GBITS — Learn Bayesian Probability Through Adventure, by Z. Press any key or click to continue.

Dad Is Missing

Three days now — the search begins

Papa Joe — Grandfather (tap to hear)

Kaylee. Your father went out to hunt for food three days ago, and he hasn't come home. I know you're frightened — so am I. But we won't find him by running in circles out there. We're going to think our way to him, the way I taught you.

Kaylee — inner voice

Dad... where are you? I'm going to find you. I promise.

The Bayesian Rhyme

Papa Joe teaches. Kaylee remembers. Dad is waiting.

Papa Joe — Grandfather (tap to hear)

This is GBITS, Kaylee — it stands for Game Based Interactive Tutorial Systems. It's how I taught you to think, and now we'll use it for real: the same clear thinking will help us find your father and bring him home. You remember the Rhyme I taught you when you were little? Time to use it. Listen close.

Papa Joe — Grandfather What if you lost a favorite book, or a toy? You know you only spend your time in three rooms — the living room, the dining room, or your bedroom. To use Bayes, you start where you most likely left it, then check where you'd most easily spot it. Watch — it is the very same thinking we will use to find your father.

A Story · The Lost Book

Three rooms. One lost book. Press play and we will find it the way Papa Joe taught.

Kaylee's Bedroom

33%

chance

Living Room

33%

chance

Dining Room

33%

chance

Papa Joe — Grandfather That is the whole secret, Kaylee: list the places, weigh them by what you remember, search the most likely first — and when it is not there, think again and move to the next. Now — we apply the same process to finding Dad.

The Bayesian Rhyme

Press a button to hear the Rhyme

Papa Joe — Teaching the Rhyme

Something is lost. Where might it be?
Is each place an equally likely hiding place for what I seek?
Or, is one place more likely than another? Let me think.

If each place has the same chance — the percent is the same for each, adding up to one hundred percent.
If any place is more likely than another, we count by how much more or less.

Then I think about where I was when I last saw it.
Remembering, I decide what is likely or less likely.
Not every place is equally easy to explore. I might miss what is hiding there.

Now that I have taught you the rhyme, let me review the steps again. But this time, I want you to know what each of the steps is formally called in Bayes.

Step 1

List all the places Dad may be. The list of places are called Priors.

Step 2

Guess how likely Dad is in each zone. These guesses are called Likelihoods.

Step 3

Multiply Prior times Likelihood. The results are called Posteriors.

Step 4

How likely you would miss Dad even if he is there. This is called the Detection Rate.

Step 5

Probability of finding equals chance he is there times detection rate. This is called Expected Findability.

Step 6

Search the highest probability zone first. Found him? You win!

Step 7

Not found? Update Bayes. Search the new highest zone.

Step 8

Keep going until Dad is found. The End.

Kaylee — reciting to herself

Something is lost... where might it be?
I was little when Papa Joe first taught me this. My favorite book was gone.
He made it rhyme so I would remember. I still do.

Dad — in Kaylee's memory

"You got this, kiddo. Just think it through. One step at a time."

Kaylee — continuing

If each place has the same chance — every percent adds up to one hundred.
If one place is more likely, count by how much more.
Think about where you last saw it. Use that memory.

Dad — in Kaylee's memory

"Do not rush it. The best guess is not always the obvious one. Trust the process."

Kaylee — the steps

Step one — list the places. Priors.
Step two — how likely each one? Likelihoods.
Step three — multiply them. Posteriors.
Step four — how likely I would miss him even if he is there. Detection.
Step five — what is the real chance of finding him. Findability.
Step six — search the highest first. Always.
Step seven — missed? Update. Move to the new highest.
Step eight — keep going. Do not stop. Bring him home.

Dad — in Kaylee's memory

"I will always be here, Kaylee. You just gotta find me."

Zone	Prior	× Detection	= Find Chance
Forest	20%	50%	10%
River	20%	80%	16%
Mountains	20%	50%	10%
Cave	20%	60%	12%
Plains	20%	80%	16%

🎙 Narrator On

Find Dad

5 zones · Each starts at 20% · Search the highest Find Chance (Prior × Detection) first

Decision Score

0

Daylight

10

Best Zone

—

$Papa Joe$

Papa Joe (tap to hear)

Choose carefully, Kaylee. Every zone is equally likely to be hiding Dad — 20% each, no clues yet. But some places are far easier to search than others. So your Find Chance — the chance you actually spot him this trip — is higher in open ground like the River and Plains than in thick brush or rock like the Forest and Mountains. Find Chance = how likely he is here × how well you can search it. Search the highest Find Chance first.

searched not yet searched Dad could be found

Every zone is equally likely to be hiding Dad — 20% to start. The Find Chance % differs because some places are easier to search: it is that 20% × how well you can see into the terrain. Search the highest Find Chance first; the green % marks the Highest Zone — or “Equally High Zones” when two are tied. On the map below, each square is a spot — gold = already searched, dark = not yet searched. Re-search a location to cover its dark spots.

Field Report

Zone	Prior %	Detect Rate	Miss Rate (1−Detect)	P×Miss (unnorm.)	New Prior % (normalized)	Status
Search a zone to see the Bayesian calculation update in real time

WE WON! WE WON!

Kaylee

We won! We won! Use of the Bayesian probability helped us find Dad! WE WON! WE WON!

Your Result

Speaking Bayesian — Bonus Round

Match each game concept to its Bayesian term:

🌑

NIGHT FELL

Your Result

The Bayesian Trials

Five levels — climb from doing the process to mastering the equation.

Level 2 · Speak Bayesian

Score 0Time 90s

Tap a term, then tap its meaning.

Level 3 · Read the Equation

Score 0Time 120s

Phase 1 of 2

P(H|E)=P(E|H)·P(H)P(E)

H = “Dad is in this zone” · E = the search result

Match each game label to its Bayesian symbol.

Level 4 · Fill the Blank

Score 0Time 75s

Tap a tile, then tap the blank where it belongs. Build Bayes’ Theorem.

▢=▢·▢▢

Tiles: P(H|E) posterior · P(E|H) likelihood · P(H) prior · P(E) evidence

Level 5 · Master the Scenario

Score 0Time 150s