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Not only do I disagree with this "rule", I don't even see how it is playable. Maybe you should change it to "return to 4 of a major is always a place to play when we have not agreed any other suit." What does "agreed" mean for purposes of your rule? Does it mean that the logic of the auction says we will definitely play in this suit? either in this suit or NT? Does the present auction constitute agreement of clubs? Please show me a few. I don't recall ever being discomfited by this old Acol rule, and have seen many times where it helped. I can well imagine that, if the partnership puts no price on a proliferation of detailed agreements, this rule like any simple rule will be slightly non-optimum on occasion. But you said "very obviously."

This is a definition that doesn't make sense for this problem. If partner had a flat NT hand, he can bid 2NT after 2 spades, especially if 2 spades was natural originally. We were told that the person opposite would recognize the bidding as a 6-5 in clubs and spades, and, after having shown delayed support in clubs, which usually indicates 3 cards, decided to bid 3NT anyway. If they were interested in 4 spades, they would bid it right away. After that action, partner removed to 4 clubs. At some point you have to assume partner isn't crazy and start cooperating. 4 spades almost has to be a cue-bid. My examples showed Ax of spades, with which 4S instead of 3NT would not be tempting. When you can't state a hypothesis without including qualifiers like "especially" and "usually", your conclusion also won't be any stronger than "usually". I'm sure partner has the ♠A, not xx, but only by looking at my hand do I know it's not ♠QJ. Judging from the discussion you posted earlier where we differ is only in that you think partner has ♠A singleton. With the example you gave as a 4♠ bid I'd prefer to bid 4NT anyway.

1. Natural -- "return to 4 of a major is always a place to play". Without this rule there is no sanity. 2. Ax,J10xx,AQxxx,Qx. Or Ax,KQxx,J9xx,Jxx. 3. 5♦.

trump Declarer appears to have 6 hearts (else pd is what -- xx,10xxxx,KQJxx,x? 1=5=6=1 leaves declarer an absurd, even for LHO's friend, 5=5=2=1) and a singleton. Trusting pd doesn't hold xxxx,Q109x,QJxx,x I'll win the club continuation and continue with a low diamond.

How poor? 3♦ tricks are available unless LHO both has and won't lead ♦Qx. Then it's 60% to make 3 ♥ tricks, and finding either the ♣J or a black suit squeeze (whichever seems best late in the day) adds to 12 tricks.

East. 3NT is already questionable. 4NT is highly craven. I don't think West can be blamed for giving up at that point. It's a tough hand though. If the partnership had brightly bid to 6♣ I'd probably agree with their judgment more, but it's only marginally better than the actual contract. Finding 6NT (or 6♦) requires genius.

yes, 4NT. Even 18 point hands like Kxx, A10x, AJx, AQ10x give a shot, and pd may have much more or a long suit. In view of my extra diamond stopper and prime cards 4NT is unlikely to be in danger (unless pd is truly threadbare -- is Qx, Kxx, A10x, AJ10xx possible?). So I think it's close but worthwhile.

2NT. I feel terrible about this. Low heart seems safer than A, occasionally gaining entry to partner for a club play. Heart pass

Win in hand, ♣, ♣ ruff, ♦Q. I think there is a good chance trumps are breaking; sometimes West would double with a singleton. In any case, the hearts may be easier to guess after testing a few other suits.

I assume that West would not open 1H with 41 in the red suits. Hence West is probably 2515 or 3514 or less understandably 4513 or 2614. I'll play for the 1st two. Low club. I'm playing that West has AJ98(x) and East will play a true card. West may as well play ♣A, ♣. If West seems to have only 4 clubs, bang out the spades. If East played clubs down the line, play the ♠A. If West unblocks the ♠K, the cash ♦K (♥ discard from West), cross in ♠, play ♥ to the 9. If no unblock, continue with ♠ is good enough and safer against a misread.

Why does everyone assume we're going to play in spades? A large part of the reason that I choose the 3D call is because if the bidding continues 3H - 3S - 3NT that's probably our spot. Yes, partner could have x, AJ109xx, Kxx, K10x where spades is better, but there's also --,KQJ9xx,K10x,Kxxx.

♠. I have some respect for the dummy's minor suit -- perhaps in a 5-card major world a 1♦ opening doesn't mean anything and I am wrong. However, if the dummy has ♦KQxxx then a passive lead will be wrong. If the dummy does have a real diamond suit and the spade lead blows our potential 3rd round winner, it's a winner we'd never come to anyway. Yes, clubs are safer in a sense because of the 9, but also they are less likely to be productive because of the extra length. Spades are more likely to be 4333 around the table. Finally, there's something unrealistic about trying a passive defense in an individual event.

I wouldn't worry about the BAM scoring. As it happens the board was won (or lost, depending on how you look at it) on the lead. Just play to make your contract. I'm not trying for an overtrick (!) and am not "worried" about the BAM scoring. But LHO may be. That's the point.

Win in HAND and play a low diamond. This has a small chance to lose when diamonds are 2-1 and a significant chance to gain when LHO has all three, given the uninformative bidding and the fact of BAM scoring.

When playing 3/5 I have always led 3 from KJ93. I consider it a routine application of the principle that you don't signal with a card you can't afford. Good to meet you (and to be met). Charles

I think Cherdano's argument is telling. Practically speaking -- as of the time the hand was posed, not some mythical perfect-bridge future -- players don't lead the Q of trumps from QJ. So the actual lead of the J obviates restricted choice. By the way, after Frances revealed that the J was led at both tables, I had an impulse to reply that in that case I would be confident that the lead is from QJ. It's a joke of course, but isn't the point correct? Wouldn't you feel that both players might find the lead from QJ but for both to lead the J would be remarkable? If you agree with that, then you are agreeing that also at just one table, J from QJ is far more likely than from J alone.

I see reasons to SAY I would lead a non-♠: 1. Asking the question suggests something. 2. quotes around the word "expert" -- maybe the hand was followed by a lecture about "What am I doubling on -- has to be a void!" or "How can I be doubling without the ♦A -- lead one so I know you have the King!" (I lead a ♠.)

♦. Admittedly ♣ gives us a clearer route to 4 tricks. However, passive defense may be sufficient if we can kill dummy's entries and ♦ is better for that.

In 3S, pull the trumps & play on clubs. Ok if LHO has the ♥ and ♣ aces. In 4S, win ♠Q & try ♣K. If it holds, revert to the legitimate line: ♠ to Ace, ♣Q.

If you're not kidding, Google "most prolific mathematician". Charles

From South's perspective 5♠ might have been better than 5♥ -- say if N were 4432. On the given hands I don't see how anything makes. S's venture to the 5 level looks a bit pushy, but probably the auction was ill-defined. Mainly I'm interested in the first bid, the 1♥ overcall. There was a time that double seemed obvious. Then players learned to bid so extremely well that bidding 1♥ supposedly shows a profit. However, this hand makes the point that to show a profit by overcalling you need to have an extremely fine understanding of the remainder of the auction. As the auction went South did not know N's major suit distribution, and neither player knew accurately how much strength each had shown in the bidding. Hence a random result.

I like.

I'd like to bite, but there's a problem. dQ, hesitate, dA. heart to A. heart J. If LOL goes through her act again, play the h King & try the clubs for 6-odd. If LOL plays low promptly, then put the uncompleted heart trick to the side, cash the other diamond, then resume the heart trick & duck. Is it ok?

Whether to call it "restricted choice" IMO is a bridge terminology semantics issue, not a math question, since RC only appears as a term in bridge articles AFAIK. In one view "restricted choice" is a single term and as such it's meaning is inferred from the usage as a phrase with no attempt to interpret the individual words. The classical examples involve defender's play from touching cards. Since that's the overwhelming usage, that's the meaning. There are even some people who further limit usage of RC to cases where you really should finesse. Thus, if RHO drops the Q or J but LHO has such a long side suit that a finesse into RHO is nonetheless not percentage, they would say "It's NOT a restricted choice situation." Perhaps they would say the same even if the percentage play in the suit is to finesse but the sensible play overall is not to. Another view -- more authentic in my opinion but it really comes down to taste -- is to interpret "restricted choice" as a phrase in which the two words retain their individual significance. With respect to the present problem a defender with A9 has only one sensible choice, whereas the defender with Q9 has more latitude. The fact that the hypothetical A9 defender has a more restricted choice of plays is -- or may be -- a relevant consideration in deciding declarer's strategy. Furthermore, the pattern of mathematical reasoning for analyzing the A9/Q9 and the QorJ/QJ situations are the same. Incidentally I'm a mathematician (http://dna-view.com/math.htm), which in this case is perhaps more a disclaimer than a credential. No doubt it colors my preference of definition. Charles Brenner

I better add a hint. Lew Stansby, who was declaring, of course couldn't know definitely if his target should be 8 tricks or 9. However, it was striking that from the play of the ♠A one might imagine the actual layout for the remaining cards [hv=d=e&v=n&n=s7hk987dc109&w=shq106dckq65&e=s1085hj4d108c&s=skj64ha5d7c]399|300|Scoring: imp[/hv] and that the best double dummy play from here is not obvious. I wondered if anyone might find the double dummy play for the specific layout and consider whether it is the best single dummy play. That kind of thinking is routine for computer declarers but maybe the hand is too difficult for humans. Or maybe Stansby saw all the possibilities but nonetheless judged to settle for down 1.