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This follows my recent question about how to bid a small slam in clubs with <30 HCP; but this time the partnership only had 25 HCP in toto (board 15 TCG). The optimal contract was 6 diamonds by West; but even fewer couples bid and made that compared with the 6 club slam in my previous question. In fact, only 1 of 1807 partnerships bid and made the small slam in diamonds.

My partner and I bid 3 diamonds; but in fact ended up making a total of 12 tricks. East opened the bidding with 1 club and West responded with 1 diamond. East responded with 3 diamonds, which jump raise by Opener is usually forcing in our partnership. West chose not to be forced and ended up playing 3 diamonds. There were no intervening bids by our N-S opponents. enter image description here

My question to you, gentle reader, is how would you bid this hand in order to end up in a small slam contract of 6 diamonds by West. Should East have shown his strength (17 HCP + 2 shortness points for the singleton heart) more forcefully ? Should he have indicated an interest in slam investigation with a control-showing cuebid bid during the second round of the auction. I look forward, as usual, to reading your comments, criticisms and words of wisdom.

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    Looking at just the E/W hands, 6!D has about a 20% chance of making. So you don't want to be in it (unless you've peeked at the N/S cards). At matchpoints, you should be wondering about how to get to 3N. With my preferred bidding system, it would go 1D-3C(*)-3S-3N (where 3C shows 7-9 high card points and 5+ diamonds)
    – Alexander Woo
    Commented Mar 15, 2019 at 23:43
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    Without the 3C gadget, I would suggest 1D-1N-2N-3N or 1C-1D-1S-1N-2N-3N or 1C-1N-2N-3N. If South opens 2H (which some will), I think you'll get something like (2H)-P-(3H)-X-(P)-3N (yes that double is for takeout)
    – Alexander Woo
    Commented Mar 15, 2019 at 23:50
  • @AlexanderWoo: Please don't put answers into comments - especially good ones!
    – Forget I was ever here
    Commented Mar 16, 2019 at 12:21
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    Making or not, if you find yourself wandering into this low-odds slam you should be asking why your bidding system, or perhaps use of it, is preventing you from stopping in 3 or 4 NT on a minor-suit fit. Finding this slam indicates a flaw, not a strength, of your bidding system.
    – Forget I was ever here
    Commented Mar 16, 2019 at 13:11
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    Lack of entries to West , and the need to preserve them for other suits, makes odds of avoiding the diamond loser 53% (40% to be 2-2, 13% to be singleton Q). Then odds of finding Club Q is 50%, providing a place to park the second Spade of West's. Then you need to avoid two Heart losers, either because Diamonds were originally 2-2 (40%) or the Heart A and Q are split (50%). Total odds are then about 53% * 50% * 70% = 19%. Perhaps there is a small additional chance in there somewhere, but 6D is NOT a contract you want to be finding frequently.
    – Forget I was ever here
    Commented Mar 16, 2019 at 16:28

2 Answers 2

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Looking at just the East West hands without looking at the North South hands, 6D is a fairly poor contract. It has only about a 20% chance of making unless you have peeked at the North South hands.

There are a number of choices that East/West can make during the bidding, but all of them should end up at 3N.

Possible auctions (depending on various subtle differences in partnership agreements and player judgement, all of which are playable) include:

1D-1N-2N-3N

1D-1N-2S-3D-3N

1D-2D-2S-3N (if not playing "inverted minors")

1D-3C(*)-3S-3N (inverted minors with a 3C mixed raise - I've also seen partnerships that use 2S or 2H instead of 3C for this purpose)

1D-3D(*)-3S-3N (inverted minors without a special mixed raise)

1C-1N-2N-3N

1C-1N-2S-3N

1C-1D-1S-1N-2N-3N

The calculation of slam success (thanks to Forget i was ever here) is as follows:

  • You need to guess who has the club Q so that you don't lose a club trick. This is 50%.

  • You also need to avoid the diamond loser. If the diamonds are 2-2, then you can ruff 2 hearts in the East hand. There is another way to avoid a diamond loser, which is if the Q is singleton. In this case, you need a heart finesse to work to avoid a heart loser, and whichever heart finesse you choose to try is 50%. This comes out to 40% + 1/2*13%, so 47%.

Total odds are then about 50% * 47% = 24%. This isn't exactly correct, as there are a few additional unlikely chances to make the contract as well as a few other unlikely chances for it could go down, but 6D is NOT a contract you want to be finding frequently.

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  • Feel free to edit my addition to suit your style; or to remove it if desired.
    – Forget I was ever here
    Commented Mar 22, 2019 at 6:16
  • Actually, I think there are 2 roughly cancelling mistakes in the calculation: (1) the avoidance of heart losers and avoidance of diamond losers aren't independent, so you can't just multiply those probabilities, and (2) you can't pick up Qxxx from South and need the heart finesse (regardless of the diamonds) to pick it up from North.
    – Alexander Woo
    Commented Mar 22, 2019 at 18:33
  • There is no need to pick up HQxxx from South; just the need to guess correctly - once only - which of split honours is in South. Of course one can squeeze a little more out of the percentages, but that's close enough to ballpark the overall odds. You are correct on the other point - but I'm doing all this in my head w/o pencil and paper and ust looking to be close; not dead-on. Feel free to edit however.
    – Forget I was ever here
    Commented Mar 22, 2019 at 19:01
  • (I'm checking because I might be the one who's wrong.) If Qxxx of clubs is with South, how do you get rid of the spade loser?
    – Alexander Woo
    Commented Mar 22, 2019 at 19:05
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    oops - i see now
    – Alexander Woo
    Commented Mar 22, 2019 at 20:37
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Six diamonds is an aggressive contract that "makes" by luck. But you should have been in FIVE diamonds.

By rebidding three diamonds, East is showing about 17 points. He actually has 17 high card points, plus another three for his heart singleton. You have eight points (nine, counting your spade doubleton).

You should have taken the "force" to four diamonds. With a bare minimum for this three diamond bid, East might have passed, but he had "extras" (relative to 17), and would then bid five.

You and East have 29 points (counting distribution) and nine trumps (instead of the usual eight). Five diamonds is a comfortable contract.

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