Big Slick on the flop?

[LastKnight]

I've been doing some calculating on my own(a dangerous proposition) as to the probability of flopping a straight draw with Big Slick in the pocket. I've looked hard to find this in Matthew's probabilities book but all I could find was the chance of flopping an outright straight for these "three-gapper" type hands. I came up with about a 10.5% chance of flopping say a Q-J-x or a 10-x-J or the likes. Can someone please comfirm or correct my calculations. Thanks a lot!! LastKnight

[Fenris78]

Ok, here is how I would solve this problem:

Please note that Q-T-x also gives you a gutshot.

Your first card has to be a Q, J or T. The probaility for this is 12/50 (50 unseen cards). Your second card has to be another one of those three, or 8/49 (e.g. a J or T if the first card was a Q). The last card can be any card except the one that would make a perfect straight or 44/48.

So in case my math is right the probability is 12/50*8/49*44/48 = 7.18%

Unfortunately I am not sure if I am right as I am lazy/tired/drunk atm and this was the best I could come up with in 5 mins

[Bugsbunny]

I can tell you that that answer is incorrect, but my brain is too frazzled to get the exact correct answer. I've run it 2 different ways and come up with slightly different answers - but they both indicate that the correct answer is a bit over 10%, assuming you allow a paired board or an A or K to be on board.

With No A, no K, and no paired board it looks like this:

(12/50 * 8/49 * 32/48) *3 = 0.0783673469 ~= 7.837%

The 32 is because there are 32 cards in the deck after you remove all the broadway cards, and since the board can't pair, give a straight, or pair our hand that means the 3rd card must be non-broadway.

The times 3 is because that's a simplified form of:
(12/50 * 8/49 * 32/48) + (12/50 * 32/49 * 8/48) + (32/50 * 12/49 * 8/48) =
since order does matter with this type of calculation.

OK let's look next at hitting an A or a K along with the gutshot:
(12/50 * 8/49 * 6/48)*3 = 0.0146938776 ~= 1.469%

Next the board pairs one of the gutshot cards:
(12/50 * 3/49 * 8/48) + (12/50 * 8/49 * 6/48) = 0.00734693878 ~= .735%

Finally - you flop a straight:
12/50 * 8/49 * 4/48 = 0.00326530612 ~= .327%

Ok - those are correct, and everything checks with my second method. The results are mutually exclusive so you can just add percentages together.

So you'll flop a gutshot, with a possible paired board or a card matching your A or K about:

7.837 + 1.469 + .735~ = 10.04%

[LastKnight]

Thanks Bugs, 10% is what I came up with for an unpaired board and I agree with your calculations. Thanks for taking the time to figure it all out. As always there is a motivation for nearly every question and mine was to find out the overall percentage that Big Slick (s) would improve to at least a TPTK, a flush draw or a nut straight draw on the flop. I had confirmation on all the other parts of the formula and needed some help on the str part. I think the total is around 53% which is not bad at all. Thanks again. LastKnight

[shallam]

[Fenris78]

[Bugsbunny]

[AlamedaMike]

I cheat and use this site

Flopping a 3 gap straight using offsuit cards is 310-1.

I missed the DRAW part.

You might want to look at this site for the proability of completing with a straight for AK and A2 since it is the same.

[shallam]

1. No paired board and no AK

(12/50) * (8/49) * (32/48) * 3 = .0784 or 7.84%

Consistent with previous post.




2. Paired board but no AK

(12/50) * (8/49) * (38/48) * 3 = .0931 or 9.31%





3. Paired board and AK

(12/50) * (8/49) * (44/48) * 3 = .1078 or 10.78%

Slightly inconsistent with previous post.




Summary: You flop an inside straight draw about 10% of the time. Actual probability ranges from about 9% to about 11% depending on details.

[Bugsbunny]