What are the odds of flopping a straight flush with 62s?

Question

I've been wondering what the odds are of flopping a straight flush with 62s.

Answer 1

You need to calculate the odds of getting the exact flop that you need.

Since the order doesn't matter, the first card dealt would have three possibilities, and then if you got one of those you would have two possibilities on the second card, etc.

It would look like this:

3/50 * 2/49 * 1/48 = 1/19,600 = 0.005%

---

EDIT

Updated based on your comment/updated question to show how to calculate the odds for any straight flush by the river when starting with 62s:

Odds of making a straight flush using only one hole card:

4/50 * 3/49 * 2/48 * 1/47 = 1/230,300 +
4/50 * 3/49 * 2/48 * 1/46 = 1/225,400 +
4/50 * 3/49 * 2/47 * 1/46 = 1/220,704 +
4/50 * 3/48 * 2/47 * 1/46 = 1/216,200 +
4/49 * 3/48 * 2/47 * 1/46 = 1/211,876 
                          = 1/14,839

Since you have four different straight flush possibilities using only one of your hole cards (T9876, 98765, 87654, & 76543), that increases the chances of making a 4 card straight flush to:

                          =  1/3,710

Odds of making a straight flush using both hole cards:

3/50 * 2/49 * 1/48 = 1/19,600 +
3/50 * 2/49 * 1/47 = 1/19,192 +
3/50 * 2/49 * 1/46 = 1/18,783 +
3/50 * 2/48 * 1/47 = 1/18,800 +
3/50 * 2/48 * 1/46 = 1/18,400 +
3/49 * 2/48 * 1/47 = 1/18,424 +
3/49 * 2/48 * 1/46 = 1/18,032 +
3/48 * 2/47 * 1/46 = 1/17,296 +
                   = 1/2,318

Add the two possibilities to get your answer:

Straight Flush with 1 card:    1/3,710 +
Straight Flush with 2 cards:   1/2,318
Any Straight Flush           = 1/1,427
                             = 0.07%

Answer 2

Out of possible 19,600 flops, which is C(50,3), you can only have 1 to flop the Straight Flush, that is 3,4,5 of your holecards' suit. Thus the probability of flopping SF with 62s is 1/19600.