Probability question

[WiSeIVIaN]

What are the chances of two seperate hands having identical flop, turns, and rivers (same cards and suits) and also having two players dealt the exact same hole cards (same cards and suits).

This is not a hypathetical question since appearently this happened at mansion poker (AA and 10-10 being the dealth hands).

Thank you guys.

[bigpooch]

Well, if this happened at a poker site, it is very likely
that a predealt deck was used more than once. It would also
be useful to know the relative seating of the two hands and
the EXACT order those cards came on the FLOP. If the cards
also came on the flop in the same order, then I would NOT
doubt that indeed the site was using predealt decks and
somehow the same deck was dealt out more than once
(something that should never happen at the real money
tables). [I'm assuming that the flop cards are not in any
way "ordered" according to some rules, but just come out in
any order.]

Some poker sites claim that external inputs do influence
the turn card and river cards, and although it is not hard
to program this in, it's much easier to have the turn and
river card "predetermined" but known only by the server.

In any case, the probability that simply the flops are
identical on two deals is 1/C(52,3)= 1/22100. Then, for the
turn cards to be identical and the river cards to be
identical, the factors to be multiplied are (1/49)*(1/48)
and so the chances are 1/51 979 200.

For two of the players having the same hole cards, the
chances depend on the number of players dealt in. If it is
heads up, then the factor is (2/C(47,2))*(1/C(45,2)) or
1/535 095. Even when ten-handed, the factor is C(10,2)=45
times less and the odds would be about 618 billion to one
against for the identical flop, turn and river and the two
competing hands held the same cards (with all the suits
being relevant).

In any case, even in a ring game, the likelihood is less
than one in a trillion if you had another piece of evidence:
the EXACT order of cards on the FLOP, since the order being
the same is just a factor of 6.

There isn't much doubt that the same predealt deck was used
on the same hand.

[SamIAm]

Come on, man. On my screen, this thread is 4th from the top of this very forum.
-Sam

[WiSeIVIaN]

The flop came in the exact same order in both hands...

Thx.

[Shroomy]

[ QUOTE ]

There isn't much doubt that the same predealt deck was used
on the same hand.

[/ QUOTE ]


we are not talking about two hands picked at random. How about trying to compute how often this would happen if we deal 100 million + hands per day

[bigpooch]

Well, first of all, it's at Mansion Poker and secondly, I
don't think they have even close to that many hands dealt
per day. Just look at the order of magnitude: EVEN IF it's
over 100 million hands, this would happen less than 1 in
10,000 times! It could have been a total fluke, but it's
extremely unlikely. If you have any doubts, why would you
believe ANYTHING at all? [img]/images/graemlins/smile.gif[/img]