[Siegmund]

I make the number of distinct deals (suits matter) as 1.2x10^36 ~ 52!/(27! 2^10 * 6). Each of these, however, can have a very large number of betting sequences laid on top of it.

The expected number of trials to get every member of a set at least once is about N ln N -- so, we need time to deal about 10^38 hands before we have a good chance of having hit every one of them (even if the betting went differently!)

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But since each event in isolation seems likely to have occurred in the past,


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A simple failure of intuition. The biggest internet sites have dealt only a few billion hands in their lives; the internet sites and live games combined will be a few tens of billions of hands that have ever been dealt. This means that the chance of any given full deal having ever been dealt before anywhere is less than 10^-25.
That in turn means that the expected time until we see our FIRST duplicate hand is more than 10^12... in other words, most of us will live our WHOLE LIVES without EVER playing a single full-table deal that has ever been played before by anyone else.