[NickRW]

This is something similar to a hand I saw the other day and features I play I don't recall seeing in basic books - but is not too hard to work out - so a clever beginner should be able to get it:

Scoring: MP

---

Opps have competed in hearts and (rightly or wrongly) allowed you to buy the contract in 3♦. They begin the defence with three rounds of hearts - how do you propose to tackle this hand for maximum benefit to your side?

Adv+ - unless I've overlooked something I think this is easy enough - let the intermediates and below have a go.

Nick

[vuroth]

I would

Spoiler

ruff, pull trump and concede a club. Should give me chances for 3/3 club split to pick up an extra trick, or finesse if a club honour falls out of LHO's hand.

[quiddity]

You might also be able to ruff the 4th club in dummy, depending on how many rounds of trumps you draw...

[quiddity]

Since no one else is biting, I have a follow-up problem. I can think of two possible lines. They both start with ruffing the third heart and cashing a top trump. Assume the T does not appear (otherwise dummy's trumps are high and the fourth club can always be ruffed). Then a club is ducked, both opponents follow and no honor appears. A spade is returned, won by dummy's ace, and a second high trump is cashed. Someone shows out (if diamonds were 2-2, again the fourth club can always be ruffed).

Line 1: Draw the third trump and play a club to the ace. If LHO follows with an honor, lead a third club to the T. Otherwise lead a third club to the K.

Line 2: Play a club to the ace and a club back to the king. If clubs are not 3-3 (and the T is not good), ruff the fourth club in dummy.

Which line is better and why? Does it matter who showed out on the second round of diamonds?

[hanp]

I will assume the auction has gone 1D - 1H - Dbl - 2H - 3D all pass. This seems relevant.

I ruff the third heart low and play a high trump. I'll assume first that both follow, neither with the 10. I duck a club, say a spade comes back (hopefully a count card but I will ignore that). I play one more high trump. If both follow I can claim. If LHO shows out I think my best chance is to play ace and king of clubs, hoping RHO has 3+ clubs.

However, if RHO shows out on the second trump then this would be a bad choice. LHO is not 1534, that would give RHO a 7-card spade suit. Instead it seems best to draw all trumps and hope LHO started with Hx in clubs.

I'm guessing this is not the solution that Nick had in mind.

[NickRW]

hanp, on Jan 28 2010, 08:55 AM, said:

I'm guessing this is not the solution that Nick had in mind.

Yes, you're getting a little more involved than I had in mind for this section of the board. I guess if I were a teacher and had set this for homework I would have been looking for something along the lines of:

1. We have 9 tricks (1♠, 6♦ and 2♣) [1 mark] and only 3 obvious losers (2♥ and 1♣) [1 mark]. So the contract is not in danger, but it is matchpoints and an overtrick could be vital [1 mark].

2. I ruff the third heart and draw 2 rounds of trumps. If the diamonds break 2-2, we can always ruff the fourth round of clubs even if the clubs don't break 3-3 for the overtrick. [2 marks].

3. If the trumps don't break I can continue playing trumps until I have only 1 left (the defenders might make a mistake and discard a club) [1 mark]

4. (The main point of the problem) Play K and A of clubs, then lead low to the 10x, playing the 10 if RHO does not play an honour. Anything works when clubs are 3-3, this also works for a 3rd club trick when there is Jx or Qx on my left (they both drop under the A/K) [3 marks].

My feeling is that beginners that have learnt something of how to play NT contracts might tend to duck the first club or perhaps play A then low to K10x finessing the 10 the 2nd round.

Nick

[quiddity]

I agree with Han that, after ducking the first club, if RHO shows out of trumps it is best to play LHO for Hx. If LHO shows out I think it's clear to play for the ruff, since this will provide an overtrick when clubs are 3-3 or when LHO has ANY doubleton (LHO is out of trumps and RHO has 4 clubs).

Nick's line gains when
- LHO has QJx of clubs and RHO has a singleton diamond (not the T)
- the defenders make a mistake on the run of trumps

The other line gains when
- LHO has xx of clubs and a singleton diamond (not the T)

Did I miss anything?
At this point I'm stuck. It looks like Nick's line gains in 12 specific cases (4 cases of QJx * 3 cases of singleton diamond) and the other line gains in 18 specific cases, but these might not be equally likely. How should I continue?

[jdonn]

I'll ignore trump breaks worse than 3-1 and club breaks worse than 4-2 for simplification.

Nick gains when LHO has 3 trumps and Hx of clubs. Han gains when either player has 3 trumps with any 4 clubs. In both cases you can ignore QJ of clubs since both players make, and you can ignore singleton ten of diamonds since after one round you would then play three rounds of clubs to easily ruff the fourth.

Anyone want to do a quick calculation on those two events? Han covers 2 holdings to Nick's 1, but Nick's holding is more likely. My gut says Han wins pretty easily though, since I don't feel the holding Nick gains against is anywhere near twice as likely as either of the holdings Han gains against.

[quiddity]

jdonn, on Jan 28 2010, 01:59 PM, said:

Nick gains when LHO has 3 trumps and Hx of clubs. Han gains when either player has 3 trumps with any 4 clubs.

I don't think this is right. Han is playing LHO for Hx of clubs (by drawing trump and leading a club to the ace) if RHO shows out of trumps.

[jdonn]

Yes I didn't see that he changed his line depending who showed out.