The opponents were vulnerable when my partner dealt me this unimpressive collection on one of the last rounds of an equally unimpressive session at the Hartford Bridge Club:

♠A 9 7 4 2   ♥10 6   ♦Q 10 8 6 3   ♣7My partner opened 1♥, and I quickly responded 1♠. After his jump to 4♠ I paused to assess the situation. His rebid generally showed a hand with twenty or so points and five losers. My hand had only six HCP, but there were only seven losers. Losing Trick Count (LTC) analysis said that we could make six. I was most worried about diamonds, so I lied and bid 5♣. My plan was to try 6♠ if he bid 5♦ and to stop at five if he did anything else. Sure enough; he bid his diamond control, and I went straight to 6♠.

LHO made the very passive lead of a diamond. This is what my partner set down on the table:

♠K J 8 5 2   ♥K 8 7 4   ♦A K   ♣K Q 6 Could I complain? Well, yes, his opening bid was a bit strange, but he does have nineteen points and five losers. Nevertheless, against best defense this slam was down one off the top, and it would require a bit of luck not to be down two or even more. However, I realized that with a diamond lead it was still theoretically possible to make the contract if both spades and diamonds split, and the A♥ was on side. The fact that LHO did not lead the A♥ even gave me a little encouragement. However, RHO pitched a diamond on the second round of trump. I ended up down two, but it could actually have been worse. Every card was wrong. The opponents could have taken two hearts and a club off the top. If they did, and I made the percentage play of the drop in spades (as I did), I would have only managed nine tricks.

So, what went wrong with LTC? Well, the basic problem was clubs. Partner’s King and Queen were so worthless to me that I ended up pitching them on the diamonds. Add a little bad luck to that, and you end up with an LTC calculation that is off by three tricks!

I later (the game ended shortly before 11 p.m.) remembered that Bergen’s method was better on contracts above the four level. My research had revealed that Bergen’s superiority was usually derived from the fact that LTC’s assessment was too conservative. I decided to reassess my hand using Bergen count. For the starting count Bergen would have added to my six HCP one point for my fifth spade, and one for my fifth diamond to a total of eight starting points. Once partner supported my spades I could claim two for my singleton, one for my doubleton, and one for my long second suit. To him my hand would therefore be worth twelve points if I was declaring spades. Even if partner had had his twenty, we would still have been a little short of the thirty-three that he recommends for a slam bid. I deduced that Bergen would say to pass. At least his method says to pass; my understanding is that Marty himself held the green card in great disdain.

But wait. Partner actually could claim twenty-two dummy points! He has two quality suits and a doubleton in diamonds. In fact, if the suit that my partner actually opened, hearts, had been one of the quality suits, and if the suit without quality had been the one suit that he never mentioned, clubs, I would have had a pretty good play at making the hand. Maybe my bid was not as stupid as I thought when I saw the dummy.

It may be worth noting that we do better if my partner declares the hand. It would have been theoretically possible for him to garner eleven tricks.