The Venue: Rio De Janeiro - the Bermuda Bowl of 1979. Lets place you in the driving seat of decision making. You hold (non vul against vul), as west. The following hand: J93, Q86, A743, A53. On your left, opening is 1D, your partner overcalls 1H, your RHO bids 1S, you raise to 2H, LHO now bids 3C, which is passed over to you in the last seat for decision making. What is your bid?
Do you bid 3H or not? Well if you did, you are at the wrong side of the stick - 2 down for - 100 instead of the sure 3C one down + 100 positive score - a difference of mere 5 imps no doubt but such small margins can add up against you to cost you the match. Let us now analyse the decision making process in the text of the law of total tricks to rid you of the uncertainty and hesitancy that you face in such situations.
The law of total tricks states that if both sides have found a fit in their respective suits, then the total number of trumps that both sides hold in each of their suits shall equal the total number of tricks available for both sides barring a few unusual situations where your assumption needs minor negative or positive adjustments.
In other words say if EW have a 9 card heart fit and NS a 9 card spade fit then assuming a 18 trump 18 trick arena, if EW can score 9, so can NS and therefore if EW bid on to 3H, at the level of their trumps holdings for example 9 trumps equalling 9 tricks, law of total tricks dictates to always outbid the opponents on the three level with 18 trumps. Hence to bid 3S over 3H in such a context would give you + score but assuming say 17 trumps, it is usually still right to outbid them on the three level for don't let them play at the level of their total trumps.
Of course you must keep the vulnerability in mind and the form of scoring too. The law of 16 tricks however is more common in a typical 8-8 situation that keeps coming all the time. Here the strength is evenly divided between NS and EW as both sides have 8 trumps. Once one side gets to the 3 level, it is not good bridge to bid on, for you will always be losing on the logic of the law of total tricks-chart of 16 trumps as under:
Irrespective of location of high cards, total cards count shall be constant ie total number of tricks never change. 17 total tricks chart is relevant as under: From the above, no matter how 17 tricks get split, scores on left side of the chart always produce better results then the right side. What does it tell us then? That we should compete to 3H over 3D, if we believe there are 17 trumps, not otherwise.
Coming to our hand now in the light of the above knowledge that you have gained, how many hearts does partner, promise? Probably 5, as with 6 he would have himself come to 3H over 3C. So total trumps for you are 8 and probably in clubs, there trumps are barely 5+3 = 8 making 16 total tricks, which makes a 3 level bid on their part already an overbid which needs to be passed to give you a positive score surely.
Let see the actual layout now of all 4 hands: East was held to 7 tricks 2 down for bidding 3H - 100 instead of + 100, if he had passed out 3C, there were in fact only 7 trumps for NS, not even 8, and therefore they would have suffered a 2 tricks set if left on their own.
In future in such situations, you would make a wiser and a more correct decision wouldn't you? And bid better then Passel of USA who bid the erroneous 3H against his LHO-the great Italian BellaDonna. Perhaps Passel did not have faith in the theory of the Law of Total Tricks which left his judgment down. But I hope you keep faith in the Law of Total Tricks and score positively on your judgment based on that law. Better luck next time.
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North West East South
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A2 J93 Q106 K8754
105 Q86 KJ932 A74QJ86 A743 K9 1042
KQ972 A53 J86 74
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Chart of 16 total tricks:
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We play hand in They play in
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2S 2H
Our number of Their number of
total tricks plus score total tricks plus score
Tricks 8-our score + 110 Tricks 8-our score - 110
Tricks 9-our score + 140 Tricks 7-our score + 50
Tricks 10-our score + 170 Tricks 6-our score + 100
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We play the hand in 3H They play in 3C
Tricks 9-our score 140 + Tricks 8-our score + 50
Tricks 10-our score 170 + Tricks 7-our score + 100
Tricks 8-our score - 50 Tricks 9-our score - 110
Tricks 7-our score -100 - Tricks 10-our score - 130
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