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When stupidity leads to an advantage...

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Mithrandir

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I'm reminded often that sometimes doing completely stupid things can often work to your advantage.


For example, in the 1991 Gulf War, Iraq had modified their SCUD's so that they were a lot less reliable, in a half-assed attempt to make them have a longer range.

The effect that this had was that the missiles would often break up when they re-entered the atmosphere, leading to an incredible loss of accuracy. The warheads were almost always still intact and still on the general trajectory, but they lost all maneuvering capability.


But at the same time, this break up actually came to the Iraqi's benefit, as the Patriot missiles launched to intercept the SCUD's found it virtually impossible to actually hit the warhead, since now there were many targets, rather than the expected 1, and almost never hit the actual warhead.



Today I encountered this phenomenon again. I have been trying to figure out a strategy to win "Hexcite", a game where you place tangram-like game pieces on a triangle grid. For each side you place that is adjacent to the board edge or another existing piece, you get 10 points. For filling in the last triangle of one of the 6 triangular sectors on the game board, you are awarded an additional 10 or 30 points, depending on the sector (dark sectors are 30, light are 10). For every piece you do not place at the end of a round, you are penalized 10 points times the number of sides on each piece left unplaced. And finally, whenever you place a new piece, every side must be completely adjacent to a wall, another piece, or nothing; you cannot place a piece where half of one side is adjacent to a piece, and half adjacent to nothing.


I've been addicted to this game for a while, but I've never been successful on the hardest difficulty level. Today, I had an epiphany. I assumed that they used a min-max algorithm for the AI (since almost all games do this).

The basic premise of a min-max algorithm is that it computes a game tree for X levels. "low-level" AI's will probably only look at the next move. The more levels it looks down, the more difficult the AI will be. Unfortunately, each level takes an exponentially larger amount of processing time to complete as well. Once it has computed this game tree, it will traverse down a "min-max" path; it assumes that the player will move to maximize his own score, and minimize the AI's score. So it will pick the path that will limit the player's beneficial moves the most.


Basically, it assumes that the human player will think about his moves, and act accordingly, and ignore the paths that the player won't pick because they're dumb.



I, am happy to announce, that I beat the highest-level difficulty in Hexcite by being a total retard. I've found that the min-max algorithm falls apart if you act stupid at the beginning, because the AI never bothered searching down those paths where the player makes stupid moves; and many times, those paths have a lot of beneficial moves available to the player.


So I start off the game by making the dumbest move I could possibly make, and then going from there. So far, I've got an 84% win rate using this tactic.
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Many people consider things like this to be "cheating".

I don't.

I prefer to call it "The Captain Kirk method of Winning".

You don't beat the game, you beat the mechanism that controls the game :)




I'm interested in seeing how well this works in other games. Deep Blue used min-max trees too, if I remember correctly...

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I've read that chess masters often used tactics similar to this against computer opponents too. Usually it was a move to sacrifice a piece to gain a better position. Since most heuristics weigh the number of pieces a lot higher than the territory you control, the min-max algorithm wouldn't consider plays where you sacrifice a knight in order to totally screw up your opponents defensive structure and gain control of the centre of the board.

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