KAKURAKU

KAKURAKU is an interactive educational app for experiencing probability paradoxes through hands-on simulation.

The 10th installment in the SUUGAKU / BUTURAKU / DENRAKU / HARAKU / NETURAKU / KORAKU / RYURAKU series. The theme is "probability." Experience 12 famous probability paradoxes through four interactive phases.

[4 Phases for Deep Understanding]

1. Intuition Quiz

Answer with your gut feeling first. Most people get it wrong.

2. Simulation

Run hundreds of trials and see the results with your own eyes.

3. Explanation

Why does intuition fail? Mathematical explanations bring that "aha" moment.

4. Comprehension Check

Test your true understanding with applied questions.

[12 Probability Paradoxes]

1. The Door Trap — Monty Hall Problem (switching wins 2/3 of the time?)

2. Miracle Classroom — Birthday Paradox (50%+ chance with just 23 people?)

3. The Gold Box — Bertrand's Box (your 1/2 intuition is wrong?)

4. Reversal Statistics — Simpson's Paradox (parts and whole tell opposite stories?)

5. Envelope Dilemma — Two Envelope Problem (should you always switch?)

6. Test Trap — False Positive Problem (positive result yet only 16% infected?)

7. Sleeping Princess — Sleeping Beauty Problem (1/2 or 1/3? Still unsolved)

8. Endless Bus — Bus Waiting Paradox (average 5 min but you wait 10?)

9. Red Streak — Gambler's Fallacy (black is "due" next?)

10. Infinite Gamble — St. Petersburg Paradox (infinite expected value?)

11. Warden's Verdict — Three Prisoners Problem (does A's fate change?)

12. The Predictor's Boxes — Newcomb's Paradox (one-box or two-box?)

[Features]

- Interactive simulations — see it to believe it

- Run single trials, 100x batches, or 1000x batches to watch probabilities converge

- Live formulas and numerical values

- Dark mode / Light mode

- Japanese / English support

- Works offline (network is used only for ad delivery)

[Monetization & Ads]

- This app is free to download and use

- No in-app purchases, no subscriptions, no paid unlocks

- A banner ad (Google AdMob) is shown at the bottom of the screen

- An interstitial ad may be shown when you clear a stage

- On iOS, personalized ads are only delivered after the user grants App Tracking Transparency (ATT) permission

[Recommended For]

- Students studying probability and statistics

- Anyone curious about the gap between intuition and mathematics

- Teachers looking for interactive teaching materials

- Anyone who wants to truly internalize "why is it that way?"