My question is this: When two players are delt ten cards each from a
standard 52 card deck, what is the average number of groups and
sequences that a player will form?

A "sequence" is defined as three or more cards of the same suit in
consecutive order (for example, a four of clubs, a five of clubs, and
a 6 of clubs).

A "group" is defined as three or four cards of the same rank (for
example, three sevens of any suit).

The answer should include the probability rules, calculations, and an
explanation of the logic used to reach the conclusion. This is really
the most important part.

Jon

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Request for Question Clarification by hedgie-ga on 28 Nov 2005 20:23 PST

With replacement  (1) or without (2) or conditional (3)  

Meaning:
case 1 is really one question repeted twice:
 After you deal 10 cards to player 1, you put them back
         shifle and deal 10 cards to the second.
 

 case 2: You deal 20 cards from the deck
            and ask for probablity that first 10 has  ...
             AND the second 10 has ..

definition of sequence is also ambiquous:
 A four of clubs implies two sequences of three
  Do you count 4 in a row as  one or three sequences?

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Clarification of Question by jonmali-ga on 28 Nov 2005 22:29 PST

I'm asking for case 2 -- each player is delt ten cards as in player 1
receives one card, then player 2 receives one card, then player 1
receives his second card, then player 2 receives his second card, etc,
up to 10 cards each.

I see what you mean about the sequence concept. I overlooked the fact
that a sequence can be a variable number of cards, and thus it throws
a wrench into things. A sequence can technically cover every single
card in the hand of a player, and that would only count as one
sequence by definition.

What I'm really looking for, then, is the average number of cards
which fall into a group or sequence when the two players are delt ten
cards as described above, not the average number of sequences and
groups themselves.

Also, a card used in a sequence cannot be used in a group.

Thanks,
Jon