Ted's Bridge World Simulatron

Is 5-3-3-2 Really Better Than 4-3-3-3?

Reader Rod Bias is interested in the relative value of a fifth card in the long suit.  The following pair of simulations yields some idea, in terms of trick-taking potential.

12 HCP opposite balanced 8-20 HCP:

*

This result is surprising to me.  The five-card suit produced only 8.06/7.98 as many tricks on average — an increase of just 1%.


16 HCP opposite balanced 8-18 HCP:

*

This time the 5-card hand generates 9.90/9.75 as many tricks — a 1.5% improvement.

Note that in both comparisons the 5-3-3-2 hand has greater results at the extremes — more hands taking a lot of tricks, and more hands taking few tricks.  When the diamonds are weak in both hands, bad things happen; w hen north covers that suit, life is good.  At a later date, SIM will study this phenomenon in detail.

Yet why is the second differential greater than the first?  It must have something to do with the combined strength of the two hands.  More 1,000-deal simulations yield these results:

*

These data seem inconclusive to me; larger samplings might prove more meaningful.  On this chart, however, the average gain from the longer suit is 2.4%, or approximately the value of a jack.  It appears that Charles Goren might have been correct!  Using Standard American methods, the hand with the 5-card suit, featuring a doubleton perforce, is worth 1 point more — the value of a jack.  (Please do not take this as a personal endorsement of S.A. valuation!)

* In notrump, the fifth card in a suit is not as valuable as is commonly perceived.

It also appears that the 5-card suit is maximally useful when the combined strength is in the 29-32 HCP range — enough to more or less ensure the utilization of the long-suit card, yet not so much power that the long suit becomes redundant.  Those numbers suggest this directive:

* When considering a marginal slam, invite only when holding a 5+ suit.

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Actually, I was just guessing that an extra jack would represent 2.4% of the the total tricks.  It might well take more than that on average to produce such results.  Mr. Bias suggested that a queen might be closer to the truth; he could be right.  Eventually, SIM will get busy and determine The Way It Is.

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