What are the odds of getting a straight flush while holding 2 (straight flush) cards and flopping all 5?

Question

...community cards?

Ex. Being dealt a 7d, 6d
and then drawing 5d, 4c, 4d, 2s, 8d getting a
8d, 7d, 6d, 5d, 4d
straight flush...
what are the odds of getting any straight flush as in this situation?

Answer 1

yes, it depends, but I can give you a formula for figuring it. May be a bit confusing...

First consider a case where you would flip all 5 cards,
regardless of the 2 cards you started with.

There are 52C7 ways to deal 7 cards from a 52 card deck. (nCp = n!/(p!(n-p!))

That is, 52!/(7!45!) = 133,784,560.

there are 10 possible straight flushes per suit, assuming the ace counts in two different flushes, for a total of 40.
For each of these, in a 7 card hand, there are 47C2 possiblilites
for the other 2 cards. 47C2 = 1081
giving a total of 4 * 1081 = 4324 straight flush 7-card hands.

Thus the probability of being dealt a straight flush out of any 7 cards is
4324/133,784,560 = .00003232 or about 3.2 in 100,000. (not good but better than for a 5 card hand)

In your case two of the flush cards are in the first 2 cards dealt. Knowing you've got 2 potentials will increase your odds but it does depend on how many straight flushes the 2 cards can be a part of.

If you've got for instance 4d, 5d, you could get ad, 2d, 3d, or 2d,3d,6d, or 3d,6d,7d, or 7d,8d,9d. That's 4 different ways the
next 5 cards could give you a straight flush.

There are 50C5 = 2,118,782 possiblities for the next 5 cards. for each of those winning combos above, there are 1 * 47C2 = 1081 cominations of the three winners with 2 other cards from the deck. so the odds in that scenario are
4 *1081/2,118,780 = .0020 or about 1 in 500. MUCH better odds than a stud hand.

In general, use

(Number of potential straight flushes) * 1081/2,118,780. = your odds of getting a straight flush.



(btw don't be alarmed by the recurrence of the number 1081 it is simply that the number of ways to pick 2 cards from 47 applied twice)

Answer 2

Boaz, you are an idiot. This is a question on probability, not some religious morality question.

The answer, unfortunately, depends on what cards you hold - eg with 8D and 4D you are less likely to get a SF than with an 8D and a 9D.

In the former, you have to get three specific cards (5D,6D,7D). In the latter, there are several possible combinations. So the question needs to be more specific.

Answer 3

Winning hands in order from lowest to highest Pair Two pairs Three of a kind Straight Flush Full house Four of a kind Straight flush Royal straight flush

Answer 4

Since you do no know who has which cards and which cards the dealer has, unless you are playing cards with your family for fun, leave gambling alone. The odds are stacked always in favour of the house. There are millions of things you do not know that can ruin your life, the life of your family, your finances etc: Ask Mike Jordan if you do not believe me.

Boaz.

Answer 5

odds of a straght flush are 1 in 72193.33