This is a search game that demonstrates Bayesian Search Theory.
This is a 2-person game. The first player hides the battleship, and the 2nd player tries to find it using Bayesian search.
Movement of the boat and plane is in 8 directions (horizontal, vertical, diagonal) or stay in place.
The center square (H8) is the base of the plane. Each square on the map will show the probability that the boat is in that location. Squares are also color-coded, with white being the highest probability, and dark blue being the lowest.
Player 1 - hide the boat: Click on "Assign the boat". Click on the center square to start moving the boat. Click on adjacent squares (8 possible directions) to move the boat, or the same square to stay there. Keep the movement hidden from Player 2! You can move the boat 10 times, then it will be hidden.
Player 2 - assign the prior: Click on "Draw the prior". Information from scouts will appear in the bottom-right of the screen. The scouts information is also noisy. To give an area higher prior probability, click on the search area and drag a circle around the region that you think has the boat. The circle corresponds to 1-standard deviation of a Gaussian (bell curve). I.e., the probability will be concentrated inside the circle region. You can draw multiple circles and the priors will add together.
Player 2 - search for the boat: Click on "Find the boat". Click on the center square to begin searching, then click adjacent squares (8 directions) to move the search plane, or the same square to search it again. After each step, the probability map will be updated. The search reliability of the plane is 80%. The plane has limited fuel for 18 steps only. Return to base (center square) to refuel the plane. If the plane runs out of fuel you lose!
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More options:
Keyboard shortcuts: You can also use the keys "yuihjknm," on the keyboard as the 9 directions to move the boat, and "a" for auto-search.
Auto-search mode: This mode provides a demo on how to move the plane based on the prior probability. After the first two steps (hide the boat and assign the prior), You can click 'Auto search' button to enter into the auto-search mode. The 'Auto search' button is then changed to 'Next step' button. Clip 'Next step' for each auto move. The plane's strategy is to move to the highest probability square within fuel range of going there and back to base. Along the way, it will choose the move based on the neighboring square with highest probability. That means the plane may move to the second or third high probability square, since the highest probability square is too far away for the plane to fly back to base to refuel. This setting makes sure that the plane will never lose.