Ray Lee

Going with the Odds

Having just finished editing Bob MacKinnon’s forthcoming book, Bridge, Probabilty and Information, I think I may be more sensitive to these issues and ideas.  For whatever reason, my eye was caught by this deal which came up in the BB semifinal this afternoon.  The deal is rotated for convenience:


China’s Wang Weimi heard Zia open a Flannery 2 on his right.  He passed, Hamman bid 2, and North chimed in with 3.  South took a punt at 3NT, and the lead was the 5.  Clearly the key is guessing diamonds.  Playing all out you win East’s K with the A, and cash the A.  Everyone follows, so no 4-0 breaks.  You cross back to the A, and play another diamond, to which West contributes the last outstanding small card.  You know East started with 9 cards in the majors: does that mean you should finesse?

There are 3 ways to analyze this decision as far as I can see:

1) It seems that spades are 4-4 and hearts 3-5, leaving 2 more Vacant Spaces in the West hand.  Other things being equal, you should therefore finesse.

2)  The a priori odds are 50% for a 3-1 break, 40% for 2-2.  Of course, we are only interested in the 3-1 breaks, since 1-3 won’t help us. But the odds aren’t 40-25 in favour of the drop, because the order in which the spot cards are played reduces the number of possible combinations and therefore the 2-2 probability.  Actually, we are all familiar with this answer: it’s 52-48 in favour of the drop.

3) However, so far we’ve looked at diamonds in isolation — which is wrong.  You need to look at both minors together.  Is it more likely that clubs are 4-2 and diamonds 2-2, or clubs 3-3 and diamonds 3-1?  The two suits are not independent of each other.  My arithmetic (Bob, please post a comment if I’ve done this incorrectly) gets me to 9.6:9 in favour of 2-2 diamonds — about 7%.

4)  Yes, I know I said 3 ways, but the final piece of information you have is that East opened the bidding and 18 HCP are missing.  Looks like West has the Q, and East certainly had the K.  Give him even a minimum 11 for his opening, and he needs 8 of the missing 13 HCP — 8:5 odds that he has the Q.

So IMHO, (3) and (4) being the most compelling arguments, the odds favour playing for the drop, which is what Eric Rodwell did in the Closed Room, while the Chinese declarer took the finesse in the Open Room.  Granted, Rodwell had a slightly different auction but not much:  East opened 1 and spades were known to be 4-4, so declarer was in fundamentally the same position.  Now bridge is one of those annoying games where making the right play is no guarantee of victory, but on this occasion virtue was rewarded.  Diamonds were 2-2, and USA picked up a game swing as they steamrollered to a 57-IMP pickup in the set, and an overall lead of 83 IMPs after only 32 boards.

Can a 96-board match be over this early?  It sure feels like it.


Nigel KearneySeptember 9th, 2009 at 6:56 am

Just considering known distribution but not HCP, surely vacant spaces makes the finesse better by a ratio of 4:3. I don’t understand your point 3 but perhaps you can elaborate on it.

Re point 4, I would be inclined to place both spade honours in East since West preferred hearts on Qxx when holding 4 spades. So East has KQxx KJxxx in the majors. If Qx of diamonds and two small clubs is not an opening bid then East has a club honour as well. But in that case East also has an opening bid without the queen of diamonds as he is at worst KQxx KJxxx x Qxx. This is quite speculative but, depending on style, having the queen of diamonds may actually make no difference to East’s ability to open the bidding here.

I tend to think the Chinese declarer was right to finesse.

Ray LeeSeptember 9th, 2009 at 8:12 pm

I got a chance to ask Rodwell today what his reasoning was. He told me he had thought about it for a while, and decided that there were far more opening bids for East which included the DQ than ones that didn’t — my point 4. He was, as I suspected, pretty sure East was 4-5 in the majors, even without the Flannery opening.

Point 3 is one that Bob will make at length in his forthcoming book: you can’t look at suits in isolation. In other words, if diamonds are 2-2, then clubs have to be 4-2, and if diamonds are 3-1, clubs are 3-3. Thus you have to look not just at the a priori odds of the diamond break, but at the odds that the two suits will lie in exactly that way: the club odds affect the likelihood of each diamond break.

ross taylorSeptember 10th, 2009 at 1:01 pm

Rodwell’s point is certainly valid but the 8:5 argument put forth by Ray and Nigel’s points above make this a toss up it seems. The winning play can often be found only “at the table” where there are vibes and contexts that the reader in isolation is not privy too.

Credit to Eric for getting it right. That’s what counts.

Gad ChadhaMarch 12th, 2010 at 1:23 pm

Is this book ‘Bridge, Probabilty and Information’ now available?

Ray LeeApril 27th, 2010 at 3:47 pm

Sure is.

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