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

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1 Answer 1

up vote 4 down vote accepted

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%
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stupid mistake by me :) you are correct –  RayofCommand Jun 20 at 12:50
    
This is correct if we are only considering a straight flush of 65432. Once you factor in the one card straight flushes (one from our hand, four on the board) such as T9876, 98765, 87654, and 76543, it's clear that we can't just calculate the probability of hitting one specific flop. We need to figure out the combined probability of hitting one of these five flops. I don't know how to calculate this, hence my question. –  Brent Morrow Jun 20 at 21:44
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Brent, regarding your edit, you can not "flop" any of those other hands, because there are only three cards on the flop and you need four community cards to make a straight flush that way. Are you wanting to know you odds of making a straight flush by the river with those hole cards? –  lnafziger Jun 21 at 4:46
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Yes, I apologize. I should have listed that as a separate question. I'll accept this answer for now since it answers what was originally asked. –  Brent Morrow Jun 21 at 19:26
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Wow, thanks for the updated answer. Really great info. –  Brent Morrow Jul 10 at 23:43
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