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DISCOVERY 05 · A LITTLE PLAY, A LITTLE PROBABILITY

Silent Water.

You saw it there. Where is it now?

READY TO DIVE02:30

HIDE. WATCH. ANTICIPATE.

One ocean.
Five chances.

Steer with the arrows.
Click or tap a glimpse to launch.

One hit wins. Both sides have five torpedoes.
YouLast sightingFilter estimate

An ocean of uncertainty. Inspired by radar tracking; designed for play.

A QUICK BRIEFING

Hide-and-seek.
With five torpedoes.

  1. Steer. Use the arrow keys (or WASD) on a computer, or the on-screen arrows on a phone. Up points north, right points east, and so on. Your sub turns by the shorter route and keeps moving on that course. The center button or Shift stops and resumes movement.
  2. Watch. The line circles every six seconds. Objects light up as it passes; those sightings stay put and fade.
  3. Aim and launch. Move your mouse over the radar to place the crosshair, then click to fire. On a phone, tap the radar to launch toward that point. Space and Launch also fire toward the current crosshair (straight ahead until you set an aim). Steering and aiming are independent: either submarine can fire in any direction without turning.
  4. Dodge. Nearby incoming torpedoes trigger frequent detections, giving you a chance to turn.

One hit wins. Five torpedoes each. If both run out after their torpedoes expire, or 2½ minutes pass, it’s a draw. The opponent has its own sweep and tracker, and cannot see your hidden position.

A GUESS THAT LEARNS

Predict. Observe.
Correct.

A radar contact is an imperfect sighting from the sweep. It stays where it was detected.

The red ghost estimates where that object is now. After several sightings, the filter learns a direction and speed, and keeps predicting between observations.

The red ellipse represents uncertainty. It generally expands while waiting, then contracts with another sighting. Unexpected turns can put the real submarine outside it.

Velocity predicts continued velocity with random acceleration noise. Velocity + acceleration also estimates acceleration and predicts it will continue, with random changes allowed. Both are linear Kalman filters, fitted to exactly the same sightings. Extra flexibility may help with sustained acceleration or overshoot after a turn. Torpedoes always use Velocity. The ellipse is a nominal 95% region under its model, not a guarantee for a maneuvering submarine. A first sighting gives position, but little knowledge of velocity.

Both models run from the first sighting, even when the overlay is off. Switch models during play or a paused replay to compare the same moment. The opponent always uses Velocity for its decisions; its acceleration overlay is a comparison of what the other model would have estimated. Selecting an opponent shot shows its Velocity estimate.