RP5 "randomizer"

[kem]

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Seems like the chance of getting the exact same cards (suits included) are about 1/2652. So if you have 10 people sitting at a table that's 1/265 that someone at the table gets the exact same cards twice in a row. Now figure that a site like Party is dealing about...1500 games a minute? Depends on when you are playing. That means on average about 6 people should get the exact same hand they just had per minute.

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Actually it's more like 2/2652, since it was never stipulated to that you had to be dealt the same cards in the same order. For instance, if you had A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/heart.gif[/img] in hand 1, there's a 1/2652 chance you're dealt A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/heart.gif[/img] and a 1/2652 chance you're dealt K[img]/images/graemlins/heart.gif[/img]A[img]/images/graemlins/heart.gif[/img] in the next hand. 2/2652 is 1/1326.. 1326 is commonly referenced as the number of different starting hands in Hold 'Em, which is basically what this question boils down to. So if you've played more than 1,326 hands in your life, odds are that you have been dealt the same exact hand twice in a row [img]/images/graemlins/smile.gif[/img]

And calculating these odds for the entire table at once is not so simple. Hands are not independent -- if Player 1 is dealt the same hand twice in a row, everyone else has a slightly greater chance of being dealt the same hand as well, as compared to the case where Player 1 is dealt a different starting hand. To see this even more clearly, if the first 9 players are dealt the same hand as their last one, then our 10th player still has his 2 cards left now (his 2 cards from the previous hand) in a deck of 34 cards (52-2*9). Clearly his odds are greater of randomly receiving the same hand that he had last time. If everyone at the table had a different starting hand than they had previously, then our 10th player's 2 cards might already be dealt out hence lowering his odds of getting a repeat hand. I don't think it's necessarily a hard calculation, but much grungier than I'm willing to do at the moment [img]/images/graemlins/smile.gif[/img]

[John Feeney]

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That's randomness for ya. It can be pretty... uh... random.

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That sums it up.

In Inside the Poker Mind I included an essay related to this called (IIRC) "On Randomness, Rushes, Hot Seats, and Bad luck Dealers." I don't recall, though, if I mentioned that a long sequence lacking these sorts of "odd" instances would not, in fact, be random, now would it?