Try talking to the person and be polite. Explain that the casino is crowded and you would like to use one of their 3 machines. If they're polite, there shouldn't be a problem.
Of course, if they were polite, they wouldn't be taking up 3 machines in the first place.

Your most realistic alternative is to inform a casino employee and have them go over and talk to the offender. This will get you an empty slot, but you'll also have to sit next to the person (who will probably make ugly comments and give you dirty looks for the rest of the evening).

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"I am in so far in blood, that sin will pluck on sin" - Richard III