two running cards

I believe - correct me if I'm wrong - that the odds of catching two running cards to a three card straight or three card flush on the flop are about 20-1. (I mean if you have one of the straight or flush cards in your hand and two of them are on the flop).

Does anyone know the odds of catching two running cards to a straight or flush (or straight flush) if you have a three card straight flush on the flop?

I dont' know this statistic for straights but it is easy to compute:


Lets say you have the best case scenario for your straight (lets say you have AT and the flop is 9 8 2r) (things dont' change it you have JT and the flop is 9 3 2...).


P(making straight )=P(Qhigh st )+P(Jhigh st)+P( T high st)= 3(16)/47C2)= 0.044 or about

21.5 to 1.


Now lets say you have JsTs and the flop is 9s 3c 2d.

P(making st or flush)= P(flush) +P(st thats not a flush)= 10C2 +3(15)/ (47C2)


(I counted the straight flushes along w/the straight flushes). (It shoudl be clear that there 15 such ways to make a Q high st that isn't a flush similarly for J high etc)


= 45 + 45/ 47C2 =.08


which is about 11 to 1.