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    <p>Nice question, and I like your idea for statistical approach. <br>I think I would have tried a <a href="http://en.wikipedia.org/wiki/Supervised_learning" rel="nofollow">machine learning</a> approach for this problem as follows:</p> <p>First model your problem as a <a href="http://en.wikipedia.org/wiki/Statistical_classification" rel="nofollow">classification problem</a>. <br>The classification problem is: Given a square <code>(x,y)</code> - you want to tell the likelihood of having a ship in this square. Let this likelihood be <code>p</code>.</p> <p>Next, you need to develop some 'features'. You can take the surrounding of <code>(x,y)</code> [as you might have partial knowledge on it] as your features.</p> <p>For example, the features of the middle of the following mini-board (+ indicates the square you want to determine if there is a ship or not in):</p> <pre><code>OO* O+* ?O? </code></pre> <p>can be something like:</p> <pre><code>f1 = (0,0) = false f2 = (0,1) = false f3 = (0,2) = true f4 = (1,0) = false **note skipping (1,1) f5 = (1,2) = true f6 = (2,0) = unknown f7 = (2,1) = false f8 = (2,2) = unknown </code></pre> <p>I'd implement features relative to the point of origin (in this case - <code>(1,1)</code>) and not as absolute location on board (so the square up to <code>(3,3)</code> will also be f2).</p> <p>Now, create a training set. The training set is a 'labeled' set of features - based on some real boards. You can create it manually (create a lot of boards), automatically by a random generator of placements, or by some other data you can gather.</p> <p>Feed the training set to a learning algorithm. The algorithm should be able to handle 'unknowns' and be able to give probability of "true" and not only a boolean answer. I think a variation of <a href="https://en.wikipedia.org/wiki/Naive_Bayes_classifier" rel="nofollow">Naive Bayes</a> can fit well here.</p> <p>After you have got a classifier - exploit it with your AI. <br>When it's your turn, choose to fire upon a square which has the maximal value of <code>p</code>. At first, the shots will be kinda random - but with more shots you fire, you will have more information on the board, and the AI will exploit it for better predictions.</p> <hr> <p>Note that I gave features based on a square of size 1. You can of course choose any <code>k</code> and find features on this bigger square - it will give you more features, but each might be less informative. There is no rule of thumb which will be better - and it should be tested.</p>
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