What are the odds of drawing 7 cards that end up sequential - from a 52 card deck? (7 card poker straight) While playing a friendly game of Texas Hold'em poker, a player drew a 7 card straight. 
Although in texas hold'em a player may only use 5 of the possible 7 cards, the discussion about odds immediately came up. What are the odds of getting a 7 card straight?
For those unfamiliar with poker, the question can be asked this way: What are the odds of drawing 7 cards from a 52 card deck, with those cards ending up sequential? *
I tried searching the vast knowledge of the internet, but was unable to come up with an answer. the closest i get is the probability of drawing a 5 card straight in a 5 card stud game (0.00392465), but i got lost trying to add the probability of the next 2 cards - due to the complexity of the straight (the next 2 cards can complete the straight - if the first 5 cards drew 4.5.7.8.9 and the next 2 cards were 6.10).
Any help or pointers on this subject would be extremely helpful. calculating a straight  
*) An Ace card can be used to start a low straight or to complete a high straight - both A.2.3.4.5.6.7 and 8.9.10.J.Q.K.A are legal. but it cannot be used to wrap - J.Q.K.A.2.3.4 is not legal.
 A: In short, the probability of a 7-card straight when drawing 7 random cards from a standard deck of 52 is $0.000979$.
To calculate this value, we note that all 7-card hands are equally likely, of which there are ${52 \choose 7} = 133,784,560$ possibilities.
Next, we compute the number of 7-card straights. Ignoring suit, we note that there are $8$ possible straights (starting with {A, 2, 3, 4, 5, 6, 7} through {8, 9, 10, J, Q, K, A}). For each card in the straight, there are 4 possibilities for the suit, such that there are $4^7 = 16384$ ways to assign the suits to the 7 cards. However, $4$ of these suit assignments yield straight flushes (all clubs, all diamonds, etc.), so the actual number of suit assignments that can yield a straight (but not a straight flush) is $16384 - 4 = 16380$.
Putting all this together, there are $8 \times 16380 = 131,040$ possible 7-card straights out of $133,784,560$ possible 7-card hands, yielding a probability of $\approx 0.000979$.
A: Hao Ye has not quite got it. Each one of those 131,040 possible 7-card straights can be ordered $7!=5040$ ways, only one of which is the cardinal ordering from least to greatest. So the probability of observing a sequential 7-card straight is much lower: $1.94*10^{-7}$.
A: Here is a little different approach for those of us who prefer to make the computer work hard instead of making ourselves think hard.  I wrote the following R function to simulate a single draw and check if it is a straight:
straightsim <- function(ncards) {
    hand <- sample( rep(1:13, 4), ncards )
    hand <- sort(hand)
    hand2 <- hand - hand[1]
    straight <- 0
    if( all( hand2 == 0:(ncards-1) ) || all( hand2 == c(0, (14-ncards):12) ) ) {
        straight <- 1
#       print(hand)
    }
    straight
}

This ignores the suits, so does not distinguish a straight flush from a regular straight (will slightly over estimate the probabilities if you want straights that are not flushes as well).
When I ran it 1 million times (1,000,000) on my laptop it found 978 straights for an estimate of 0.000978 (surprisingly close to Hao's answer).  When I ran it for 50 million (50,000,000) times on a 100 core cluster it found 48,965 straights for an estimated probability of 0.0009793 (approximate 95% confidence interval: 0.0009707 - 0.0009880).
