[Ed Miller]

Its the backdoor straights I have trouble calculating.

Eight cards (4 queens and 4 eights) will give you an open-ender. Eight cards (4 kings and 4 sevens) will give you a gutshot. Thus, you make a straight:

(8/47)(8/46) + (8/47)(4/46) = 96/2162 ~= 21.5-to-1