In Texas Hold em, what is the probability of the guy to your left having only one card in common with you?

Question

For example, you hold two aces as hole cards. What is the probability that the guy to your left has one ace and some other card?

Working it out mathematically suggests the probability is around 7.8% of the time. However, simulating 1 million possible hands on the computer suggests ~.5% of the time. The program's probability calculations are dead on for many other scenarios.

Answer 1

When math says one thing (and actually your calculation there is correct) and a simulation says something different like this then there's an error in the program.

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