Teaching: the best way to learn

"No one learns as much about a subject as one who is forced to teach it," according to Peter Drucker [incidentally someone who was, before he died in 2005, a second-degree connection of mine]. I certainly have found this observation to be true throughout my lifetime, never more so than when I rashly took on the teaching of relational databases to graduate students at one of Boston's major universities a few years ago.

So, how does this relate to bridge? In preparation for the final day Swiss at Mansfield this last weekend, I was going over some hands on the computer with our twelve-year-old CJ who recently started playing bridge. A hand came up where dummy had AQT82 and our hand had K3 of a suit (it happened to be clubs). We were in 6NT and needed all five tricks. What's the best line, assuming you know nothing definitive about the opposing distribution?

Most of us would probably say this is very close and there's not much in it. Those of you who are students of the suit combination tables, might know that playing for the drop is the best play. There are two potentially favorable distributions: 3-3 and those 4-2 splits where the knave is doubleton [I like to use the English name - it sounds so much more elegant]. Notice that 5-1 splits are no good because while the J may occasionally be squished, on these occasions, the nine will rear its ugly head. The 3-3 splits give us about 36%, as everyone knows, but those doubleton Js add up to a very surprising 16% yielding a total chance of 51.67%.

This is only slightly better than taking the finesse, right? No, the probability of success by finessing (recall that we can only finesse once) is only 42%. So the drop is significantly more likely to work.

But on this particular hand, after losing the first trick (diamonds), and winning the spade return,

unblocking three top hearts in our hand indicated that RHO had five hearts to LHO's one. That suit was completely known so could be used in a vacant places calculation. But vacant places are tricky, as anyone who has studied the associated paradox knows. Suppose that against 3NT, opening leader leads what we discover to be a five card suit and his partner has three cards. Does that mean that the vacant places are 8 to 10? No, it doesn't because we were "fed" this information by virtue of the lead being from the longest and strongest. If partner was declaring 3NT instead, our RHO might have led from his five-card suit and we might have concluded that the vacant places were 8 to 10 the other way.

No, the only suits we can really use in a vacant places calculations are those whose layout we have discovered for ourselves. Otherwise, the information is "tainted" or biased to use the proper mathematical term.

So, we go back to our 6NT contract and, ignoring any presumed layout of the diamonds (the suit led), we simply take the hearts into account. Thus, for the purposes of handling the clubs, LHO has 12 vacant places to RHO's 8. This means that 60% of the time, LHO will have the missing club knave. Is this enough to change our play?

I thought so and, in my teaching moment, I recommended a finesse of the ten [no, I did not go into details of vacant places -- just a vague description of how LHO was now more likely to hold the critical card]. And, I might add, CJ was very much in favor of playing for the drop.

Well, you probably guessed it by now. That rascally knave [please excuse the tautology] was tripleton offside. The cold 6NT was down two! Naturally, I justified this result by observing that if you play the probabilities, you won't get every situation right, but you'll come out ahead in the long run.

But would I have come out ahead in the long run? I decided to consult that excellent tool SuitPlay (mentioned several times before in this blog). Oh dear! The vacant places calculation doesn't make all that much difference. It's still right to try for the drop, although the edge has been reduced a bit -- drop: 47.68%; finesse: 43.98%.

So, from trying to teach -- and getting it wrong -- I have learned something myself. I still don't quite understand why the finessing percentage didn't increase by something close to the factor of 1.2 which would be expected. But maybe I'll figure it out, though I suspect it will be quite difficult.

But the really tricky part now is that I will have to explain to CJ that I gave him bad advice. Incidentally, his team won two matches for 0.44 red points which is enough to put him over the one point mark.