I'm at work so I can't go into great length but you can calculate the probability of more than one consecutive identical outcome.
I'm not a mathematician (and I'm short on time) so [url=http://mathworld.wolfram.com/Run.html]here's[/url] a link to a Wolfram article on the subject.
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I got this confused with law of averages, sorry about that! you're right
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No worries. Thanks for letting me know the confusion was cleared up.