[FrancesHinden]

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South opens in fourth seat:

1♥ - 3♥*
4♣** - (dbl) - 4♥***
4♠ - 5♥
Pass

*about 4-8 HCP, usually 5332 with 5 hearts, might be 5422 with a 5-card side suit, no shortage

**shortage

***unsuitable minimum

South should really have passed 4♥ but didn't.

King of clubs lead

Exercise I: This is an absolutely textbook hand at IMPs: the contract can be 100% guaranteed as long as the opening lead is not ruffed.

Exercise II: This is from the mixed pairs in Philly. What's the right line at matchpoints?

[Simplicity]

At MPs it just looks right to cash the ♠A, eliminate clubs and play a spade to the jack. That makes 12 tricks with Q third or Qxxx onside immediately which is around the 20% mark? Meanwhile we are in danger of going off only when LHO has ♠QT9x and a diamond honour.

Nice book problem at imps.

[helene_t]

I eliminate clubs and trumps, and then:
IMP: spade to the 8
MP: diamond to the 10.

[ceeb]

MP: Same as IMP, play absolutely safe (because the contract is 5♥, but gamble if it were 4♥).

On trick expectation gambling for 10 tricks or 12, versus safe for 11, is obviously a somewhat close question

By my calculation the best gambling line is strip then spade finesse, 21% for 12 tricks and 18% for 10, but the exact result doesn't matter, only that it's close enough that, correctly (which I think it is) or not, some 4♥ declarers will gamble.

For the sake of MP strategy we can put aside the hands that make 11 tricks and assume the gamble matters. Just assume we make 10 or 12 tricks about equally often, about half of (the relevant) time each.

Against the 4♥ declarers who gamble we are in terrible shape. If we play as they do, we expect only about 1/4 of the matchpoint -- half when making 12 tricks but nothing when making 10 tricks. Comparatively our expectation by playing safe is much better even though it is less than 1/2.

Against the 4♥ declarers who play safe, we would get a slight edge by gambling but not nearly enough to compensate for what it costs us against the gambling 4♥ declarers.

[MFA]

At MP I think it's clear to start:

♣A, heart to dummy, ♣ruff (with ♥A), ♠A, heart to dummy and a spade.

We only have a problem now, if all we have seen so far are three low spades. Otherwise we just hook the J and have west endplayed if it loses.

Hooking the jack anyway (instead of playing the 8) is only wrong if west has all of them; QT9x - and we can't solve diamonds.

If we finesse J and the suit is Tx to Q9xx (or 9x to QTxx) then we have an excellent shot for 12, since we can go to dummy and play a diamond to the T. There is a squeeze coming against east. Finding Qxx in the slot is nice too.

So I think it's clear to hook the ♠J on the second round in all scenarios, (except when east shows out or plays the ♠Q, of course).

[lamford]

Agree with MFA.

[ceeb]

I agree as well. I overlooked MFA's point about the benefit of cashing a top spade, which has the effect that the chance for 12 tricks is double the chance for 10. In terms of matchpoint odds that means that, compared to other declarers who play in 4♥ and find MFA's line we have the identical expectation -- 1/3 of the matchpoints -- whichever line (MFA or safe for 11 tricks) we choose. The edge for choosing MFA's line thus comes from comparison with the remaining declarers in 4♥ or 5♥.