How many high-card points does a partnership need to bid 6NT? About 32, but fewer when there’s a running suit.

How many HCP for a small suit slam? You wouldn’t believe how few.

Here are three concepts flourishing in modern bridge.

• The splinter bid. One level higher than a jump shift, a splinter shows 4+-card, 13-15 point support (counting distribution) for partner’s opening bid, and a singleton or void other than an ace or king in the bid suit. Let’s say partner opens 1♥️ and you hold these cards as North:

♠️ K 4 3
♥️ J 10 9 8
♦️ A K J 4 3
♣️ 8

Bid 4♣️. Despite only 12 HCP, North’s singleton club and diamond strength re-evaluates the hand to about a game-forcing, 15-point support.

• Losing trick count. To determine how many tricks you can lose after you find a suit fit with partner, count every suit through the first three cards from the top down. An ace or king counts as one trick, a queen half a trick.

Here’s a case in point, with South dealing and no one vulnerable:

                                           NORTH
                                          ♠️ J 10 9 4
                                          ♥️ K 2
                                          ♦️ 8 •
                                          ♣️ A J 10 8 6 5

WEST                                                                       EAST
♠️ 6 2                                                                      ♠️ 7 3
♥️ 8 5 3                                                                   ♥️ J 10 7
♦️ A J 6 3 2                                                             ♦️ K Q 10 7 5
♣️ Q 9 4                                                                  ♣️ K 7 3

                                        SOUTH
                                       ♠️ A K Q 8 5
                                       ♥️ A Q 9 6 4
                                       ♦️ 9 4
                                       ♣️ 2

The bidding proceeds as follows:

South               West           North           East
1♠️                   Pass           4♦️               •   Pass
4NT                  Pass           5♣️               ••   Pass
6♠️                  All Pass

• Splinter showing at least four spades, game-going support and either a singleton or void in diamonds.

• • Using the 1430 bidding system, North’s 5♣️ bid shows one very key card, the club ace.

The hand is duck soup for South. Seeing the splinter, South salivates. And things keep improving. The biggest worry, diamonds losers, is reduced to one, and clubs to none. A minimum opener typically has seven losers, and that’s what we see from North. South’s losing trick count is four: two diamonds, one club, and one heart. The ♥️ Q is too valuable here to count as half a point.

• The guideline of 24. Add your losers to partner’s and subtract the total from 24. That’s the level you should be aiming for. In this case 24 minus 11 equals 13 — a small slam. South’s only question is club losers. With the ♣️A in hand, declarer bids a safe slam.

Unless the ♦️A is led, South takes 13 tricks. Returning to this column’s initial premise, please note that North-South have all of 24 points between them.