How accurate is Clonie Gowen's estimate?

[LetYouDown]

Typically for questions like the hand above, it's much easier to calculate the probability of missing and then subtract from 1. There are 21 cards that will improve you to a pair of Q's or better. There are 47 cards left in the deck.

So basically, to miss entirely, the turn/river need to be 2 of the remaining 26 cards that don't improve your hand. There's C(26,2) ways for this to happen. There's C(47,2) possible ways for the turn/river to come.

So, in English it's:

1 minus the probability that I'll get 2 cards from the 26 cards that don't help me divided by the total number of ways the remaining cards can come.