A slightly different question is what is the number of people required to have a greater than 50% chance of two sharing the same birthday? I think the answer to this question is 22.
Your question of "On average, how large a group is required for two people to have the same birthday?". Has a slightly anal answer of 367! That is the only way to guarantee two share the same birthday based on there being 366 days in the longest year (leap years must be included as people can be born on the 28th Feb) and an extra person to share the birthday.
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