Posted 2019-February-16, 17:12
It's a good slam. An illustration of how the robots can't bid after splinters. IMO North is supposed to cooperate with 4H after 4D with 3 bullets and minimal wastage in the diamond suit, 14 alleged working pts out of a 15-17 NT. I think if South is needing North to wait until holding perfecto xxx in diamond suit to cooperate, South is being too aggressive with slam tries. When North signs off in 4S IMO South is supposed to give up, as 5S can be in jeopardy opposite some bad North holdings. When South tries again, it's criminal for North not to cooperate having signed off the first time.
You'll pick up the spade suit about 46% of the time. 52% is when you have 9 cd missing Q, but holding J, and you have *already* cashed one honor and the Q didn't drop and have led a 2nd card up and have choice of finesse/drop. At that point it's approx 52:48 in favor of drop not having info in bidding or play about the other suits. Before playing the spade suit at all, it's about 53% to pick up the suit, as you just need 2-2 spades (~40.7%) or stiff Q(~12.4).
But that's not when missing Q and J. When you are missing Q and jack, but hold the T, essentially you are supposed to play for the drop unless an honor drops first round on the favorable side and leaves you a finessing position. This is the so-called "law of restricted choice". The idea is that QJ tight, Q alone, and J alone are all approximately equally likely to be dealt (QJ being very slightly more common than one of the honors). So by hooking, you pick up two of the positions but lose to one, a net gain. So you will pick up Qx/Jx/J/Q with west, but lose to all QJx(x) and QJ tight with West. West with QJ alone is assumed to play randomly either honor. So tally all this up and you get a bit above 46, it's essentially the 40% for the 2-2 breaks, but lose QJ tight with west (a bit over 6%) but gain the stiff honors (a bit over 12).
If the spades don't come in, and it wasn't the disaster QJxx with west, where you are down already, then the hearts have to come in. Since you don't have critical 9/8 spots essentially you need 3-2 with the K onside which is ~34%. So overall it's around 62% which is a decent slam to be in, unfortunately it goes down on the actual deal; it would have made if the E/W hands swapped.
estimate = (46% spades come in, + 34% (hearts behave) *49% (spades don't come in but not QJxx offside)), not totally accurate since hearts behaving isn't totally independent of spade behavior, but close enough.