In a recent teams match I was the declarer in a 3NT contract. I bought the contract on the idea of running a seven-card club suit missing the queen. It ended down 5 because West held Qxx. I did a calculation of the probability the suit would run, which resulted in a surprisingly high 0.77293. But is the calculation correct? Your feedback is welcome. ------------------------ probability calculation------------------- Problem: calculate the probability that in a NT contract with a 7-card club suit missing the queen and no entry to dummy you'll be able to run the suit for seven tricks. Solution Use notation P[e] for the probability that event e occurs, P[e,u] for the probability that both e and u occur, and P[e|u] for the probability that e occurs given that u occurs; all these probabilities under the assumption that South has a 7-card club suit missing the queen. P[can run suit] = P[Q in dummy] + P[Q not in dummy, Q is singleton or doubleton] P[Q in dummy] = 13/39 P[Q not in dummy, Q singleton or doubleton] = 2 x P[Q with West, Q singleton or doubleton] = 2 x P[Q with West] x {P[Q singleton | Q with West] + P[Q doubleton | Q with West]} P[Q with West] = 13/39 P[Q singleton | Q with West] = (26/38) x (25/37) x (24/36) x (23/35) x (22/34) = 0.13105 P[Q doubleton | Q with West] = 5 x (12/38) x (26/37) x (25/36) x (24/35) = 0.52835 P[can run suit] = 0.77293