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Law of Total Tricks
Simply stated, the Law of Total Tricks tells us that there is a direct correlation between total trumps and total tricks. For example, if we have a 9-card Spade fit, and they have a 9-card Heart fit, that's 18 trumps, and the total number of available tricks is predicted to be 18 also. It could be 9 tricks each, or 10 for us and 8 for them, or whatever. The Law is far from infallible, but it's a useful benchmark, and it reminds us what we already knew, namely that the more trumps we have, the more we'll bid. Going a step further, we'd also say that many (actually most) 3-level competitive bidding situations are based more on the number of trumps than they are on the number of HCP's. Perhaps these examples will clarify things.
2nd February, 2011 None Vul
East might try some Total Tricks analysis here. He counts West for 6 Clubs, that gives his side 10 trumps, and he counts the opponents for an 8-card fit, giving a grand total of 18 trumps. So, if “The Law” is working well, there will be a total of 18 tricks available: - If N-S can make 9 tricks in 3♠ then 4♣ going down one will be a good result, even if doubled. - If N-S can make only 8 tricks in 3♠ then 4♣ will make 10 tricks for a better score. So, East bids 4♣. As it happens, E-W actually make 11 tricks. As N-S can make 8 tricks it turns out that The Law is out by one trick, but at least it helped East come to the winning decision.
5th August, 2009 E-W Vul
A Takeout Double is not an option here, we don’t do that with a doubleton in an unbid major (unless the hand is really strong, let’s say 18+ or thereabouts). Does that mean that we tamely pass? Perish the thought, that Diamond suit needs to be bid! Of course, you’ll bid 1♦ here, lying about the suit length, and getting into trouble with the disciples of the Law of Total Tricks. But it’s worth all that to get in a valuable lead-director in the (not unlikely) event that West ends up declaring a major suit contract.
2nd July, 2008 Both Vul
West’s 3♥ in this situation is usually based on an extra trump rather than on extra strength, so we can be reasonably sure that there are 17 total trumps. If that translates into 17 total tricks then the chances are that one side can make 9 and the other can make 8. That being the case, and if both sides were non-vulnerable, it would always be right to bid 3♠ here, because either 3♠ makes or else it is a good save against 3♥. With both sides vulnerable, a double of 3♠ would change the arithmetic, but we would bid 3♠ anyway, it’s the bid with different ways to win: - Maybe 3♠ will make - Maybe 3♠ is down one but the opponents won’t double (we do have strong trumps so the likelihood of a Double is correspondingly reduced) - Maybe 3♠ can be beaten but won’t be due to an unfortunate lead or defense
On the actual board, the Law of Total Tricks is out by one, as there are only 16 total tricks, 8 for each side. Does that mean that bidding 3♠ was wrong? Not at all, in practice it worked out just fine, as the defense to beat 3♠ will not be found in real life and 9 tricks will be made.
17th January, 2007 Board 27 None Vul
Perhaps East could have stretched to a 1♠ bid over 1♥, he does have a decent suit with shortness in the enemy Hearts. But Pass was reasonable, and now East must decide whether to come in over 4♥. We’d say “Yes!” Partner’s Double showed some extra values and interest in the unbid suits, so Spades should certainly be playable.
We have no idea what contracts are making here, but it’s a fact of bridge life that it is so often right to bid 4♠ over their 4♥. Let’s look at the Total Trick situation … we have 8 or 9 trumps … the opponents surely have 10 maybe 11 (Partner’s Double suggests no more than two Hearts), so the total trumps are in the 18-20 range. Assuming that the Law of Total Tricks stands up on this deal, and even assuming the worst case of only 18 total trumps, the only time when it will be wrong to bid 4♠ is when both sides can make precisely 9 tricks. So, provided that we do not expect 4♠ to be down three, which seems unlikely, it’s surely worth bidding 4♠.
On the actual board, there were 8 Spades and 11 Hearts. In 4♠ doubled, E-W would escape for down two, a good save against their game. As for N-S, they can make 11 tricks in Hearts, but at least our 4♠ bid put them to the test of whether to double or bid 5♥.
The moral of the story is that when there is an abundance of total trumps (let’s say 18 or more), and when the points are fairly equally divided, it usually pays to push on to 4♠ over the opponents’ 4♥.
24th May, 2006 Board 12 N-S Vul
The Law of Total Tricks certainly suggests bidding one more time … E-W have a 10-card fit, N-S presumably have an 8-card fit … that’s 18 total trumps, so the expectation is 18 total tricks … if N-S can make 9 of them, then 4♦ (even doubled) is a good save for down one … if N-S can only make 8, then 4♦ is making. We would find this logic compelling enough to bid 4♦ here.
Well, the Law of Total Tricks is not a great success on this hand. It turns out that there are, indeed, 18 total trumps, but there are only 17 total tricks, and that both 3♠ and 4♦ are down one. Oh, well!
26th July, 2006 Board 5 N-S Vul
Let's suppose that we make the seemingly obvious call of 3♥. Do we expect to be allowed to play it there? Fat chance! Our opponents always seem to compete to 3♠ in these situations. If they do, we might find ourselves going through this Total Tricks analysis: - They probably have 9 trumps (no guarantees) - We have 9 or 10 trumps - It looks as if there are likely to be 18+ total trumps, so 18+ total tricks - If they can make 9 tricks in Spades (or fewer) then we would be better off bidding 4♥ here.
At this point in the analysis, we should no doubt be wondering why we didn't bid 4♥ directly over their 2♠! Yes, forget the "obvious" call of 3♥ and bid 4♥ instead ... put the opponents to the guess.
On the actual hand, 4♥ turns out to be a poor contract, but it makes, thanks to 2 working finesses. Lucky? Absolutely not! ... if the cards had been less favorable, 4♥ going down would have been a good save against 3♠.
20th February, 2008 Board 5 N-S Vul
In part-score battles, when deciding whether or not to compete further, it’s usually a 9th trump or extra distribution which persuades us to go to the 3-level. As far as South can tell here, her side has only 8 trumps, but she does have that nice singleton in the enemy suit. Does that make the hand worth a 3♥ bid? Considering the vulnerability we would categorize 3♥ here as highly risky. The strong hand is on our left so both of the Kings may be badly placed and we have miserable trump quality. We think that bidding 3♥ is just asking for trouble, and trouble is what it gets on the actual hand when West doubles and the opponents extract a 500 penalty.
16th April, 2008 Board 31 N-S Vul
In competitive auctions, when we cue-bid the opponents’ suit we are generally showing some values and support for Partner’s suit. Here East has the values and he has the support and he also has two cue-bids available. So, what is the difference here between a 2♣ cue-bid and a 2♥ cue-bid? Our own preferred treatment here is to use the cheaper cue-bid to show three-card support, and the more expensive cue-bid to show four-card support. This treatment makes it easier for Partner to judge the auction from a “total tricks” perspective, and it has the added benefit of getting the auction higher more quickly when there is the bigger fit.
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