Source: IBPA Column Service JAN. 2020

Tim Bourke
Tim Bourke

**Source: wikipedia. Tim Bourke “is an Australian bridge player and writer. His joint project with Justin Corfield “the Art of Declarer Play” won the International Bridge Press Book of the Year award in 2014.

IMPs Dealer East. Both Vul

K 9 4
A J
A Q 8 2
K Q J 9
A Q J 10 6
8 4
7 6
A 5 4 2
West North East South
3 3
Pass 4NT Pass 5
Pass 5NT Pass 6
Pass Pass Pass

After South’s slightly frisky overcall, North drove to a small slam via Roman Key-Card Blackwood. South admitted to two key cards and the queen of trumps with his five-spade bid, and then denied holding a side suit king by bidding six spades.

West led the 9, which was consistent with holding a doubleton. Declarer took this with dummy’s ace then cashed the king and ace of trumps, thereby discovering the 4=1 break in the suit. Declarer placed West with six cards in the majors to East’s eight.

Using the principle of Vacant Places, declarer knew West had seven such spaces for the king of diamonds compared to East’s five: the diamond finesse was thus nearly a 60% chance to win. While that was a pretty good shot, declarer found a better approach: he led a club to dummy’s king and observed East’s eight, suggesting an even number of clubs. Then he cashed two more rounds of clubs ending in dummy and played the jack of hearts.

East won the queen of hearts and with only hearts and diamonds left had to play a red suit and he chose a heart. Declarer threw a diamond from hand and ruffed the heart in dummy with the nine of trumps. Then, after cashing the ace of diamonds and ruffing a diamond, declarer claimed twelve tricks: five trumps, a heart, a heart ruff, a diamond and four clubs.

Why did declarer take this line? He said it was by general reasoning that, as there are five cards unknown in the East hand, the odds strongly favour the minor suits being 3=2 or 4=1 rather than 2=3 or 1=4. In fact, declarer was correct, the odds were slightly better than two to one that East would have at most two clubs. There was also the additional indication from East’s carding, for even defending against a slam, most people tend to tell the truth.

The complete deal:

K 9 4
A J
A Q 8 2
K Q J 9
8 7 3 2
9 2
10 9 5 4
10 7 3
5
K Q 10 7 6 5 3
K J 2
8 6
A Q J 10 6
8 4
7 6
A 5 4 2

WIKIPEDIA: In the card game bridge, the law or principle of vacant places is a simple method for estimating the probable location of any particular card in the four hands. It can be used both to aid in a decision at the table and to derive the entire suit division probability table.

At the beginning of a deal, each of four hands comprises thirteen cards and one may say there are thirteen vacant places in each hand. The probability that a particular card lies in a particular hand is one-quarter, or 13/52, the proportion of vacant places in that hand. From the perspective of a player who sees one hand, the probable lie of a missing card in a particular one of the other hands is one-third. The principle of vacant places is a rule for updating those uniform probabilities as one learns about the deal during the auction and the play. Essentially, as the lies of some cards become known – especially as the entire distributions of some suits become known – the odds on location of any other particular card remain proportional to the dwindling numbers of unidentified cards in all hands, i.e. to the numbers of so-called vacant places.

The principle of vacant places follows from Conditional Probability theory, which is based on Bayes Theorem. For a good background to bridge probabilities, and vacant places in particular, see Kelsey; see also the Official Encyclopedia of Bridge

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