After an unopposed auction of
♠Q7 ♥K532 ♦743 ♣A832
It's nine points, which is a maximum. But using Losing Trick Count it has but nine losers, which is a minimum. So, should you bid game or not? It's actually a bit of a trick question, as the 3♥ bid was not an invitation to game, it just showed long Hearts and is designed to make it harder for the opposition to enter the auction. If opener actually wants to invite to game, he bids something else. You should just pass whether maximum or minimum. Opener has:
♠65 ♥AJT876 ♦AQ8 ♣75
The same meaning applies to the final bid in the similar auctions
So what about when opener actually does want to invite to game? Suppose the auction so far is
|Long suit trial||Shows a good second suit, looking for a double fit, e.g. bid 3♣ with ♣KJxx|
|Help trial||Shows a suit with losers, e.g. bid 3♣ with ♣Qxx|
In all cases responder re-evaluates his hand, and based on that decides whether or not to bid game. Against the long suit trial an ideal holding is something like ♣Qxx. Against the help trial an ideal holding is something like ♣x or ♣Axx. If responder is maximum he always bids game.
I'm now going to propose a third system, which is something like a Short suit trial. It's based on the observation that low point count games tend to be the ones where there is something like ♣xxxx or ♣Axxx in one hand opposite ♣x in the other. It's actually specifically looking for singletons. It also has the advantage of finding a singleton in either hand.
After 1M-2M opener bids:
|Cheapest Bid||Asks responder for a singleton.|
|Suit at three level||Shows that singleton.|
Just for clarity here's what opener bids after 1♠-2♠:
|2NT||Asks responder for a singleton.|
|3♣/3♦/3♥||Shows that singleton.|
It's slightly messier over 1♥-2♥, as both opener and responder have to use the available bid of 2NT to show a Spade singleton:
|2♠||Asks responder for a singleton. Responder bids 2NT with Spade singleton.|
|2NT||Shows a Spade singleton.|
|3♣/3♦||Shows that singleton.|
Finally here's a (made up) example of the devastating power of these singleton trials.
West open 1♠ and East replies 2♠. West has 6 losers so is worth a game invite. He ask East for a singleton, with the artificial bid of 2NT. Although East is minimum with 9 losers he shows his Heart singleton and West bids the game. Declarer should make ten tricks; five Spades, four Hearts and one Club.