Bbradley62, on 2012-September-10, 09:49, said:
3. If pard has one spade, chance of 3-3 split is 35.5% and chance of Jx is 16%, so the chance that your spades run is just over 50/50. If pard has no spades, it's 27% for Jxx plus about 1.5% for J9.
I think you might have your probability wrong, you don't add them together, but rather multiply their chances of not working. For example if there are four finesses to take and you need one to work to make your contract, you wouldn't add 50% + 50% + 50% + 50%, which would give 200%. You would multiply 0.5 X 0.5 X 0.5 X 0.5 = 0.0625 so the chances of making your contract would be 93.75%.
In the case of pard having one spade, using your quoted probabilities, 1-0.355 = 0.645 and 1-0.16 = 0.84, 0.645 * 0.84 = 0.5418, which gives a 45.82% chance of the spades running.
When pard has no spades, using your quoted probabilities we have 0.78 * 0.985 = 0.7683, so you have a 23.17% chance.
If you weight these two possibilities (pard with one spade and pard with no spades) equally, you'll get a total 45.82 * 0.5 + 23.17 * 0.5 = 34.495% chance of the spades running.