probability of flopping 4 to a straight?

[jaydoggie]

Is there a way to determine flopping 4 to a straight with connecting cards 45, 56, thru 9T, TJ?

If so what about cards like 57, 68 thru 8T, 9J?

Im no expert in math, i woulda never figured out 2 /forums/images/icons/diamond.gif + 2 /forums/images/icons/club.gif = 4 /forums/images/icons/heart.gif without someone telling me.

thanks in advance

[doormat]

jaydoggie,
I haven't seen this calculation done anywhere but I did see a similar post by Mike Caro elsewhere and as a rule find his calculations to be accurate. The example he gave was this: You have J Q, what is your probability of getting an open-end straight draw on the flop? He gives the answer of 6.04 percent. Since it is open-end, you must flop either a 9-10 or a 10-K. I would think that for the 9-10 part, there are 4 nines and 4 tens and then 40 cards left to fill the remaining spot on the flop (48 minus 8,since you eliminate the 8 cards which would make a 5-card straight), so 4*4*40=640, then multiply by 6 ways they can be arranged and double that because of the 10-K possibility and you get 4*4*40*6*2 / 50*49*48 = .0653.
However, this differs from Caro's calculation of .0604. If instead of using 40 remaining cards to fill out the flop, you use 37 instead, you would get 4*4*37*6*2 / 50*49*48 = .0604 exactly. So either my approach is all wrong or Caro somehow considers only 37 remaining cards instead of 40 - if someone can fill me in on why this should be, I would appreciate it.
Back to your question, if you are holding say 6 7, then you may draw 4-5 or 5-8 or 8-9 but none of the 8 cards that make a full straight. So my calculation, which may be wrong, would be 4*4*40*6*3 / 50*49*48 = .098. If you are holding 5 7 as in your next question, I would think the answer is the same as Caro's example of J-Q flopping a straight draw.
doormat

[Dynasty]

I'll give you the answers for JT-54. If you want the detailed math for this and all other hold 'em problems, I suggest you buy a copy of Hold 'em Odds Book by Mike Petriv.

Odds against flopping

a straight: 76:1
an 8-out straight draw: 8.6:1
a 4-out straight draw: 3.6:1
all of the above: 2:1

I had to do a double-take on those last two numbers. But, they are accurate.