Law of Total Tricks

The Law of Total Tricks (LOTT)

Question: when do you use it?

Answer: It is most useful when you and partner have a probable part score or lower  pair of hands, and a trump fit and may be contemplating a raise to a higher contract in competition where opponents also have a trump fit in another suit. It can be used for preemptive purposes or for a raise (which may or may not be a sacrifice). You should ideally have at least 9 total cards in the suit you want the contract to be in between you and partner. Do not use it for very weak hands (unless you have a very long fit) or very strong hands (you need other evaluation methods).

In a nutshell: The simplified form of LOTT says that you can usefully bid a suit contract to a particular level by assuming you can make the same number of tricks as your total count of the cards in that suit. This means you can sometimes bid to a high level even if you don't have the constructive points to justify it.

Caution: LOTT is very effective for competitive bidding, but you can get more out of it if you use cuebid limit raises in your bidding.

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When do I use it again?

These are the most common occurences

• Case A (pre-empt). Based on the bidding, and what you see in your own hand, you believe the opponents have a game or slam contract. You want to bid high quickly to preempt them from reaching the optimal contract for themselves.

• Case B (part score competition). Based on the bidding, you believe that you and your partner have a combined total of 17-23 HCP, but a good fit in a suit. Your opponents also have 17-23HCP and probably have a fit of their own as well.

The formal definition /  References

Literally entire books have been written about this. For expert players, the nuances can matter. Fortunately, for the rest of us mortals, a simplistic treatment is possible - that's what I use. You may skip this section if you want.

First though I want to get the formal definition out of the way and point you to a few references. There's plenty out there on the internet.

Formal definition

The total number of tricks available on a deal is equal to the total number of trump cards both sides hold in their respective best suits, where the total number of tricks is defined as the sum of the number of tricks available to each side if they could choose trumps. 

Goobledegook right? 8-). Don't worry too much about it. I will simplify it for you later.

Some References

• https://en.wikipedia.org/wiki/Law_of_total_tricks

• https://www.bridgebum.com/law_of_total_tricks.php

• https://kwbridge.com/law.htm

The simplified version that you will use

In a very common competitive situation, you and your partner have a trump suit fit. Your opponents also have a trump fit. In some cases, opponents have only bid once, but you can strongly suspect they also have a trump fit if you are short in their suit.

You can safely bid to the level of the number of tricks you have. e.g. if you have 9 cds in the suit, you can bid to 3 level, with 10 cds, 4 level.

That doesn't mean you can make the contract, but on average, you will arrive at a satisfactory result if the opponents let you have the contract. Sometimes you will make, and sometimes you may go down 1 trick but it will have been worth the sacrifice.  Just treat it as "magic" 8-)

Case A (preemptive)

You may already have used LOTT unintentionally when you did something like below. This is something taught in basic SAYC, but not mentioned by name.

Your partner bid 1H. You have <10HCP, but 5 hearts. You immediately bid 4H over the opponent's 1S overcall.

As south, you only have 4HCP. But the key facts are:

• If your partner has an opening hand of 13HCP, you and partner only have 17HCP.

• Your partner has 5 hearts, and so do you. 

• The above 2 mean that this makes it even more likely that opponents have only 0-1 losers in your suit if the contract is in spades. i.e. your opponents may make 4S even with relatively few HCP (e.g. 20), and even if your partner was stronger than 13HCP.

Applying the simple version of LOTT, you count 10 hearts, and think there's a reasonable chance to make 4H or worse case go down 1-2 tricks. This is better than opponents making 4S. You then pre-empt the opponents by bidding 4H (you don't even give West a chance to bid spades at a relatively low level).

Here is one more example of case A.

Your partner opened 2H, showing 6 hearts, 5-10HCP. You have 4 hearts and 7HCP. East has doubled. You and partner have a total of 12-17HCP only.

The likelihood is that opponents have a game or even slam.

To apply LOTT, you realize that you and partner have 10 hearts between you. Immediately jump to 4H to try to confuse the opponents. You may not prevent game, but perhaps you can prevent a slam.

Case B (part score competition)

A more common case is when you and partner have 8-9 cards in a suit together, and you estimate that you and partner may have 17-23HCP between the 2 of you. You then use LOTT as a secondary method of evaluation to decide how far you can raise.

Note that if opponents bid only to the 2 level and look like they are going to pass, this is a clear case where opponents have about 17-23HCP. My regular partner likes to say "Find an excuse not to leave them at a 2 level contract" - that's a general statement that is not wrong a lot of the time.

Scoring (brief note)

A part score made is typically 100+ points - for example 2H+1 scores 140 pts. 

if you are vulnerable and go down 1 trick, that's -100 pts. That's still better than opponents scoring 140 pts. you will come out better in duplicate tournament results! if you are non-vulnerable, and go down 2 tricks, that's -100 pts as well! Your opponents are unlikely to double you for penalties unless its an extreme situation.

In short, if you think that you and opponents are competing in part score, you can afford to go down 1 trick vulnerable and 2 tricks non-vulnerable. Be more aggressive when non-vul.

Competitive bidding

You can use your knowledge of the relative scoring and LOTT to compete better in competitive bidding when the likelihood is a part score, and both you and opponents have a trump fit each (or likely to have a trump fit).

You only have 4HCP, but 4 hearts. First, you make an initial estimate that 9 tricks is possible in a heart contract based on LOTT, even though you don't have the points.

Therefore you bid 2H even though you only have 4HCP + 2 distribution points. Then West bids 2S and East passes. At this point you should realize that opponents probably have around the same or slightly higher strength than you and partner. 

You can then choose to compete further by bidding 3H. It's relatively safe. It's probably the opponents spade contract anyway. if you force them higher, its possible they'll go down. If they let you play, going down 1 trick is better than letting them make 2S+1.

Note that if you have a cuebid limit raise in your agreement, you can go further by immediately bidding 3H instead of 2H first. That is outside the scope of this article.

Conclusion

The simple way to look at LOTT is that you can bid a suit contract as high as the total number of tricks you and partner have in that suit (9 tricks or more is better, but 8 is ok.). You will either make, or prevent opponents from making a better score.

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