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How's My Plan?
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This was an interesting play problem at the weekend, and a 'textbook' one in the sense I thought for a very long time at trick two and then played the rest of the hand quickly.I thought I would explain my thought process at the table and let you pick holes in it.

You are playing the one-day final of a national teams event. 8 teams have qualified and you play 8 boards against each team, IMPs converted to VPs. Opponents on this hand are not world champions, but they are strong players who have played on their countries’ open teams. Their style is to open most balanced 11-counts.

North
J97652
K6
Q96
A10
South
A
QJ84
AK5
Q9862
W
N
E
S
P
P
P
1NT
P
2
P
2
P
3
P
3NT
P
P
P

1NT = 15-17. It is legal in England to agree to open 1NT with a singleton. Your partnership agreement is ‘infrequent butOK, usuallywith singleton honour, if the hand otherwise looks like a strong NT’.

3 =game forcingwith 6 spades

3NT = bottom 1/3 of the range in context; not forcing. Opponents ask if a singleton spade honour is likely for the 3NT bid and are told it is possible but all soft hands with 2 or even 3 spades may bid 3NT if it looks like a better contract.

Opponents don’t bother asking about inferences from partner not opening a weak 2; a dummy with bad spades and outside honours is what all the players expect.

4 lead (2nd and 4th), 10, 5, 2. In theory RHO’s card is standard count, but he is not a religious signaller.

Plan the play.

North
J97652
K6
Q96
A10
South
A
QJ84
AK5
Q9862
W
N
E
S
P
P
P
1NT
P
2
P
2
P
3
P
3NT
P
P
P

I considered the play as follows:

After knocking out the ace of hearts, I will have 8 tricks. Barring a miracle in hearts, I need a second spade trick or a third club trick.

To set spades up, I need the suit 3-3 or someone holding two honors doubleton. I also need the ace of hearts onside as I need three more entries to dummy (two to set spades up, one to cash them). If my passed-hand LHO has the KJ of clubs and the ace of hearts, he almost certainly does not hold the king of spades, and is unlikely to hold both the SQ and the DJ. If he has a 5-card club suit he would always have opened with 11 HCP; with a 4441 or 4333 this is possible but slightly less likely. If RHO has the ace of hearts then he can hold any combination of the other missing honours and still not have an opening bid (with the exception of hands such as KQx A109xx Jxxx x or KQ10xx Axxx xxx x). It is thus more likely that RHO has the A.

To set clubs up, I need to lose two club tricks. With the ace of hearts to lose, I can’t afford more than one spade loser. When I don’t play on spades, opponents will suspect the position. So I need some good things the happen: either the spade suitis genuinely one loser (singleton K or Q, or KQ), or it is both blocked (Kx/Qx/small singleton) and there is either no entry with the long spades, or I must knock out the right entry first. For example: if RHO has K10xx Axx xxxx xx I need to knock out the ace of hearts before losing any club tricks.

My at-the-table guess at the relative likelihood of the winning spade layouts for each case (3-3 or KQ/K10/Q10 vs the various blocked positions) was that they were roughly equal. (Subsequently I have calculated the a priori odds and I think they are indeed similar.) A straight odds calculation doesn’t account for (i) having to guess which entry to knock out first, or (ii) any inferences from the club break and opponents not having an opening bid. The latter are both very hard: KJxx is an unattractive lead compared to 3 low or 4 low hearts, which makes 5-1 clubs more likely (and 3-3 spades less likely); but if LHO does have four spades they may have fewer attractive suits to lead elsewhere. The conditional probabilities of the various layouts based on no-one opening make this even harder.

I thought this was all too difficult to calculate exactly, but that the probability of the A being onside was sufficiently low that I should work on setting up clubs.

North
J97652
K6
Q96
A10
South
A
QJ84
AK5
Q9862
W
N
E
S
P
P
P
1NT
P
2
P
2
P
3
P
3NT
P
P
P

I cashed the ace of clubs. RHO followed with the 3 and LHO with the 7.

All things being equal, with clubs 4-2, the likelihood is that the spade length is on my right, therefore I should play a heart first.

There is another reason to knock out the heart entry first. I know that RHO cannot usefully duck the K, because if I play a second heart he has to duck that as well (or I have 9 tricks) and then I am a tempo ahead. There’s always the chance that, not knowing the full hand, he ducks the K.

If instead I want to start on clubs, I have to cross on diamonds to play a club. Now I wonder if I could be in danger of losinglong diamond tricks. Diamond to hand, club, diamond, club, diamond sticks me on table. king of hearts ducked (say), heart to the queen and ace, diamond cashed… but I have 9 tricks and only four losers. So this is only a problem if LHO has five diamonds, say, x Ax xxxxx KJxxx as I don’t believe he would lead from KJxx in clubs instead of Jxxxx diamonds. The alternative of having the heart suit set up against me by playing on hearts is only a risk if LHO is 5-5 in hearts and clubs. This is also possible, but the 8 gives some protection e.g. against A9/9x or A10/10x on my right, and a 5-card heart suit is very likely to have been led.

At the table, I didn’t manage to work this fully through as my brain was threatening to explode.I saw the two reasons to start on hearts andlost track of whether or not there was a potential problem in the diamond suit.

I next played the king of hearts from dummy - so the play so far has been club to the 10, ace of clubs, king of hearts.

To recap, I was playing for LHO to have something resembling

Qx

xxx

Jxxx

KJxx

and RHO to have a hand such as K10xx Axxx xxx xx

RHO thought for a while on the king of hearts (and I’d already spent a long time thinking before playing to trick 2 as well as a short pause at trick 1). He eventually took the heart and … played a second heart. I won, conceded a club, won the heart return (all following) andconceded a club. LHO cashed the fourth heart and I claimed.

Just another well-played hand?

Well, yes and no. RHO had Q10 A10x 10xxxxx 53. My analysis was correct but I played the wrong suit first. RHO then misdefended by not switching to spades.

In the brief postmortem at the end of the match RHO said his spade holding was so bad that he thought it was pointless playing one while if I had QJ8x of hearts it was a good idea to play a second heart through to stop a possible endplay. Perhaps I had Kx QJ8xAKx QJxx (or K QJ8x AKxxQJxx) and was about to go off of my own accord. This analysis may not entirely stack up, but it’s not obviously stupid.

I don’t know if they discussed the defense in any more detail later. However, it’s a useful reminder that what may be clear to declarer is not so to the defense: I thought I obviously had a singleton spade because I wasn’t playing on them, but that wasn’t obvious to East.

I have also reconsidered my line while writing this article. I did some of my thinking at the wrong time: having decided to play on clubs, I should cash the ace and only then think about which suit to play on. When clubs are 4-2, the 4-card spade suit on my left is actually more likely as with only 2 spades LHO has a 4-card red suit and might have led it. In fact, with LHO’s actual hand (K8xx 9xxx J KJ7x) I think a heart lead is a live possibility … but against that the bad spade pips argue in favor of a more aggressive lead (imagine Ax opposite Q109xxx with partner’s singleton J dropping).

At the other table, North opened a Norwegian 8-11 2S and they bid 2-2NT-3NT-Pass (max high cards, bad suit). A club was also led and declarer went off playing on clubs. I’d like to say my teammates defended brilliantly but declarer used the ace of spades as his first entry. Teammates defended sufficiently well in that West did think to play a second spade while he still had a club entry.

What are the morals of this hand?

- Opponents do not always defend perfectly (we all knew that already!)

- Some calculations are too hard, and too subjective (When would Westlead from a 4-card club suit? When would East open in 3rd seat?) to do at the table

I am sure the armchair critics can explain exactly why East was wrong, and why I should have got the hand right. Once you start thinking about a hand in a particular way it can be hard to see alternatives – you get caught thinking down one particular route - so all comments on what was missed are welcome.

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