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Hand played on |
May 29th 2008 |
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Board number |
3 |
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Dealer |
South |
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Vulnerability |
East West Vulnerable |
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Submitted by |
Theo Todman, with added comments from Ian Moss, Mike Graham, and Alaric Cundy |
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North ♠3 ♥JT862 ♦T852 ♣T86 |
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West ♠AK762 ♥A9 ♦A ♣AKJ73 |
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East ♠JT4 ♥Q54 ♦KQJ93 ♣54 |
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North |
Bidding:
East |
South |
West |
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♠Q985 ♥K73 ♦764 ♣Q92 |
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No No No No
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2♥ 3♦ 4NT 6♠ |
No No No No End |
2♦ 2♠ 4♣ 5♦ |
When I scored Board 5 in the Blue Section from 29th May 2008 I got the impression there was something interesting about the hand. Results ranged from 3NT three off to 6NT making, with various alternative results in between, including 6♠-1 – the subject of this note. Theo Todman kindly provided a note of events at his table, and Ian Moss and Mike Graham have also provided comments.
At Theo’s table, he and partner arrived in the perfectly reasonable contract of 6♠. Without seeing the North / South hands I’d opt for 6♠ in preference to 6NT any day. However, the play in 6♠ poses some interesting mental challenges involving calculations of odds that are all very marginal… Theo and his partner play a "Benjy ACOL" style, the 2♦ opening being equivalent to a normal ACOL strong 2♣ opener.
Theo wrote:
"North led ♥J. covered with ♥Q, ♥K, ♥A. I have two problems – avoiding losing more than one out of a trump, heart and a club; and getting to Dummy. Anyway, I took the simplifying assumption that trumps were 3-2 and that clubs either broke kindly, or ♠Q was with North. I took the obvious line: cash ♦A, ♣AK, then lead ♣x to dummy. Now the critical decision - ruff high or low? I decided to ruff high, so ♠J, and South's ♣Q dropped and my clubs are good. So, I played ♦K discarding ♥x. Returned to hand with ♠x to ♠A and cashed ♠K revealing the bad break for one off. Oh dear!
'Obviously' I should have ruffed low. Then I just lose one trump. Equally obviously, I was trying to optimise probabilities - if South has only 2 clubs and can over-ruff dummy, he can lead a heart for at least 1 down. However, does it actually ever solve the problem? If South has only two clubs, but cannot over-ruff, then even so I now have a club loser which I'll need to ruff in Dummy, and then communications are pretty awkward. Also, if South only had two diamonds, he could discard one on the club, and then I wouldn't be able to cash ♦K for the heart discard. However, if South has 3 or 4 diamonds, then I can get back to hand with a heart ruff, ruff a fourth club with the 10 and then return to hand with ♠x, when I make my contract if trumps are 3-2.
So, should I rely on a 3-3 club break, in which case ruffing low protects against the 4-1 trump break? The counter-argument is that, even with a 4-2 club break, I can still make the contract if diamonds are no worse than 5-2 and trumps break with the ♠Q with North. It's all a balance of probabilities. These things are a bit difficult to calculate at the table especially when rushed after a slam-auction with the mandatory amount of trancing and subsequent bidding-explanations.”
Comments from Ian Moss
“After AK clubs the odds have changed in favour of a 3-3 break given that some possible distributions are now ruled out - more so when North follows to the third round. Ruffing high assumes a specific 4-2 break with the doubleton with South. Off the top of my head those odds are worse than trumps breaking 3-2. Ruffing high assumes also that North has ♠Q in this case, even so you still have to negotiate the ♣Q and the trumps. If South false cards with ♣Q on the second round you will go down for sure and shake his hand. Or his neck. Ruffing the third round of clubs low looks ok on this analysis.”
Mike Graham commented as follows:
“After ♥A, cash ♣AK; if clubs are 6-0 or 5-1 you are going off anyway. When West follows to the third club, then the 4-2 with East having four is now out as well. There was no interference bidding, so we have no good count of the heart suit. The point is, I think, that if East can immediately over-ruff dummy then we are down. I reckon best is to ruff with the ten, then:
* If clubs are 3-3, take the discard on ♦K and hope trumps are 3-2 (play the ace first in case of singleton queen). * If East discards, play ♦K and hope East has 3+ diamonds (quite likely if he only has two clubs), come back to ♠A and lead another club, ruffing with the jack. Then come back to hand with a heart ruff and play for trumps 3-2. This line succeeds when trumps are 3-2 and clubs 4-2. On the actual hand, of course, you go down.
I fed this hand through Dealmaster and it seems to think that this is the highest percentage line (4% better than ruffing low, playing for 3-3 clubs)”
So Mike supports Theo’s unlucky choice of play. Ian Moss commented on Mike’s comments:
“Here is some more analysis on that hand. The various lines are very similar odds. Basically if you ruff high you are playing for North to hold ♠Q plus some not too unfavourable diamond position, as clubs 3-3 is odds on after 2 rounds. I can’t see that ruffing low is worse and it protects against bad spade break.”
And the final words from Theo:
“Very interesting! Ian has a good point and I think his intuition is correct.
The odds change each time a card is played. It's true that after 2 rounds of clubs, the odds are something like 52-48 for 1-1 versus 0-2, so that the likelihood of South specifically having a doubleton is only 24%. But I think the odds change after North shows up with a third club. By this stage we've played one round of hearts, one of diamonds and 2.5 rounds of clubs, so there are then 9 places in South’s hand that could contain the last club as against 8 in North's hand, so the odds are about 47% that it's in North's hand - i.e. there is a 47% chance that South is now void. There's consequently something like a 23% chance that ruffing high will gain (because I also need the ♠Q with North, another 47% chance). This has to be off-set against the odds of a 4-1 trump break, which is 28% (I probably go off anyway if there's a 5-0 break). There are various other factors, negative or positive - nasty breaks in diamonds or a singleton Queen of trumps with North.
So, on reflection I have to agree with Ian's conclusion. However, I must read Kelsey and Glauert's "Bridge Odds for Practical Players" as it's easy to get into a muddle with all these probabilities!”
For anyone who finds these mental gymnastics too daunting, I have added my own comments about the play of the hand in No Trumps. Having looked at all four hands it is easy to see why there could be such a variation in the outcomes of the hand when played in No Trumps.
If the hand is played by East, then 6NT should always make. If a heart is led, Declarer has no choice but to duck it round to the queen, and when that play succeeds, unblock the Ace of diamonds and play the ♠A followed by a small spade, losing to the Queen. Declarer can now choose 12 tricks out of 4 spades, two hearts, 5 diamonds, and two clubs. In fact the only lead from East that could cause Declarer to go wrong is a spade. On that lead Declarer does best to resist the temptation to run the lead round to the jack, but rather to play high from Dummy, then unblock the Ace of diamonds, and then force an entry to Declarer’s hand by leading small spades off table to allow the unblocked diamond suit to be enjoyed. If the spade lead at trick 1 is run round to the Jack, Declarer will be cut off from the diamonds.
However, if No Trumps are played by West then disaster strikes following the very likely lead of the Jack of hearts. Declarer’s only hope is to play for the Queen of spades falling in two rounds and when that all goes wrong, the roof falls in, and the contract should be held to 6 tricks. As it happens, it is better either
* to play on clubs rather than spades, or
* to concede defeat by immediately giving up a spade and four hearts
However, Declarer can still only get to 8 tricks via either of those routes.
So to summarise, anyone choosing to play this hand in a No Trump contract faces a simple black / white situation: if your bidding has left East as Declarer you should collect 12 tricks, but if West is Declarer you will fail to make even 3NT. But if you want an interesting challenge bid 6♠ instead…