[danq]

Any Q or any 7 beat you, so 8 of the 45 cards you can't see can't be in any of the three hands if you're good. The probability that nobody has a straight is therefore

37/45 * 36/44 * 35/43 * 34/42 * 33/41 * 32/40 = 28.5%

so it's just over 71% that someone has a straight.

When nobody has a straight, there are 15 cards (out of the remaining 38 non-7-or-queens) that pair the board, and anyone with two of them beats you. The probability that at least one of the three hands has two pair or a set, given that nobody has a straight, turns out to be 43.2%. So the chance that you're beat is

.715 + (.285 * .432) = .838

or you lose about 5 times out of 6.

Dan

(Edited cause I can't count)