Part VII - Old School
(Page of 2)

This time out, I want to consider two hypothetical competitive problems.  In both cases, North opens 1 holding a minimum, with five spades, and South raises.  The bad guys push up to 3.  Should North-South defend, or bid on?  Everyone is vulnerable.

Case 1:  North is 5-2-3-3, South 4-2-4-3.

Case 2:  North is 5-1-3-4, South 4-3-4-2.

Case 1 shows how bidding has changed since I started (back in Shakespeare’s day).  To an Old School player, competing to three spades on two balanced hands, vulnerable to boot, is insane, but most of the old-timers would take the push with North’s hand two.  They told me, in clipped Olde English, “’tis easier to win five tricks o’er nine,” and “flat hands defend.”  Today, we see nine trumps on each side, and count eighteen total tricks, and bid on to three spades.  Does SF (the Second Fit number) give a different result?  No.  SF is 16 on both hands, with no downward adjustments for short trumps, so SF also predicts 18 winners.

Old-fashioned bridge upgrades for North’s singleton.  Modern bridge upgrades for South’s fourth trump.

This problem is ripe for simulations, and I ran double-dummy simulations for both cases, giving North 12-14 high-card-points, and South 5-9.  Here are the results:

Case 1

The results were very close.  In the simulations, there averaged 17.11 total tricks, a number that makes bidding or defending essentially a toss-up.  Defending turned out to be .17 IMPs better than bidding, a difference due almost entirely to the vulnerability.  Change the colors and it would be correct to bid.  In practice, one should look at honor location to make the final decision, bidding on unless we hold too many honors in our short suits.

Case 2:

This time, bidding was a huge winner.  There were 18.05 total tricks on these hands, and bidding netted +3.37 IMPs per hand over defending.

These are fascinating, and surprising results.  In both cases, using either SF or the Law, we expect 18 total tricks, but Case 1 falls short by nearly a full winner.  All that changed was North’s singleton.  If I had to guess a rule, it would be this:

• Total trick prediction is valid if our side has a singleton somewhere, but we should deduct a full trick if we lack a singleton.

This guess will turn out to be a bit extreme, but it is still fairly close.  Next time out, I will analyze, in boring and excruciating detail, the impact of shortness in our hands.