Posted 2015-February-08, 17:34
Let's try to look at this carefully.
1. I doubt that bidding 4♣ is going to lead to our best result very often. So I am going to just analyze whether it is right to bid 3NT or pass for penalty.
What do we need to make 3NT?
A. If we have a double stopper (any diamond honor in N, or a singleton honor in E, or a doubleton honor in E coupled with an honor lead by W), then our chance are probably pretty good - in this case we need to take 7 (or 8 if our second "stopper" is a blockage) tricks outside diamonds, without letting W in twice. I would guess that we would make 3NT more than 80% of the time when we have a double stopper or a blockage. On defense, however, it makes a big difference. When we have a true double stopper, then their expected number of tricks is probably equal to LHO's number of diamonds or number of diamonds +1; we will get 100 or 300 against a 7-card suit and 300 or 500 against a 6-card suit. A diamond blockage will have little effect on their number of tricks as declarer, though, and the suit will never block when E has Hx. So they will get 1 more trick, and we will get +100 or +300 against a 6-card suit but +100 or -470 against a 7-card suit.
To summarize this case, if we have a true double stopper we will score +400 on offense 80% of the time and -100 to 200 about 20% of the time. Our expectancy is probably +290 or so on offense, and +300 or so depending on the frequency of the various results on defense. When there is a blockage, we will still have an offensive expectancy of +290, but our defensive expectancy plummets to -20 or so. So in this case it's right to bid.
B. When we have a single stopper, then we will either need to have 8 fast winners outside diamonds or find W with no entry. I would guess that these combine to about 1/3 of the time. And we will beat 3♦X about 3/4 of the time as above in the blockage case. So our offensive expectancy is probably around +50 and defensively about -20. Once again it is right to bid, at IMPs, to avoid the occasional huge loss (perhaps even a double game swing) by offering up a lot of small losses. Note, however, that it is right to pass at matchpoints because we will likely go plus instead of minus about half the time, and other times we will collect +500 for a larger plus.
C. If W is the sort who might "fool around" with, say, ♦KQJ10xx and a minimum opening bid, then 3NT is going down practically all the time, likely doubled. (My experience has been that when W has opened 3♦ with this hand type, and we bid 3NT, W will double far more often than not.) In this case, the odds are heavily with passing, since a W with this hand type is likely to take nearly as many tricks on defense as on offense, and we have no intersecting case where bidding would result in a poorer result than passing.
So now, your job is to decide how likely cases A, B, or C are. My guess would be 25%, 70%, and 5%. But note that only in case C is is right to pass at IMPs under my assumption that 4♣ is futile. So I think the IMP odds for bidding are enormous; we will win 5-7 IMPs for 3NT making a large percentage of the time in case A and about 1/3 of the time in case B, while losing 3-6 IMPs most of the rest of the time. Only in case C, where passing is our only hope of a non-disaster, do I think passing has the better of the IMP odds. At matchpoints (or board-a-match) I think it is right to pass based on the frequency of small gains in case B.
Thus the basis for "Wolff's Law." It truly is wrong to pass just because you are afraid to bid. You will find that in most cases where you do an analysis of high-leverage auctions such as this one, the odds will come out similarly.
Help
wanoff, on 2015-February-07, 13:14, said: