More often than not declarers in bridge are confronted with a monumental decision on which hinges the fate of the contract. It is only in these do-or-die situations that the above average player uses his wits and knowledge about probable ratios, percentage plays and plain common sense to his advantage in making a decision that invariably in most of the cases come out in his favour.
It is not that declarers have hindsight to know the feel of the cards and therefore by intuition, that they can tip the balance in their favour. On the contrary, such declarers rely more on specific data available and make the best use of it, as did the declarer in the following hand, playing 3NT on a club lead of KC after east had opened IC.
There is no need to give the E-W hands. Only the N/S hands will suffice in today's problem for the declarer to make 3NT. The contract is 3NT after east opened IC and south bid 1NT, which was raised by north to 3NT. East began with KC, AC, and JC to declarer's QC, with west discarding a heart on the third club.
One look at the dummy and we have our problem neatly cut out. There are 4 solid diamond tricks, one QC already taken and 3 solid spade tricks making a tally of 8 tricks. The declarer has little chance of developing a heart trick, although he has the KH in hand and QH in dummy, for the simple reason that east is poised to take his remaining 2 club winners from his 5 card club holding. There is little doubt at all that east would not open 1C without holding the sure shot AH which would be his entry to run the clubs.
The fact that knowing that south held the QC, east was yet in a hurry to yield that QC winner to the declarer to enable him to run his club suit to his advantage clearly marked AH with east, and leaves no other option for the declarer than to decide either to run the spades relying on a 3-3 break or take the finesse of the JS through west towards the K10 in the hope that spades are not breaking 3-3 but are rather 4-2 which odds, according to the standard percentage table, are more favourably inclined for the 4-2 break.
For in Bridge, a simple rule to remember, avoiding the more complex a prior tables and percentage calculation is that when the opponents hold even cards in any suit, the chance of the suit break is more odd than even, and vice versa, ie if the opponents hold odd number of cards in any suit, the chances of break in that suit are more even than odd.
To take a simple illustration, suppose N-S hold 8 cards between them and need to find the queen of that suit with the opponents, the tables of percentage will show that with 5 cards of the suit lying with the opponents, that is odd distribution, the cards will break as evenly as possible, meaning 3-2. But with say 6 cards out, the odds favour a 4-2 division, an odd break on an even holding of cards.
Coming back to our problem in this context, how do we make 3NT? Here the spade distribution is 4-3 with the declarer having 6 even cards out and therefore the break reliance should be more inclined towards a 4-2 division rather than a 3-3 break, clearly favouring the finesse of the JS after south runs with 4 diamond tricks and plays the A & Q of spades with both opponents following with low cards. On the third spade, west follows low and the critical point of play has been reached.
The point I wish to convey to my readers is that in bridge, you have to gather all clues before taking the final plunge. At this point of play, from the bidding you know east started with 5 clubs, and has followed to three diamonds as has west with diamonds breaking 3-3.
On the fourth diamond, both defenders pitched a low heart. So east has shown up with 5 clubs, a low heart, 3 diamonds and followed to 2 spades. Thus 11 cards have been accounted for. The 12th card is surely the AH leaving him with the illusory 13th card which could either be a heart or a spade. It is in such situations, knowing the probability table that spells a 4-2 break, that the declarer can use the common sense variant of the "vacant places" method.
From our knowledge of east's sure holding of 5 clubs, and 3 diamonds, plus ace of hearts and 2 spades followed yielding 11 places, the vacant position odds with east are only 2 to hold JS, compared with west's known 3 diamonds, two heart discards, on the third club and fourth diamond, followed by 3 spades, coupled with 2 clubs, yielding 10, leaving 3 vacant positions. Thus, there is no harm in tipping the balance in favour of the finesse of JS.
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North South
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K1064 AQ5
Q83 K74
AJ74 KQ6
82 Q764
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