LTC - illogical gimmick

[omarsh10]

Last THREE issues of the Bridge Bulletin featured notes about Losing Trick Count (LTC). I felt that intelligence of faithful readers of the Bulletin had been insulted by the levels of publications. The notes in question lacked any logical consideration of the LTC approach or explanation of the LTC “formula”. LTC algorithm is as good as any other seemingly reasonable approach/mnemonic-rule, and one could come up with dozens of them.

 

Let us talk only about LTC “formula”: 24-LT. Why 24? Personally, I like number 23, for it’s a very cool Prime number. Or it can be 25, yes, that’s a nice round number! Now, where did LTC come from? LTC came from WTC - Winning Trick Count. Indeed, if both partners have all winning cards then one has 13 winners and the other has 13 totaling to 26. In case, if they have losers, then WT=26-LT. Now we do a verbal hocus-pocus with maximum losers in each suit being 3. Thus, we get max 12 losers per hand totaling to 24. As for the set aside 2 cards to be a winners... we just forget them.

 

Let us now imagine games with 48 or 56 cards decks. In these cases that hocus-pocus with max number of losers in each suit dose not work and we get LTC formulae 24-LT and 28-LT respectively. Easy to see the problem here. So, LTC (24-LT for 52 cards deck) is just a mnemonic rule, nothing more.

 

The examples given in the articles are also quite silly. :)

Well, enough about LTC.

[ArtK78]

With all due respect, your dismissal of LTC and the logic behind your dismissal of LTC is quite silly.

[gordontd]

With all due respect, your dismissal of LTC and the logic behind your dismissal of LTC is quite silly.

Yes - there are plenty of valid criticisms that could be made of LTC, but these are not.

[mikeh]

Last THREE issues of the Bridge Bulletin featured notes about Losing Trick Count (LTC). I felt that intelligence of faithful readers of the Bulletin had been insulted by the levels of publications. The notes in question lacked any logical consideration of the LTC approach or explanation of the LTC “formula”. LTC algorithm is as good as any other seemingly reasonable approach/mnemonic-rule, and one could come up with dozens of them.

 

Let us talk only about LTC “formula”: 24-LT. Why 24? Personally, I like number 23, for it’s a very cool Prime number. Or it can be 25, yes, that’s a nice round number! Now, where did LTC come from? LTC came from WTC - Winning Trick Count. Indeed, if both partners have all winning cards then one has 13 winners and the other has 13 totaling to 26. In case, if they have losers, then WT=26-LT. Now we do a verbal hocus-pocus with maximum losers in each suit being 3. Thus, we get max 12 losers per hand totaling to 24. As for the set aside 2 cards to be a winners... we just forget them.

 

Let us now imagine games with 48 or 56 cards decks. In these cases that hocus-pocus with max number of losers in each suit dose not work and we get LTC formulae 24-LT and 28-LT respectively. Easy to see the problem here. So, LTC (24-LT for 52 cards deck) is just a mnemonic rule, nothing more.

 

The examples given in the articles are also quite silly. :)

Well, enough about LTC.

 

It is foolish to post at such length on a topic of which you clearly, from the contents of your post, have no understanding at all.

 

LTC is a useful tool, as an adjunct to other valuation methods. But one does have to understand it in order to use it....or to criticize it.

[awm]

Here's some logic behind LTC:

 

We basically assume there will be three tricks in each suit. This is not strictly true, but it's a reasonable approximation. The number of "losers" in my hand is the number of those tricks that I expect to lose. Note that we assume a trump fit, so I can reduce my losers both by holding high cards and by having shortness.

 

The number of these twelve tricks I expect to win is exactly those I don't lose, so 12 - losers.

 

Combining these for the two partners gives you 24 - (sum of losers) as an approximation of the number of tricks we will take.

 

Of course, this does leave the question of "what about the thirteenth trick?" We don't really know what suit this trick will be played in (and the idea of playing three tricks in each suit wasn't really accurate either). Of course there is also the issue of mesh, for example KQJx in a suit is one loser and singleton is one loser, but those two holdings across from each other still produce one loser. There are also frequent adjustments for honor strength (for example Qxx and Axx are really not equivalent holdings, so typically people credit ace as 1.5 tricks and queen as .5 in these situations).

 

Nonetheless, LTC is fairly accurate as a rough guideline. It's not the "ultimate hand evaluation tool" or anything.

[nige1]

LTC is logical and effective for ordinary players. I've found such tools useful all my life.

But judging from replies to a previous topic, LTC does get up some expert noses :(

[Finch]

Last THREE issues of the Bridge Bulletin featured notes about Losing Trick Count (LTC). I felt that intelligence of faithful readers of the Bulletin had been insulted by the levels of publications.

 

Why complain here? Write to whoever publishes the Bridge Bulletin, that's not BBO as far as I know.

[hrothgar]

From my perspective, the primary value of LTC is illustrating that there's more than one way to skin a cat.

 

The ACBL Bridge Bulletin doesn't target expert players. It's content is appropriate for beginners and some intermediates.

Many of these folks were raised on High Card Points and aren't aware that anything else exists.

 

Showing them (almost) any alternative can only be a good thing.

 

With luck they'll draw the correct inferences

 

It would be a shame if anyone concluded that "LTC is the be all and end all" rather than "There are many ways to value a hand"...

 

Oh yeah, if you're truly worried that the ACBL Bulletin insults the intelligence of its readers, there are plenty of better examples than an article about LTC...

[nigel_k]

My general view on these kinds of rules is that, if you are an expert, you can do better by looking at the actual hand and using judgment. If you want to be an expert, you should look at the actual hand and use your judgment in order to become better at doing so. If you are not an expert and have accepted that you never will be, by all means go ahead and use whatever rule-based approach works for you.

[HighLow21]

The logic behind LTC is that provided you've found a trump fit (at least 8 cards), you cannot lose more than 3 tricks in any side suit. Neither can your partner. The reason for this is that any longer cards can either be established as winners or ruffed in the other hand. There are some assumptions behind that but for normal hands, it works fairly well.

 

Thus anything that doesn't lose, wins. Hence, start off with 24 winners, and subtract up to 3 losers for each partner in each suit.

 

Assume for a second that you and your partner are in a spade contract, both holding ♠xxxx ♥xxx ♦xxx ♣xxx, where 'x' is any card 9 or lower. Thus you both have 12 losers, and 24 - (12 + 12) = 0 tricks, which is how many you have (the defenders can hold you to 0 tricks by playing long plain suits after the 9 side tricks have been taken, enabling them to score ♠J, Q, K, A separately at the finish).

 

As you can see, you will lose 3 tricks in each side suit and 4 trumps, or all the tricks.

 

Now change it so that you have ♠xxxx ♥xx ♦xxxx ♣xxx and partner has ♠xxxx ♥xxxx ♦xx ♣xxx. You've removed a loser from each hand, and now you can take 2 tricks: a ruff of the 3rd red card in the opposite hand. 24 - (11 + 11) = 2 tricks.

 

Give either player an ace, and the losing trick count falls by one. replace 2 xx's with an AK, and it falls again by another one.

 

Where LTC breaks down most often is in the following situations:

(1) You are in an insufficient trump fit. Say, something like 5-2 trumps, where the two in dummy are small and can be overruffed when you attempt to ruff losers there. This can lead to dummy's trumps being drawn by your opponent, or your losing more trump tricks than expected. (This can easily happen in a 5-3 fit as well, especially when the 3 are small!)

(2) You are in any misfit.

(3) You are in NT (the LTC is pretty much useless here).

(4) You are armed with many controls, sufficient trumps, and a long, running side suit (the defenders don't have time to get at all of your losers; this is a major reason why Aces tend to be worth much more than 4-3-2-1 point count suggests).

(5) You have unsupported honors and either can't finesse them (entry or timing problems), or the finesse fails.

(6) Key suits break badly (trumps, long suits, suits that require some ruffing, etc).

(7) Your honors are well-positioned behind, or poorly positioned in front of, a strongly bidding opponent.

(8) You have duplicated values. This is by far the most common failing of LTC when a sufficient trump suit has been found, in my experience. Some examples:

(A) Small doubleton opposite small doubleton. Within that suit, you start with 6 tricks and subtract 2 twice, for 2 tricks. This suit provides no tricks, not 2! If it were xx opposite xxxx, you could ruff 2 small ones for 2 tricks. This is an example of DUPLICATED SHORTNESS. Mirrored distributions, where you and partner hold the same length in every suit, are the absolute worst.

(B) Small doubleton opposite small singleton. Again, duplicated shortness. The same is true of shortness opposite a void.

© Minor honors opposite shortness. Like the example from a previous post, KQJx opposite x is a big problem. Both players would be counting on only 1 loser in the suit, distorting the number of tricks their side has available. Unless you have time to establish the QJ (and maybe even the K) for discards in another suit, the honors here are worthless in a trump contract. This is an example of UNNECESSARY MINOR HONORS.

(D) Trump suit duplication. Say you hold

♠

AQxxx and your partner,

♠

KJxxx. The jack in this case is worthless, and in many cases, so is the queen. They'd probably be more useful in some other suit that needs filler. (An exception: these duplicated honors will be very helpful if playing a contract on cross-ruffing lines.)

(E) Side suit duplication. This is the same concept as trump suit duplication, except only in a side suit in which your side has 8+ of the cards. Side suit duplication is especially problematic if the suit is evenly divided between the two hands and the trump suit is not. (If that's the case, it usually is much better to have the evenly divided suit as trumps and the other suit as non-trumps.)

 

Many of these problems can be diagnosed or anticipated (or, at least, the possibility that these problems may exist can be diagnosed) during the auction itself. For example, if LHO opens 1♥, your partner doubles for takeout, and you hold ♥KQJ7, you can be sure that the heart suit contains duplicated and therefore negative values. LTC will overestimate your playing strength. (Try to bid NT for this exact reason.) Or another example is when partner responds to your bid with a splinter bid. In that suit, Axx(x) and xxx(x) are excellent holdings, while KQJT is terrible, and anything else is somewhere in between.

 

To continue this point, there are a variety of adjustments that need to be made for minor honors, gaps, etc. For example, Kx is technically only 1 loser, but if your partner doesn't have the Ace or Queen, half the time the king won't take a trick because the Ace swallows it and doesn't promote the Q in the process. Here are some ideas:

- Qxx should be treated as 2.5 losers.

- QJx should be treated as 2 losers.

- QTx ... it really depends on who has the jack, doesn't it?

- AQx should be treated as 1.5 losers.

- AJT should be treated as 1 loser unless you're certain LHO has substantial strength in this suit. (Even then you might be able to force him to lead it.)

- AQT should be treated as 1 loser.

- AQJ should be treated as 0.5 losers.

- Kx is 1 loser unless you know your partner is very weak (then it's 1.5).

- Qx, Jx, Jxx, JTx, Tx, Txx --> these are 100% losers. 2, 2, 3, 3, 2, and 3 respectively.

- AJ is 1 loser.

- AQ is 0.5 losers.

- KJ(xxxx) is 1.5 losers in most cases, not 2 (especially if you also have the T).

- If partner is known to have a singleton opposite your minor honors, mentally make the appropriate adjustments. Bid much more conservatively.

- Trump hands that require some degree of ruffing in one or both hands: try to determine if the length in the suit being ruffed is with the defender to the RIGHT of the long suit (i.e., "ruff right"), or to the LEFT of the long suit (i.e., "ruff wrong"). So, for example, if you and partner are going to play a spade contract and you are long in diamonds, a diamond overcall by LHO is potentially a problem but a diamond overcall by RHO is welcomed! This is especially important when all of your trumps are not high, and can make the difference of anywhere from 1 to 4 tricks in your trick total.

 

It may seem daunting at first but you can learn to make these adjustments when necessary and in my experience, intelligently adjusted LTC is an effective weapon to figure out what level you should be playing at. For me, starting with LTC and then overlaying some of the concepts laid out by Mike Lawrence in two of his books (Hand Evaluation, and Judgment) was the beginning of a new level of sophistication in my bidding practices. I started being able to "see the hands" mentally sometimes, at least to some extent, before the auction had finished.

 

You will be wrong some of the time using LTC, but you'll be far more accurate than using strictly HCP and length/shortness points alone.

[HighLow21]

From my perspective, the primary value of LTC is illustrating that there's more than one way to skin a cat.

 

The ACBL Bridge Bulletin doesn't target expert players. It's content is appropriate for beginners and some intermediates.

Many of these folks were raised on High Card Points and aren't aware that anything else exists.

 

Showing them (almost) any alternative can only be a good thing.

 

With luck they'll draw the correct inferences

 

It would be a shame if anyone concluded that "LTC is the be all and end all" rather than "There are many ways to value a hand"...

 

Oh yeah, if you're truly worried that the ACBL Bulletin insults the intelligence of its readers, there are plenty of better examples than an article about LTC...

 

HRothgar,

 

I couldn't agree more about the HCP thing. What basically all beginners, most intermediates, and even some "advanced" players seem to forget is that HCP plus length/shortness adjustments is most useful in two situations: (1) for NT bidding, and (2) at the beginning of the auction, when no other information is known. Every bid in the auction (including passes!) adds to the information available to you and your job is to capitalize on it. In other words, HCP becomes secondary and determining the number of winning tricks is the name of the game. (Or, conversely, determining the number of losers, which is the other side of the same coin.)

 

LTC is definitely not the only valuation method but the concept is invaluable to anyone who doesn't understand it, and is especially valuable to those who do not know how to revalue their hands based on the prior bidding.

 

But most importantly, I wanted to say that the Krug's quote about Gingrich is one of the funniest things I've heard in a long time!

 

-Tate

[mgoetze]

For example, if LHO opens 1♥, your partner doubles for takeout, and you hold ♥KQJ7, you can be sure that the heart suit contains duplicated and therefore negative values. LTC will overestimate your playing strength. (Try to bid NT for this exact reason.) Or another example is when partner responds to your bid with a splinter bid. In that suit, Axx(x) and xxx(x) are excellent holdings, while KQJT is terrible, and anything else is somewhere in between.

 

Wow it sure is a good thing I visit the A/E forum once in a while or I never would have found such high-level advice!

 

BTW, have you ever heard of a thing called a "ruffing finesse"? I hear it's a truly elite-level play but I don't know what it's all about, so if you could explain it to me that would be much appreciated.

[BunnyGo]

Why is this thread in A/E to begin with? I thought inquiry policed this forum. I call shenanigans on this thread.

[HighLow21]

I am 100% certain it was in B/I when I responded to it. Something fishy is going on.

[HighLow21]

Voila. This isn't in A/E at all. It's in general bridge discussion. Surely you can't construe my comments above as inappropriately basic for that forum? Because I can tell you, in my experience most bridge players probably haven't even tried LTC out.

[Zelandakh]

LTC for Dummies (and Walruses):-

 

A = 3, K = 2, Q = 1

void = 6, singleton = 3, doubleton = 1

 

I won't go through the other MLTC adjustments but they are obvious - buy the book and think about it!

 

To find the correct levels, first convert LTC to WTC: 7 losers becomes 5 winners, 6 losers is 6 winners, etc. Then multiply winners by 2.

 

So Game = 7 losers opposite 7 losers = 5 winners opposite 5 winners = 20 points.

 

Interestingly, you can also adjust this to modified Milton by multiplying everything by 1.5:-

 

A = 4.5, K = 3, Q = 1.5

void = 9, singleton = 4.5, doubleton = 1.5

Game = 30 points

 

It should be clear from the above that shortages are overvalued. This is reflected in the requirement for game raising to a whopping 30 points. The advantage of doing things this way though is that you can use your regular point count and simply add distribution points when the fit is found rather than having to recalculate from scratch. You also have more scope to adjust the distribution ranges, for example to 5/3/1, with corresponding adjustment to requirements for game or slam. But that is moving away from the LTC.

 

The point is that (almost) every bridge player is used to counting points for honours. The above schemes are functionally identical to the MLTC and correspond to that form. So why stick with counting losers? Simple, the above is just another point count method whereas many bridge players think the LTC is something different. It is not, it is simply a (imho somewhat less accurate) version of the 4.5/3/1.5 point count method which has been around for a very very long time.

[P_Marlowe]

LTC for Dummies (and Walruses):-

 

A = 3, K = 2, Q = 1

void = 6, singleton = 3, doubleton = 1

 

I won't go through the other MLTC adjustments but they are obvious - buy the book and think about it!

 

To find the correct levels, first convert LTC to WTC: 7 losers becomes 5 winners, 6 losers is 6 winners, etc. Then multiply winners by 2.

 

So Game = 7 losers opposite 7 losers = 5 winners opposite 5 winners = 20 points.

 

Interestingly, you can also adjust this to modified Milton by multiplying everything by 1.5:-

 

A = 4.5, K = 3, Q = 1.5

void = 9, singleton = 4.5, doubleton = 1.5

Game = 30 points

 

It should be clear from the above that shortages are overvalued. This is reflected in the requirement for game raising to a whopping 30 points. The advantage of doing things this way though is that you can use your regular point count and simply add distribution points when the fit is found rather than having to recalculate from scratch. You also have more scope to adjust the distribution ranges, for example to 5/3/1, with corresponding adjustment to requirements for game or slam. But that is moving away from the LTC.

 

The point is that (almost) every bridge player is used to counting points for honours. The above schemes are functionally identical to the MLTC and correspond to that form. So why stick with counting losers? Simple, the above is just another point count method whereas many bridge players think the LTC is something different. It is not, it is simply a (imho somewhat less accurate) version of the 4.5/3/1.5 point count method which has been around for a very very long time.

My guess is, that the LTC predates the 4.5/3/1.5 point count method - the LTC is from 1934,

see e.g. http://www.bridgehands.com/L/Losing_Trick_Count.htm, the book got published 1934

 

And the origin of the LTC may well be the trick counting hand evaluation, that predates the

HCP count, which is from around 1925, see http://en.wikipedia.org/wiki/Milton_Work

 

The 4.5/3/1 point count was favoured by Jeremy Flint a partner of Maurice Harrison-Gray, if

I recall this correctly, I dont have a link to back this up.

Harrison-Grays was a advocate of the LTC - his articles regarding the LTC are from the 60s

Harrison-Gray and Flint started playing together in the 50s / 60s, ..., I am on the sure side,

if I claim after the war.

 

The main difference between the LTC and the point count method is, that the LTC stresses

distribution (and to a certain degree suit quality / honor location) over honors.

The HCP methods got developed for balanced hands, the LTC method got developed for unbalanced

hands.

Because the HCP method did get developed for balanced hands, suit quality and honor location

was not relevant, ..., balanced hands have on avergae only suits with length 3.5, i.e. the

honors will be spread out across all 4 suits.

 

The relationship between LTC and HCP is, that both basically assume, that a king is worth a

trick.

 

The difference between the 4/3/2/1 and 4.5/3/1.5 point count is, that the 4.5/3/1.5 stresses

the control aspect, which gets a little bit ignored by the 4/3/2/1 count.

 

With kind regards

Marlowe

[helene_t]

Many very good comments in this thread. AWM's post is a very good primer HighLow21's first post (#10) is excellent for those with more time to read.

 

Personally I like Zelandakh's Walrus Trick Count to LTC. If you read "I fought the law" you may notice that the WP/SST formula in that book is very similar to Zelandakh's WTC.

 

I made some statistical analysis of the GIB DD database to shed light on the accuracy of of WTC and it appeared that WTC (or, equivalently, modified LTC, i.e. LTC with 0.5 loser reduction for queens and 1.5 for aces as AWM) overestimates the value of shortnesses. This is especially true when you have only 8 trumps. HighLow21 points this out also in his remark about insufficient trumps.

 

Personally I am no big fan of LTC but I use it in specific situations. For example, it is useful to have an agreement about how many LTC (or WTC) partner should expect from you 1st or 2nd seat preempts. He may prefer to evaluate his hand (as responder to a preempt) using cover cards rather than LTC, so the rule of 24 will not be used in that case.

[WellSpyder]

LTC for Dummies (and Walruses):-

 

A = 3, K = 2, Q = 1

void = 6, singleton = 3, doubleton = 1

.....

The above schemes are functionally identical to the MLTC and correspond to that form.

Except for honours in short suits. (M)LTC treats Q and a doubleton as of equal value (2 losers), but you can't count the points twice over for Qx. Obviously it is easy enough to modify your scheme to make clear that you don't count honour points for K, Q, or Qx, but once you've done that you might just find it easier to count losers anyway....

[gwnn]

LTC is a nice linear approximation to hand evaluation. However, we all know how well x approximates sin(x), and so on. If our electric sockets worked under the assumption that sin(x)=x, our TV's wouldn't work. In practice, many people apply LTC blindly and suffer the consequences. It is often worse than an exploding outlet or TV.

 

edit: Don't get me wrong - I'm not saying that linear approximations have no place in bridge or any such thing. I'm saying that LTC is not illogical at all, but that in practice many people over-rely on it.

[Zelandakh]

you don't count honour points for K, Q, or Qx

 

You are right and I probably should have stated it explicitly. I thought it was obvious for anyone who has used the LTC. There are also a bunch of other adjustments you need to make to use the full MLTC, so many that I daresay close to 99% of players are unaware of all of them.

 

FWiiW I think the 3/2/1 (or 4.5/3(1.5) evaluation is much better than 4/3/2 (or 1/1.5/2) for suit contracts and is overall a better guide to hand value. It is nice that helene's analysis backs my assertion that shortages are overvalued, although I think it is fairly clear really; most analyses I have seen suggest that 5/3/1 is not too far off and the LTC equivalents are nearly double these values.

 

And some nice historical background from Marlowe. Perhaps surprisingly I know the HT evaluation method (which is a more direct child of the earlier methods) rather well, much better than the MLTC for example, since I learned bridge partially from a book by Culbertson. I used it for quite a while as a beginner. Also interestingly, I still think Culbertson's write-up of Playing Tricks is as good as anything else I have seen even though it was written around 3/4 of a century ago!

[pirate22]

L.T.C. was concocted by an Canadian,many many years ago,not very published,

But an Englishman Harrison Gray visited U.S.A and came across it,with the original

writers permission it was edited,and used to great effect,and it became very

popular,and was crucial on many hands fully reported...today there is law of total tricks

and many more systems available,one pays yer money and make yer choice,

personaly,i have used LTC when majors are involved as a back check,and it stands

the test of time

[Finch]

In practice, many people apply LTC blindly and suffer the consequences. It is often worse than an exploding ...TV.

 

Are you playing too much bridge?

[MrAce]

Of course it is not totally illogical.

 

Look at good players who are arround. When we read them i never see Fred or Justin or MikeH or Andy saying anything about LTC. I dont think when they play they make this magical additions and substractions either. I dont think they put new names to their raises such as "6 loser hand". They talk more about seat, vulnerability, texture of hand, texture of suits, strategy, position, bonuses, risks and all that boring stuff.

 

It is popular because the authors of books like LOTT and LTC advertise it as if they can close the judgement gap between an average player and an expert player with a magical formula. And people believe in this bs because they want to believe since it is much easier than really trying to improve one's judgement and it is more appealing.

 

When i said all of this to LTC fans about top players, i usually end up with same reaction " Dont compare with extreme players, they are way too good" etc etc. And my response is same "Maybe they are not the ones who are too good, maybe we are too bad because we try to use the shortcuts. I dont think famous people get to where they are by just being talented. I believe they made a lot of hard work too. Dont get me wrong, i am not saying "if u work hard u can be a Fred or Justin" of course talent is needed, but i know one thing, neither LOTT nor LTC alone will get anyone anywhere close to be a succesful bidder.

[CSGibson]

Of course it is not totally illogical.

 

Look at good players who are arround. When we read them i never see Fred or Justin or MikeH or Andy saying anything about LTC. I dont think when they play they make this magical additions and substractions either. I dont think they put new names to their raises such as "6 loser hand". They talk more about seat, vulnerability, texture of hand, texture of suits, strategy, position, bonuses, risks and all that boring stuff.

 

It is popular because the authors of books like LOTT and LTC advertise it as if they can close the judgement gap between an average player and an expert player with a magical formula. And people believe in this bs because they want to believe since it is much easier than really trying to improve one's judgement and it is more appealing.

 

When i said all of this to LTC fans about top players, i usually end up with same reaction " Dont compare with extreme players, they are way too good" etc etc. And my response is same "Maybe they are not the ones who are too good, maybe we are too bad because we try to use the shortcuts. I dont think famous people get to where they are by just being talented. I believe they made a lot of hard work too. Dont get me wrong, i am not saying "if u work hard u can be a Fred or Justin" of course talent is needed, but i know one thing, neither LOTT nor LTC alone will get anyone anywhere close to be a succesful bidder.

 

I disagree (not about your specific examples, but about your conclusion that top players don't use LTC). I think that top players use it, but they use it in the way that it should be used - as a tool, another way to evaluate borderline hands in their decision matrix, not as a "bible" or magic formula. I asked a top player in my area about an auction with a borderline decision about whether to make another slam try, and the first tool he trotted out was LTC.

 

Mind you, personally I don't understand the losers + losers = winners stuff involved in some people's LTC; it appears to be much easier to use LTC combined with potential cover cards, which is the way it was explained to me. But I certainly think LTC has a place even in an expert game as a tool, as long as its not the only tool.