I played live bridge last night at the local club with Cindy. The event was an Eight is Enough game with Swiss Teams format.
On one deal, 1 opened 1♠, she responded 2NT and after two rounds of control bidding, Cindy bid 4NT. I answered 5♥. From her hand (and the bidding), she knew that we had all the aces outside of the trumps suit, but were missing either the ♠K Q x x or ♠A Q x x. Also, I suppose I could have had a sixth spade, but she couldn't be sure of that (although I might show the queen with a sixth spade because I know she has at least four).
Here were our two trump suits (with the spots rearranged slightly):
♠J 10 7 3
♠A 9 8 6 4
If you knew that these were the holdings, would you want to be in 6♠, assuming you have enough other tricks (we did)?
Conventional wisdom says that you don't bid a small slam off an a key card and the queen of trumps. Sometimes, conventional wisdom isn't correct, as Cindy figured out. Here's why.
First I tried looking up the suit combinations in the Encyclopedia of Bridge, but that was a pain. Then I remembered I had installed the SuitPlay software, developed by Dutch player Jeroen Warmerdam. When I ran that, the program told me that we were a 76% favorite to bring the suit in for one loser and thus make the slam.
If I had held ♠ K 9 8 6 4 instead, SuitPlay tells me I am a 50% favorite.
Now let's look at the IMPs at stake. Let's assume the other pair who held our cards played 4♠ (and they did). When we go set, we will lose 13 IMPs (650 + 100 is 750 and 13 on the IMP scale). If we make slam, 50% of the time we will gain 13 IMPs (1430 - 680 is 750). So if I have the worse holding (the ♠K instead of the ♠A), we break even.
Now what about the case where I have the ace high holding? In that case, we will win 13 IMPS 76% of the time and lose 13 IMPs only 24% of the time. This means that roughly three times out of four, we gain 13 IMPs, and one time out of four we will lose 13 IMPs. So, it is clearly right to be in the slam based on these numbers. (Of course, state of the match, who you are playing against and other factors could change things.)
I love bridge. Everytime I play, I learn something new. Thanks, Cindy!
If you enjoy suit combinations, you may be interested in this piece from Justin Lalls' blog Squeezing the Dummy. Scroll down to Card Combo Fun after you go there.