Odds of being deal same hand twice

[Gebre]

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Ok, so I know the odds of being dealt any specific 5 card hand is 1 in 2,598,960. And I know that if you get about 30 people in a room it's likely that 2 share a birthday. So it got me thinking - how many hands do you need to be dealt to get the same hand twice in that session. So, it doesn't matter which hand gets repeated, and it doesn't matter if it's hand 4 and 546 that match. A bet a friend that it's probably likely that you get the same 5 card hand at least 2 times a year and he didn't believe me.

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Like the birthday problem, it takes a surprisingly few number of hands before it is likely that a hand will repeat. The probability that at least one hand repeats in n trials is

1 - (2598959/2598960 * 2598958/2598960 * ... * (2598960-n-1)/2598960)

This probability becomes greater than 50% for n = 1899.

This probability becomes greater than 75% for n = 2685.

This probability becomes greater than 90% for n = 3460.

This probability becomes greater than 99% for n = 4892.