To evaluate the viability of Losing Trick Count and the Bergen method of counting points, I selected hands in which there was at least an eight-card fit and a makeable (according to Deep Finesse) suit contract. I then determined the optimal bidding level for both North-South and East-West using LTC v. dummy points plus declarer Points. For the latter I used the following scale:

Bergen
PointsOptimal
Level

The table below shows what I found. The Level column shows the level of the most lucrative contract for the team as calculated by Deep Finesse. The numbers in columns two through seven are percentages. The second through fourth columns use Bergen points. The fourth through seventh columns use Losing Trick Count.

———-Bergen—————–Losing Trick Count——-LevelExact1-1.52+Exact1-1.52+

1-1.5 means that the specified level by Bergen or TLC was at least one level higher or lower than the best Deep Finesse level but not as much as two levels. 2+ means that the specified level was at least two levels higher or lower than the best Deep Finesse level.

So, the last line of the table (Level 7) indicates that in the 149 hands in which Deep Finesse determined that a grand slam was possible, the Bergen method recommended bidding it 61% of the time, but it was off by one or one and one-half tricks 34% and by two or more tricks almost 5%. LTC was right almost 42%, missed by one 33+% and by two or more 25%. By the way, if the LTC produced a result of more than 13 tricks, I treated that as “Exact.”

In general, Bergen Points appears to be far superior for contracts of level five and above. Maybe this should not be considered surprising for a system that was introduced in a book about bidding slams.

LTC produced more consistent results and had the edge on lower-level hands. In most of those cases Bergen points yielded too high of a bid. Underbidding was rare. Incidentally, the number of hands with low-level contracts is deceptive. In a considerable number of cases the opponents would have dominated the bidding. For example, in many Level 1 boards the opponents would be able to bid game or even slam. Therefore, the fact that Bergen points indicated a higher contract than could possibly be made would be irrelevant. I ran a test on Level 1 hands, however, with those hands excluded, and the results did not change much.

The optimal level calculated by Deep Finesse assumes that both sides play the hand “double dummy.” So, the opening lead is assumed to be the best one possible, and neither the declarer nor the defense make any mistakes. In the real world, of course, people do not play the hands perfectly. Even so, I can think of no better objective way to evaluate the bidding systems.

The other caveat is that some bidding mistakes are much worse than others. A conservative system that recommends bidding at too low of a level will at least produce a positive score. On the other hand, the rewards for accurate bidding at the game level or higher are substantial, especially in total points or IMPs scoring.

In the lecture cited in the first post, Ron Klinger claimed that LTC was “estimated to be at least 80% effective.” The data in this study do not seem to support that claim unless the meaning of the term “effective” is much different from the results of the “Exact” column. It is certainly true that a bid of two spades would be “effective” if nine tricks are available, in the sense that the amount of points won with a two-level bid are the same as with a three-level bid. On the other hand, most bidders would certainly like to know if that ninth trick is likely when the opponents bid three clubs.

I am no expert, but it seems to me that people who depend on LTC — and there are a lot of them — should also consider the adjustments that Bergen recommends, at least on hands with slam potential.