Probability of flopping a draw with suited connectors

[KjellBarry]

Lets say you have 67s. What are the odds of you getting EITHER a Flushdraw, open-ended straight draw, two pair OR trips on the flop.

I know the chances of flopping a flush-draw is 7.3-1 (11.79%)
flopping open-ended straight is 9-1 (10.29%)
two pair is 3.47%
and trips 1.45%.

So if anyone could give me a % or the odds of flopping EITHER of these, I would be forever grateful /images/graemlins/grin.gif

[emp1346]

this is gonna rack my brain now... thanks...

/images/graemlins/mad.gif

[Officer Farva]

Very tricky problem...I think I might have it here but would not be suprised if I made a mistake. I did not include the probability you actually flop the straight, flush, full house.

We need to count the flops that cause us our draws, so:

For 2 pair: 3*3*44 (44 cards that wont cause the boat)
For trips: 3*2*44/2
For inside straight: 3(4*4*42) (3 because the inside on say a 67 could be made with 45, 58, or 89; 42 since there are 42 cards that won't finish straight)
Flush draw using 5 spade or 8 spade but not causing straight draw (since it was already counted): 2*8*33 (8 since 3 spades are dead plus the two thatd cause an inside straight that we already counted, 33 since we dont want to complete flush our inside straight)

Flush draw not using 5 or 8 of spades: (9*8/2)37.6667 (This is the really tricky part. The 37 and 2/3 comes from the from the following observation: 1 out 36 times, the two flush cards will be the 4 and 9 of spades, in which case we don't want to fill the straight, so we have 33 (52 - 13 spades - 6 non spade straight fillers). 14 out of 36 times we will have either the 4 or the nine of spades (but not both) so we will have 36 cards that wont fill the inside striaght or flush. Finally, 21 out of 36 times we wont have either the 4 or 9 of spades, so the third card simply has to not be a spade, so 52-13 = 39 cards. Thus, using weighted probability, there will be 1/36* 33 + 14/36*36 + 21/36*39 = 37.66667 cards that will fill out our flop)

Totaling our flops:
3*3*44 + 3*44 + 3*4*4*42 + 2*8*33+9*4*37.66667 = 4428 flops

Divided by number of possible flops (52 C 3):

4428/19600 = .22592

You'll flop a draw holding an inside suited connector (34-QJ) 22.592% of the time.

Mike

[Lost Wages]

You need to double your trips since either card can make trips.

76 can also flop 8 out double gutshots with flops of T84 and 953.

I haven't worked through the rest.

Lost Wages

[KjellBarry]

Heh, I figured you would get a challenge here.

[Mikey]

know the chances of flopping a flush-draw is 7.3-1 (11.79%)


How did you come up with this mathematically? Thanks.

[Lost Wages]

The complete solution is actually quite lengthy. You may want to search the archives. I will try to post an answer on Monday if no one beats me to it.

Lost Wages