Kyle M. answered 09/15/15
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Similar to your poker problem, you represent each desired die roll as a fraction, then multiply those fractions.
A six-sided die has a 1/6 probability of rolling any particular number. The probability of rolling the same number twice is therefore 1/6 x 1/6. Try it - you should get 1/36 or 0.0555 - less than 6% chance.