[AaronBrown]

Your math is close. I assume there are ten players for 20 pocket cards, plus 4 on the board. Then there was a burn card before the flop and turn, plus another one before the second turn (the original river card). That gets us to 25 left in the deck. Is that right?

Given the 25 cards in the deck, there are two possibilities. 1/25 chance of getting the old turn card to complete your straight and 24/25 chance of not getting it, in which case you have 7 chances in 45, as you say, of completing your straight. So the correct computation is:

1/25 + (24/25)*(7/45) = 71/375 = 18.9%

not 44/225 or 19.6%. Your overall odds go down slightly from 31.45% to 31.27% (your numbers should give 31.80%, not 33.25%).