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Computer Descisions

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I was just wondering, how does a computer make a decision where two lines have preceisely te same outcome in preceisely the same amount of moves? E.g:

If I can get a computer to this position (obviously with me as black!), will it start spouting acrid smoke and mumbling 'Does not compute...! Does not compute...!' before deeming mankind to be a grave threat and deciding on our instant extermination? How does it choose?