Reward Schedule Simulator: Gamified Engagement

Reinforcement Schedule

Schedule parameter k 3

Answer success probability 70%

Engagement decay (fatigue) 2.0

Attempt speed 1.0x

Live State

Engagement40%

Streak

Level

Total XP

Attempts

How it works

Educational games hook players through operant conditioning: a reward follows a behaviour on a reinforcement schedule. B.F. Skinner's classic schedules, still used to tune quiz apps and XP systems today:

Fixed Ratio  (FR-k)  — reward every k-th correct answer
Variable Ratio (VR-k) — reward with probability 1/k per correct answer (avg every k)
Fixed Interval (FI-k) — reward the first correct answer after k seconds
Variable Interval (VI-k) — reward after a random wait averaging k seconds

Each simulated attempt updates an engagement score E ∈ [0,100]:

E(t+1) = clamp( E(t) + boost·reward·(1 − E(t)/100) − fatigue , 0, 100 )
boost   = 22          (reward impact, larger when E is low — diminishing returns)
fatigue = decay rate, doubled on a wrong answer

Rewards also grant XP (+50 each). Level follows the classic RPG curve level = floor(sqrt(XP / 50)) + 1, so each level needs progressively more XP — the same curve used by most XP/leveling systems.

Variable ratio (slot-machine style) produces the highest, most persistent engagement and resists extinction when rewards stop — the mechanism behind streaks and loot-box design.
Fixed ratio creates a predictable post-reward dip ("why bother right after cashing in").
Fixed/variable interval schedules reward time-on-task rather than correctness, producing slower but steadier engagement.

Try dropping engagement to zero under Fixed Ratio, then switch to Variable Ratio at the same k — notice how much faster it recovers.

LEVEL UP!

Engagement core Rewarded attempt Missed attempt

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