Aces on Bridge — Daily Columns

The Aces on Bridge: Sunday, March 1st, 2015

Assuming you need five tricks with no outside information, holding the doubleton queen in dummy, and A-K-10-3-2 in hand, after playing the queen, is the percentage play to play for the drop or to finesse the 10?

Witch of Eastwick, Trenton, N.J.

The answer is a tossup. The math says the chance of a 3-3 break is just over one third, and the chance of a doubleton jack is one in six. So the chance of playing from the top is just fractionally over one half. Just for the record, with Q-10 facing A-K-4-3-2 the best line is to lead low to the 10, rather than playing for the drop.

After you hear your partner open one heart, and the next hand overcalls two clubs, would you start with a negative double, as I did, holding: ♠ A-Q-3-2,  5-3,  K-Q-3, ♣ J-9-4-2? If so, partner responds two spades, and you have to make a rebid. What would be your choice now?

Finding Nemo, Asheville, N.C.

You are by no means guaranteed to have an eight-card spade fit, as partner may have been forced to bid a three-card suit, so it would be premature to raise to four spades. I would bid two no-trumps, suggesting invitational values with a club stopper, surely holding four spades, else you would not have doubled in the first place. Your partner can now choose the strain and level he wants to play at.

I'm trying to learn how to make my opponents' life more difficult as declarer. Is there a general rule as to whether declarer, as fourth hand, should win the trick with the bottom or the top card from a sequence of equals? Similarly, when following suit, should one follow with the top or bottom of a sequence?

Harry Houdini, Seattle, Wash.

There is a general rule — with one common exception. When following suit or winning a trick, play the higher of equals, which will generally help to confuse opponents about the location of the lower honor. But at no-trump, when winning the first trick when holding either the ace-king or ace-king-queen, take the trick with the king.

Were you at the recent world championships in Sanya, China? Do you have any comment on how the events were run?

Grocer Jack, Chicago

I was not at the tournament, which seems to have been less popular than many of the recent big championships. Perhaps this was the distance of Sanya from Europe and most major cities? I know there were Internet problems and logistical problems at the event, but I fear these are the norm rather than the exception nowadays.

As opener I was unsure how forcing a new suit by responder should be at his second turn. I was recently dealt ♠ K-4,  J-7-2,  Q-3, ♣ A-Q-9-7-5-4, and opened one club, then rebid two clubs over my partner's response of one spade. What was I supposed to bid over my partner's call of two diamonds — is that call forcing, encouraging or weak?

Trumpet Voluntary, Elmira, N.Y.

A new suit by responder is forcing, even by a passed hand. Your duties are to support partner's first suit with three trumps or a strong doubleton, to rebid no-trump if you have the fourth suit controlled, or otherwise to make any other natural and descriptive call. Here supporting to two spades seems right — partner should not expect you to have three good trumps, since you might already have raised him.

For details of Bobby Wolff’s autobiography, The Lone Wolff, contact If you would like to contact Bobby Wolff, please leave a comment at this blog. Reproduced with permission of United Feature Syndicate, Inc., Copyright 2015. If you are interested in reprinting The Aces on Bridge column, contact


AviMarch 15th, 2015 at 11:05 am

Bobby hi.
Just ti clarify over Witch of Eastwick.
“with Q-10 facing A-K-4-3-2 the best line is to lead low to the 10” is assuming an outside entry to dummy?

Bobby WolffMarch 15th, 2015 at 1:08 pm

Hi Avi,

Your clarification is correct. The difference in your example and the one from Witch of Eastwick is that with your example, by playing for the drop, will not include the Jack and one by either defender as successful and, of course, not necessary to be said, an entry to the now established 3 extra tricks, would need to be there also, whether or not the finesse of the ten worked).

Further, and as an added feature to learning and moving up the ladder of success, one needs to understand (as discussed above) why the above is true, since in most card combinations there are various similar type family combinations which need to be figured out at the table and, at least IMO, are impossible to memorize them all, therefore requiring the player and at the spot, to be able to think for himself.

jim2March 15th, 2015 at 3:00 pm

On that first question, I think the DROP line is better mathematically once both defenders have followed to the first round and East has followed small to the second round.

That is, when Declarer comes to the decision point, I think the DROP line is better.

Peter PengMarch 15th, 2015 at 3:37 pm

Hello Mr. Wolff:

I would appreciate comments on the following situation.

I held

S- A
H- Kx
D- AJTxx

and opened 2C

Partner held


partner bid 2D, which is a waiting bid. The bidding went (opponents pass throughout) 2C-2D-3D-3H-4C-4S-5H-Pass. I bid naturally, clubs and diamonds, I thought I had shown slam interest, and partner never supported any of those suits, bidding hearts and spades aggressively. We ended up in 5H which makes, but which partner botched. 6N, 6D and 6C all make. I think partner cannot stop bidding, as I had not limited my hand and her hearts were worse than horrible.

A local expert was called in and wrote me the following opinion. Thank you for your comments.

Please note that the said expert played the same hands. He had a 49% game, which was about what I had, my worst game in many moons.

Here are two hands from yesterday (xxxx and I were a little unlucky, plus I made some errors which added up to about a 50% game).

♠  A
♥  K 3
♦  A J 10 8 3
♣  A K Q 8 4

When you have a two suiter, especially in the minors, it’s almost always wrong to open 2C, because the bidding goes:
2C     2D
3D     3H or 3S (pard should bid this with any 4-card suit, even 5432)

and you’ve passed 3NT which might have been the best contract and you haven’t even shown your distribution yet.  Even worse is if pard had bid 3NT over your 3D, because now your 4C would be Gerber and you’re not ever able to mention your great club suit at all in the bidding!  The only time it’s right to open 2C with a 2-suiter is when you’re so strong that you just can’t take the risk that your 1-level opening bid will be passed out – like if you have 24 HCP.  Your 21 HCP on this hand is close but it isn’t quite enough to open 2C.

Bobby WolffMarch 15th, 2015 at 3:42 pm

Hi Jim2,

My belief is that your answer appears to fit logical numerate thoughts (once LHO follows suit, indicating a truth, having at least 2 small) the original odds have slightly changed.

However, Terence Reese’s brilliant, restricted choice creation, would probably think otherwise.

Since I do not trust my ability to best describe what I happen to understand and now think, agreeing with TR’s opinion (perhaps for 50+ years and growing) was as true as it can be, will leave it to a better educator and writer than I, to manufacture the right descriptive words.

Effectively what you are saying is that before the declarer is faced with that specific problem (2nd round of the suit and everyone up to now has followed low) the odds have now changed from the original mathematical percentage.

Although it undoubtedly has changed from what is originally quoted in the percentage table (elimination of 6-0 breaks, singleton jacks in either hand nor a doubleton jack with LHO), if that were so, from a bridge standpoint it would be clear to say that the drop is superior from the get go, because to assume differently would be ridiculous since unless the above stated scenario occurs, which it would in all cases when and if, the crisis arrives, there would be no problem to discuss.

Remember all possible variables (bidding, opening lead, false carding and other tendencies, psychology, etc.) are assumed to be neutral, and although rarely, if ever, is that 100% true, for discussion purposes it needs to be. Perhaps the above truths which I thought were factored in, were in actuality, not.

Your move.

jim2March 15th, 2015 at 4:01 pm

I believe the math (conditional probabilities) at the moment declarer has to choose what to play on the second lead once East has followed small to be as follows:

– 64 possible ways 6 cards can be split

– 2 are 6-0, and both can now be ruled out as not happening
– 12 are 5-1, and 5 remain possible when East follows small (x – Jxxxx)
– 30 are 4-2, and 25 remain (East holding Jx is now ruled out)
– 20 are 3-3, and all 20 remain

Thus, 50 card layout possibilities remain when East follows small. Of those 50 cases, the following 15 need not be considered because neither Declarer line succeeds:

– 5 with 1-5, East holding Jxxxx
– 10 with 4-2, West holding Jxxx

This leaves 35 cases but one other holding also can be eliminated because BOTH lines win:

– 10 cases with 3-3, East holding Jxx

This now leaves 25 cases where one line succeeds and the other fails:

– 5 cases – Jx – xxxx – DROP wins
– 10 cases – xx – Jxxx – FINESSE wins
– 10 cases – Jxx – xxx – DROP wins

So, this appears to me to make the DROP play a better line for the precise question posed by Witch of Eastwick. With 50 total cases remaining, the FINESSE line will win on 20 of the remaining layouts for an instantaneous probability of 40%, while the DROP line will win on 25 of the remaining layouts for an instantaneous probability of 50%.

The contra-intuitional result is, in part, due to 5 cases of the FINESSE probability winning having been eliminated when the 4-2 layout of xxxx-Jx has been ruled out when East follows small to the second lead.

Bobby WolffMarch 15th, 2015 at 5:03 pm

Hi Peter,

Because of your already suggested journey beginning with the Yellow Brick Road in the direction of success I will attempt to cut to the chase.

I heartily agree with not opening an artificial strong 2 bid (2 clubs) holding a 2 suiter, especially both minors (the bidding usually will get too high too soon to add the authenticity necessary to allow almost any partnership (who play a natural system) to be as accurate as is necessary to rapidly improve. Also in this specific situation, having to take 11 tricks to make game needs to leave room to investigate first as to what game and possibly then to check out a biddable good slam.

Just open 1 diamond and hope, as is usually the case, to get a positive bid from at least one of the other three.

However, and significantly worse IMO was your partner failing to, at his 3rd turn, after 2C, 2D, 3D, 3H, 4C, to not bid 4 diamonds hoping to set the suit so that both partners will then, here very belatedly, to know what suit should be trump. However, all your partner was trying to do is show positive values, which he had not been able to do earlier.

This hand is classic of crying out to show support, (I think the responder should raise three diamonds immediately to four instead of taking time to show that moth eaten heart suit of his) since to not show fits early in the auction so that both bidding partners know what suit is likely to be trump is a paramount sin and will always lurk as a major obstacle to success.

How about?: 1D, 1H, 3C, 3D, 3S(cue bid asking for direction, 3NT!!! P. Yes 6D is not an unreasonable final contract, but somewhat below 50% not making it a must bid contract.

Both stated errors, the opening 2C bid (20%) and the awful 4 spade advance cue bid intended but not so interpreted (80%) were chiefly the cause of the disaster.

Neither type error is worth grieving over, but both of you should learn from it and grow from here. Bids will hardly ever be exactly what you want them to mean, but when this is kept in mind both partners will (should) gravitate toward a better partnership, although it may take a little time.

Good luck!

jim2March 15th, 2015 at 5:07 pm

Peter Peng —

I am not Our Host but, if I had held your partner’s hand, I would not have even considered bidding 4S. I think I would have bid 4D. I would have considered 5D, but probably rejected it to allow the 2C bidder access to 4N to find out I had no aces. Still, 5D might be the value bid. especially if it would carry the implication I had no aces for you to discover via 4N.

I do have a question, though, as to what you play as a second negative over a 3D rebid by the 2C opener.

jim2March 15th, 2015 at 5:07 pm

Cross posted with Our Host!!

Bobby WolffMarch 15th, 2015 at 8:03 pm

Hi Jim2,

After due consideration I think you are 100% right with the original odds often quoted, merely applying, before any card to be counted has been played. If so, and when able to make a judgment after at least one card is known, does change the odds, albeit usually just a tiny bit, but in this close situation would break the tie in favor of a drop and not a finesse.

Also Terence Reese’s restricted choice would not apply since neither defender was making a choice between playing the jack (the only relevant card) and a lower one.

But I caution you to not get too cocky with my agreement, since how important or valid could it be, if I took this long to see it?

Finally a caveat to remember, subject to the winner’s scrutiny:

The percentage table only becomes gospel at the moment of truth and not before, since its ever changing numbers do fluctuate. You never want to be privy to, after doing the wrong thing, to cry out “flucked again”.

David WarheitMarch 16th, 2015 at 6:58 am

Jim2: the problem with your analysis is that all possibilities are not equal. For instance Jxxx & xx is twice as likely as Jx & xxxx. Proof: there are 5 ways to hold Jx (the J with each of the 5 other cards), but there are 10 ways to hold Jxxx & xx 5 ways to hold one x and 4 ways to hold the other which is 20, but divided by 2 since, for example 63 is the same as 36 so the total is 10. So our host is absolutely correct when he says the 2 lines are virtually equal. What one needs to do is look for any clue, no matter how small, which might shift the odds one way or another and then go with that.

On our host’s example of Q10 opposite AKxxx, cashing Q then AK works if righthand opponent has stiff J or Jxx. Finessing 10 works if lefthand opponent has the J, except for Jxx where either line works. So obviously, finessing the 10 is much better than the other line.

jim2March 16th, 2015 at 12:40 pm

David Warheit —

I laid out the number of “cases” specifically to address the relative frequency of each layout.

I did not address at all the Q10 example in my previous comments, but do note that no line of play succeeds if either opponent holds the singleton J.

Peter PengMarch 17th, 2015 at 4:00 am

gracias, Jim2 and Bobby
no second negative in our system…

Mircea1March 17th, 2015 at 10:42 am

If this thread is still alive, I would bring in my 2c contribution. Being a computer person, I try to use these devices anytime I can in bridge. SuitPlay is an excellent utility that calculates precisely the odds of playing a specific suit for a specific number of trick. It works very well, I’ve been using it for years. Google it: SuitPlay (one word)