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The Law of Total Tricks (LoTT) Bidding to the level of your fit

#1 User is offline   Liversidge 

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Posted 2015-February-17, 07:46

This seems too good to be true. According to 'The Law' ( which I don't fully understand in terms of why it works), if you are in a contested auction against competent players, and from the bidding it looks like the points are reasonably evenly split (let's say no side has less than 17 HCP) then it is fairly safe to bid to the level of your fit, regardless of vulnerability or point count. You just bid on combined trump holding.
So if LHO bids 1 and my partner bids 1, and LHO bids 2, I just assume my partner has at least 5 spades, so I just count my spades, and with three spades I can bid 2. With a weak hand and four spades I can bid 2 and then 3 if needed.

From what I understand, you may well not make your contract if left in it, but usually you will come out better off (even if doubled) than if you had let your opponents have the contract.

I appreciate that as I get better I will put more intelligent thought into my bidding than just this, but meantime is this a good device to use to help a novice like me compete more effectively?
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#2 User is offline   1eyedjack 

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Posted 2015-February-17, 07:53

You are sort of on the right track, except perhaps in respect of your comment regarding the values being "reasonably evenly split".

The law only claims to state how many tricks can be made by both sides combined (subject to a tolerable margin of error). What you then do with that information is up to you. If the values ARE evenly split, then both sides can expect to make something approaching the same number of tricks as their respective trump length. That may or may not dictate bidding to a particular level. But even if they are not, then your recommended action MIGHT be the same however the values are split.

Just don't put blind faith in it working every time.
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#3 User is offline   helene_t 

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Posted 2015-February-17, 08:22

Suppose opps bid to 3h and you consider bidding 3s.

If the total number of trumps is 17 you know that either 3h or 3s will make. In either case it must be right to bid 3s. Unless you are vulnerable and they double you and you go down and the rest of the field is not in 4h making their way.

So the general rule is that you should always compete to the level of the fit. And if the opponents bid to the level of their fit you can bid one above your fit level if necessary.

There are some caveats:
- sometimes you can identify situations in which the law is off. Lower honours in opps suit is a negative factor. Double fit a positive factor. For example.
- if you are in a constructive auction your bids will show some values so you can't always bid to the lawful level. You have to consider how partner will take your bid.
- if you think opps may have missed game (or slam) just let them play their pathetic contract even if it is below their fit level
- when competing at the game and slam level you still use the law but you do take the vulnerability into account
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#4 User is offline   ArtK78 

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Posted 2015-February-17, 08:27

View PostLiversidge, on 2015-February-17, 07:46, said:

This seems too good to be true. According to 'The Law' ( which I don't fully understand in terms of why it works), if you are in a contested auction against competent players, and from the bidding it looks like the points are reasonably evenly split (let's say no side has less than 17 HCP) then it is fairly safe to bid to the level of your fit, regardless of vulnerability or point count. You just bid on combined trump holding.

This statement is not true.

What 1eyedjack said is a better statement of the LOTT. The total number of tricks that both sides can make combined in their respective best trump fits is roughly equal to the total number of trumps in the two sides' best trump fits. To say that this means that it is safe to bid up to the level of the total number of trump in your side's best trump fit is another thing altogether.

Assume that you are playing matchpoints. Suppose each side has a 9 card trump fit, and that you are vulnerable and the opponents are not vulnerable. Also assume that the high card values are roughly equally split. And, let us further assume that there are, in fact, 18 total tricks available, so that the law is 100% accurate on this hand. If you just bid up to the three level in your best fit, these are the possibilities:

Opps can make 10 tricks, your side can make 8 tricks. The opps can double you in 3 of your suit and collect +200. You will lose to any pair that does not bid and make game on the opponents' hands. And since we are assuming that the high card values are roughly equally split, this result is likely to be bad for your side.

Both sides can make 9 tricks. In this case, the best you can do is bid up to the three level. If their suit outranks your suit, you will have to sell out to 3 of their suit or risk getting doubled for 200.

Your side can make 10 tricks and their side can make 8 tricks. Here, you want to double the opponents at the 3-level or, better still, if your suit is a major suit, bid game. In either case, bidding to exactly the 3 level in your suit is not the best possible result for your side.

Of course, if the trick making potential is more skewed (11-7 either way) you do not want to be at the 3 level. You want to bid game if your side can make 11 tricks and you absolutely have to avoid getting doubled at the 3-level if your side can only make 7 tricks.

This discussion assumes that the LOTT is 100% accurate, which it is not. There are many hands which have more or less total tricks than the sum of the two sides trump length in their best trump fits would indicate.

So, use the LOTT as a tool, but don't follow it blindly.
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#5 User is offline   aguahombre 

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Posted 2015-February-17, 10:55

It would be very difficult to capsulize two published works plus the thoughts of an influential detractor (Mike Lawrence), in this thread.

The above posters are making a good try.
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#6 User is offline   Liversidge 

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Posted 2015-February-17, 10:56

I have just found a chapter about LoTT in Paul Mendelson's book "Control the Bidding". He describes the LoTT as "tremendously powerful and wonderfully simple". With two caveats he says that "it is very accurate on the vast majority of hands". That sounds pretty emphatic.
Like a lot of guidelines in systems like Acol, novices like me start with black & white rules such as 12-14 HCP for a weak no trump, Rule of 20 etc., and some time later they refine it (downgrades / upgrades). I don't think I'll come to too much harm using this rather blindly to start with, when I consider the sorts of mistakes I might otherwise make, under or over bidding.

Mendelson expresses the Law as follows:
When the points between the two sides are balanced or your side holds the MINORITY of points, you are safe to compete to the same level of tricks as your side holds cards in the longest suit.

The caveats are:
1. Your side is at equal or favourable vulnerability
2. Both sides are playing and defending perfectly (!!)

He adds "in these situations, the combined length of your trump suit is the only factor which should determine to what level you should complete. I really do mean the only factor"

He goes on to say that the same principle underpins 2 level (weak 2) and 3 level preempts. In each case you can expect partner, on average, to have two of the outstanding cards in your suit.

And he says that if partner overcalls the opponent's 1 with 1 and I have four spades, I should go straight to 3 rather than bid 2 and the go to 3 if needed, to cut out bidding space for the opponents.
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#7 User is offline   Vampyr 

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Posted 2015-February-17, 11:39

View PostLiversidge, on 2015-February-17, 10:56, said:

Mendelson expresses the Law as follows:
When the points between the two sides are balanced or your side holds the MINORITY of points, you are safe to compete to the same level of tricks as your side holds cards in the longest suit.

He adds "in these situations, the combined length of your trump suit is the only factor which should determine to what level you should complete. I really do mean the only factor"


You must remember that you can't let the other side play in their own "comfort zone". If you have no reason to expect that total trumps is more than 16, you should still compete to the three level in a lower ranking suit, unless you are vulnerable and think there is a good chance you will be doubled.

So counting your own trumps only, generally bid 3/2 with eight and 3/3 with nine.
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#8 User is offline   Stephen Tu 

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Posted 2015-February-17, 12:24

It's more of an approximate guideline rather than a "law".

The basic idea is that it's OK to compete with more trumps and some shape. The times you should think about not bidding so much are:
- you are flat shape. competing to 3S on 4333 is quite a different proposition than competing on 4135
- you have lots of junk honors in your opponent's suits (bad for offense, phantom sac more likely)
- vulnerable at MP against good trigger happy opponents. But don't be overly paranoid about this. They have to find the double, and it's hard for them to do this when you hold 9 good trumps. Plus they might misdefend. -200 instead of -140 costs a lot of MP, but -100 instead of -140 saves a lot of MP also. Good players will often not find the double as it's often unclear who can make what, they don't know how much shape you & your partner have so it's hard to double without trump tricks.

So it's usually a combo of multiple of the above factors that would lead you to pull in the reins and not compete holding 9+ trumps at 3 level. You want to avoid situations where down 2 undoubled seems reasonably likely (which are also likely ones for opps to find the double and get you one or two). And ones where you think they missed game. Basically stuff when you feel more heavily outgunned and don't have a lot of playing strength. Even vul, if you are bidding 3/3 on stuff that is making like half the time, it's going to be hard for the opps to double you only on the ones you are failing without doubling you into game to compensate tops for the -200 bottoms.
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#9 User is offline   ArtK78 

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Posted 2015-February-17, 12:49

When I first learned about the LOTT, my partner at the time and I used it primarily for high-level decisions - typcially, when to sacrifice 5 over 4. We found that the LOTT worked well in that setting. This was back in the 1980s.

Since then, many fine players have argued that the LOTT does not work as well in high-level decisions as it does in lower-level competitive decisions - 3/3 decisions, such as the ones being discussed in this thread. Many have narrowed the use of LOTT to situations in which both sides have approximately the same high card strength.

I still use the LOTT in high-level decision making as a factor worthy of consideration.
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#10 User is offline   rmnka447 

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Posted 2015-February-17, 12:57

ArtK78's explanation of the thought process to use with the LOTT is excellent.

I've got just a couple of comments to make.

He presented the worst case scenario in assuming your side was vulnerable. But it was important to do so to bring home the things you need to consider.

On the other side of the coin, if you are not vulnerable, going through the same thought process will lead you conclude that competing to the 3 level is almost always right. When they are making 10 tricks and you are making 8, you'll be at -100 down one doubled playing at the 3 level. If they play 3 making 4, it will be -170 against you. When you're making 9 or 10 tricks, it's obviously right to compete.

That analysis assumes both sides have 9 card trump fits. Sometime the exact trump holdings for both sides isn't completely clear. For example, LHO opens a 5+ card major and the bidding proceeds - 1 - (1 ) - 2 - ?. Now holding 4 s, you know your side has 9+ s, but the opponents could have anywhere from an 8 to 11 card fit. It's probably best in these circumstances to assume the minimum known fit for the opponents -- here 8 cards -- and proceed with the analysis on that basis.

Also, as the auction proceeds, you can update your thinking as the opponents show additional trumps.

The main caveat with the LOTT is that it only considers trump lengths. The degree to which your hands fit and the trick taking ability of the cards in your hand also matter in the number of tricks you take. Consider 2 hands -- Kxxx xxx Axxxx x and Qxxx xxx Qxx QJx in the above auction. Both have the same length in your suit and the opponent's suit. Both have the same point count. But the first hand is far better for competing to the 3 level than the second. It has high cards which can be fast winners (As, Ks) versus cards that are usually slow winners (Qs,Js). It also has some distributional features which will mesh well with partner's hand. (Partner probably has no more than a doubleton . Your cards in the other side suits will be generally useful whatever partner holds in them.) So those factors are also something to consider in using the LOTT.
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#11 User is offline   rmnka447 

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Posted 2015-February-17, 13:17

View PostArtK78, on 2015-February-17, 12:49, said:

When I first learned about the LOTT, my partner at the time and I used it primarily for high-level decisions - typcially, when to sacrifice 5 over 4. We found that the LOTT worked well in that setting. This was back in the 1980s.

Since then, many fine players have argued that the LOTT does not work as well in high-level decisions as it does in lower-level competitive decisions - 3/3 decisions, such as the ones being discussed in this thread. Many have narrowed the use of LOTT to situations in which both sides have approximately the same high card strength.

I still use the LOTT in high-level decision making as a factor worthy of consideration.

I also use it as a factor to consider in those high level situations as well. Going through the thought process can sometimes save you from a bad sacrifice. But fit and distribution are a big factor, too.

The other situation where I find it useful is in reopening/balancing position. Sometimes, sifting through the information from the bidding along with the likely total fit in your best suit when to reopen or not.
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#12 User is offline   fromageGB 

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Posted 2015-February-17, 20:14

Another caveat is that the law's "safety guarantee" depends on the total lengths of your and your opponents' suits. You may well have bidding understanding such that you know your own minimum length, but you have to make an assumption that the opponent's bidding is sound. This is not always the case.

For example, opponents open spades, partner overcalls hearts, responder supports with 2 and you are confident of an 8 card fit and about a combined 20 count. The law supports your bid to 3. One off is a good sacrifice? No it is not ; they have bid on a 4-2 fit. And no, they are not beginners, merely incompetent. Your negative score is a matchpoint bottom.

This has happened to me, and also similarly at a higher level. Nevertheless, the law is a good guide.
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#13 User is offline   Zelandakh 

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Posted 2015-February-18, 05:38

The short answer is that yes, it is a good starting point for a new player and provides a basis for building judgement around. Others have talked about details and caveats and that is all well and good but the fundamental thing is that you have a decent guideline with the LoTT, even the very simple version in the OP, and can build up experience from that.

Here are some other guidelines based on vulnerability that might be useful as a corrolary. At Love All, if the decision is close it is usually right to bid. AT Game All, if it is close it is usually right not to bid. When one side is vulnerable, close calls can be decided on whether you think the vulnerable contract will make (irresepctive of whether the non-vul contract is making).

Obviously you want to start building real judgement asap so you should try to review competitive decisions often. This is the area of the auction where the biggest rewards and improvements are to be had for the majority of intermediate players. I do wish LoTTy had been around when I was young though. I had so many auctions that were like poker than bridge as a student and, while that was fun, it was not particularly good for improving bridge skills.
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#14 User is offline   aguahombre 

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Posted 2015-February-18, 10:24

One thing I stress (rant) to N/B players about the Law is that the effectiveness of their opening preempts is not merely in the preempts themselves, but in Partner's advances.

They like rules of "numbers" a lot more than I do...so I give them my Rule of 2/3/4 and the Rule of 2/3.

When a weak two is opened and the other guy has pretty much any hand below about a 16-count, they want to stay at 2 with two, raise to 3 with three, and bid 4 with four.

However, this doesn't work when the opener cannot be counted on to have the number of trumps expected, or if their preempts have random stuff everywhere except in that suit. Hence, the Rule of 2/3....Preempts are supposed to make life difficult for two people at the table, not three.
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#15 User is offline   Liversidge 

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Posted 2015-February-18, 12:14

View PostZelandakh, on 2015-February-18, 05:38, said:

The short answer is that yes, it is a good starting point for a new player and provides a basis for building judgement around. Others have talked about details and caveats and that is all well and good but the fundamental thing is that you have a decent guideline with the LoTT, even the very simple version in the OP, and can build up experience from that.

Here are some other guidelines based on vulnerability that might be useful as a corrolary. At Love All, if the decision is close it is usually right to bid. AT Game All, if it is close it is usually right not to bid. When one side is vulnerable, close calls can be decided on whether you think the vulnerable contract will make (irresepctive of whether the non-vul contract is making).

Obviously you want to start building real judgement asap so you should try to review competitive decisions often. This is the area of the auction where the biggest rewards and improvements are to be had for the majority of intermediate players. I do wish LoTTy had been around when I was young though. I had so many auctions that were like poker than bridge as a student and, while that was fun, it was not particularly good for improving bridge skills.

Thanks for that. In time I will be able to refine my bidding, but right now I am discussing it with my partner and we will use it next time. As you say, it has been a bit like playing poker until now. Trying to compute the implications of bidding or not bidding when it is my turn to bid can be rather stressful, and I often end up blurting out a bid or pass, and regret it a few seconds later.
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#16 User is offline   case_no_6 

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Posted 2015-February-18, 13:50

View PostLiversidge, on 2015-February-17, 07:46, said:

This seems too good to be true. According to 'The Law' ( which I don't fully understand in terms of why it works), if you are in a contested auction against competent players, and from the bidding it looks like the points are reasonably evenly split (let's say no side has less than 17 HCP) then it is fairly safe to bid to the level of your fit, regardless of vulnerability or point count. You just bid on combined trump holding.
So if LHO bids 1 and my partner bids 1, and LHO bids 2, I just assume my partner has at least 5 spades, so I just count my spades, and with three spades I can bid 2. With a weak hand and four spades I can bid 2 and then 3 if needed.

From what I understand, you may well not make your contract if left in it, but usually you will come out better off (even if doubled) than if you had let your opponents have the contract.

I appreciate that as I get better I will put more intelligent thought into my bidding than just this, but meantime is this a good device to use to help a novice like me compete more effectively?




I don't think you have this Law of Total Tricks (LoTT or "The Law") quite right for several reasons. As one of my wise teachers once counseled me, "When something seems too good to be true, it probably is." I assert that The Law is no exception to this maxim. Here is why:

1. The Law is not a law of nature as the noun "law" might suggest. Rather, it is an empirically observed statistical or probablistic tendency whereby the total tricks available to both partnerships (playing in their best respective trump fits and both sides playing double dummy) is equal to the summed total number of trumps in those best fits. That is, the correspondence between total tricks and total trumps is typical, but not guaranteed. When the total number of trumps is 18 or fewer, it is fairly unusual for The Law to disappoint but it can. When the total number of trump increases above 18, it is not uncommon for the total tricks to be off by 1 or 2 (and occasionally even more) tricks than the number predicted by the number of total trumps. Proponents and critics of The Law have identified characteristics of situations when The Law's predictive powers are diminished, but as far as I know nobody has been able to produce a set of reliable "correction factor" rules allowing players to make consistently accurate adjustments.

2. Even if The Law were a true law - i.e., an error-free or perfect predictor of total tricks based on total trumps - it would still be relegated to a tool that includes risk in use. One never knows the total number of trumps for sure. Rather, one must one estimate or infer the LIKELY total number of trumps based on the auction. Some bids imply a certain length in a suit, but a greater number (and sometimes a fewer number) may be held by a player showing length. Lively competitive auctions tend to increase the likelihood of extra length being held by one or more players, for example.

3. Vulnerability DOES matter. For example, at Match Points or Board-A-Match, even a 1 trick set when doubled and vulnerable (-200) is often a very poor result in a part score deal. Likewise, sacrifices at IMPs can be overly costly when vulnerable and especially so when the opponents are not.

In summary, the thing to remember that The Law is a first approximation guideline to be considered, not slavishly followed much in the same way that honor values are the first order approximation of a hand's offensive and defensive trick taking potential in the early rounds of the auction while being subject to (sometimes dramatic) changes based on what is learned about the degree of fit or support for both partner's suit lengths and high card values as the auction develops and unfolds. It is a simple tool and can be quite helpful when judiciously applied and considered. But simple decision support tools don't always produce accurate results when applied to complex circumstances.

Megan
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#17 User is offline   Trinidad 

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Posted 2015-February-18, 15:13

View Postcase_no_6, on 2015-February-18, 13:50, said:

1. The Law is not a law of nature as the noun "law" might suggest. Rather, it is an empirically observed statistical or probablistic tendency

That is true. But almost everything in bridge is probabilistic in nature. If you don't like that and want absolute laws, you should play chess or go. As an example: The number of high card points for our side is used to predict the number of tricks that we can take. This is based on observations and probabilities. Nobody has a problem with that.

The total number of trumps is actually a more accurate predictor for the number of total tricks than the number of high card points for our side is for the number of tricks for our side. Nevertheless, the Law of Total Tricks is continuously under attack for being inaccurate, whereas every bridge teacher in the world teaches his students the Milton Work count without any problem. And when a 26 HCP game fails, then we accept that as unlucky.

And, for what it is worth, there are many laws in nature that are also probabilistic in nature. There is a reason why scientists (physicists, chemists, biologists) and engineers are generally pretty good at statistics.

Rik
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#18 User is offline   P_Marlowe 

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Posted 2015-February-18, 16:35

Hi,

unclear if having a link to another side is allowed, but the following is an indepth
discussion
http://bridgewinners...f-total-tricks/

With kind regards
Marlowe
With kind regards
Uwe Gebhardt (P_Marlowe)
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#19 User is offline   VixTD 

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Posted 2015-February-19, 08:05

View PostVampyr, on 2015-February-17, 11:39, said:

You must remember that you can't let the other side play in their own "comfort zone". If you have no reason to expect that total trumps is more than 16, you should still compete to the three level in a lower ranking suit, unless you are vulnerable and think there is a good chance you will be doubled.

So counting your own trumps only, generally bid 3/2 with eight and 3/3 with nine.

This aspect is very often ignored in the discussion of "bidding to the level of your fit". It's not only the level you're bidding to, but the opponents' level that you're outcompeting that matters. There has to be a whole extra trump between the two sides to warrant bidding 3 over 3 compared to bidding 3 over 2.

On a part-score hand at pairs, work out the level you're thinking of competing to (the level you're thinking of bidding + the level of their contract you're bidding over, i.e. 18 for 3 over 3, 17 for 3 over 2) and estimate the total number of tricks. At game all bid to the level of the trick total, at love all bid to one more than the level. Vul vs non-vul bid one more than the level only if you expect to make your contract (you think you are the stronger side). Non-vul vs vul bid one more than the level only if you expect to go down (you think you are the weaker side), otherwise double them and try to get them one off.

This doesn't come with guarantees, all the caveats about uncertainties in the actual trick total and deviations from the law apply. It's also probably a little difficult for beginners to grasp, but it's the best advice I've ever read on the subject, in an excellent but little-known book "Competitive bidding at pairs" by Peter Hall.
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#20 User is offline   SelfGovern 

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Posted 2015-February-19, 10:23

Strategy also comes in to it.

At the Houston Regional in a team event, I heard the auction go
(1S) - 2H - (2S)

and it's my turn with a not-terribly interesting hand with a 2533 shape, five hearts to the JT, an A in one minor and a K in the other.

Now, the LoTT might say to bid 4!H. We've got our 10 trump, after all.
But something at the table told me I'd see a 4!S call, and that we'd be in a bad state if they bid 4S (actually, we were in Texas, which I consider to be a good state, but that's another story (or series of).

So I bid 3H only, and when it went (P), P, I was not surprised to hear RHO bid (3S). Now I 'back in' with my 4H call, and all pass as I had hoped.
Partner made 4H, and the opps are also on for 4S (responder happened to have five-card spade support), and likely would have bid it had I bulled into 4H.

The moral of this story is, use your head. If you don't have a history of accurate intuition in situations like this, consider bidding 3H and passing the expected 3S call -- since -170 beats -420 or -620 any day of the week.
Liberty breeds responsibility
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