Submarine Hunt

A submarine is hiding somewhere, and it moves every turn. Ping it with sonar, then sink it before it slips away.

How to play

A submarine hides on the 10×10 grid. Every turn it stays put or moves one square north, south, east or west.
Choose Sonar ping, then tap a square: you learn roughly how far the sub is from it, give or take about 1.2 squares.
Choose Depth charge and tap a square to attack it. Hit the sub's square to win. You have 3 charges and 24 turns.
The heat map shows where the sub probably is now; the gold ring is the best square for a depth charge.

Playing with a class? Tap Join a class room and enter the code you were given, and your games go on the class leaderboard.

Turn 1

One turn of the Bayes filter

Priorwhere it could be

× Likelihoodof what you observed

= Posteriorafter your observation

→ It movesthe prior for next turn

Turns left

Depth charges

Chance it is in the likeliest square

How big is the search area?

Squares you would need to search to be 90% sure of covering the sub. Each observation shrinks it; each move spreads it again.

After it moves After you observe

turn

Predict, then update

The sub starts anywhere, and every turn it holds still or moves one square north, south, east or west.

Update: a sonar ping from a square reports the distance to the sub, give or take about 1.2 squares, so the likelihood is a ring around the ping. A depth charge that misses rules out one square. Predict: then the sub moves, so the belief blurs outwards. The heat map is the result: exact, square by square.

This loop is a Bayes filter. GPS, radar tracking and Kalman filters all run it.