing it after each failure, resetting on success. This preserves the stated average rate while compressing the distribution to prevent long streaks.

7. b) Guarantees a specific outcome after a set number of unsuccessful attempts.

8. a) 10%. Total weight = 10 + 5 + 25 + 60 = 100. Sword probability = 10 / 100 = 10%.

9. b) Generating a guaranteed traversable path first, then filling remaining rooms from curated templates. The path ensures every level is completable; the templates ensure every room is well-designed.

10. b) Publishing drop rates, implementing a spending ceiling, and providing a non-random acquisition path. Transparency, ceiling protection, and alternative acquisition are the three pillars of ethical monetized randomness.

11. b) It allows exact reproduction of a random sequence, enabling shared worlds, bug reproduction, and replays. Given the same seed, a PRNG produces the exact same sequence every time.

12. b) Slay the Spire. Cards are drawn (randomness resolves), the player sees their hand (full information), and then decides which cards to play (informed decision). This is pure input randomness.

13. b) A system that slows the leader or boosts the trailing player to keep competition close. Named after Mario Kart's item distribution system.

14. b) Rarity tier; specific item within that tier. This separates the "how rare" question from the "which item" question, making both independently tunable.

15. b) Gambling. Belgium classified loot boxes as games of chance subject to gambling legislation, leading several major games to modify or remove loot box systems in the country.

16. P(no drop after 50 kills) = (1 - 0.02)^50 = 0.98^50 = 36.4%. More than one-third of all players will fight the boss 50 times (12.5 hours) without receiving the progression-required weapon. This is problematic because: the weapon is required for progression (not optional), the time cost per attempt is high (15 minutes), and there is no alternative path. Fixes: (1) Add a pity timer guaranteeing the drop after 20-30 kills (maximum 5-7.5 hours). (2) Add a token/currency system where each kill awards tokens, and the weapon can be purchased directly after accumulating enough tokens.

17. Answers will vary. Strong answers identify the randomness type correctly, connect it to the player's decision-making process, and evaluate whether the game's use of that type serves or undermines the player experience.

18. With PRD, the player would experience fewer long droughts without a critical hit and fewer streaks of consecutive critical hits. The initial probability per attack would be lower than 25%, but it would increase with each non-critical hit, meaning that after 3-4 normal attacks, the next attack would have a significantly elevated critical chance. The overall average would remain 25%, but the experience would feel more "regular" --- critical hits would be more evenly spaced rather than clustering and droughting unpredictably.

19. (a) Median pulls = ln(0.5) / ln(1 - 0.006) = ln(0.5) / ln(0.994) = -0.693 / -0.006 = 115.2 pulls. However, the pity timer guarantees the character at 90 pulls, which is below the median. Therefore the effective median is 90 pulls (the pity timer dominates). More precisely: the pity timer means any player who has not received the character by pull 89 gets it at pull 90. (b) Median cost = 90 x $3 = $270. (c) Maximum cost = 90 x $3 = $270 (the pity ceiling).

20. Answers will vary. Strong answers propose specific changes such as: (1) Convert output randomness to input randomness by showing the player what each room/encounter contains before they enter (the player sees the situation before committing). (2) Add visual or audio tells that communicate danger before it strikes, giving the player time to react (feedback as randomness mitigation). (3) Implement bad-luck protection so that consecutive difficult encounters are followed by easier ones or guaranteed resources (PRD or pity timer for encounter difficulty). Each change works because it gives the player either more information, more agency, or more protection against extreme outcomes.