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    <p>There is no way to guarantee a win. If bots/prizes are placed randomly, there are surely random placements that will put you too far away from prizes before the other bots get them. </p> <p>Since you know the exact behavior of the other bots, you can model all future moves they will make for a given board. You can then enumerate all possible moves as a tree, and board states, then look at the leaves and find the one that gives you a winning score. In other words, each branch is a move you make, and the node represents the board state including the move that the other bots will make. Also, this won't be a binary tree, each node will branch based on the directions you could move that turn. You will completely build this tree before you make a single actual move, so that essentially you will have the outcome of the game predicted once you choose the optimum path. This is possible only because the other bots move in a predictable manner.</p> <p>Also as you move, you can add checks to ensure the other bots are moving as you predicted, just as a debugging feature. Depending on how the system operates, they may see your move before they decide their move, depending on if everyone moves simultaneously, or one at a time. Either way it can be done, you just have to make sure your model of how they move is accurate.</p> <p>Note that there might be other leaves where you have a larger score but lose because one of the other bots dominated the other. I.e. (you:12, a:1, b:17) vs. (you:11, a:10, b:9)</p> <p>The paths that will probably succeed the most are the ones that exploit the behavior of the other bots, for example, grabbing the highest prize when it is closer to you, causing the greedy bot to loose moves going towards it. And also sidetracking for prizes on the way if you have enough moves to do so. You won't have to code for this behavior though, because when you create the tree and find the optimum series of moves, you it will occur implicitly.</p>
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    1. POAlgorithm to beat bots moving towards prizes predictably
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    1. COIt sounds like, aside from who gets the prize first, the bots don't actually affect each other. So rather than enumerating every possible move you only need to enumerate the different choices of which prize to go for next. This will *drastically* reduce the size of the search-tree - there's only 9! = 362880 different outcomes to examine, which can be cut down even further by pruning the search-space (stop searching a sub-tree when you are guaranteed to have won or lost)
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      1. USBlueRaja - Danny Pflughoeft
    2. CO@BlueRaja-DannyPflughoeft If you don't consider the other bots moves then you will plan a course that will involve moving to squares where there once was a prize but is snatched up by another bot before you. The fact that they move in a predictable manner I think is the key to winning. You could still reduce the search tree by stopping at subtrees where you are in an unwinnable position, I.e. your the diff between you and highest scorer is greater than amount of prizes left on the board.
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    3. COThe search tree would have to be recreated and analyzed after every single move to take into account prizes that are picked up by other bots. Instead of creating the whole tree every time, I'm thinking it would be better to only generate a partial tree to take this into account.
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