The Board Vulnerability Pattern Is Inequitable Ted Muller

Here is the long-established configuration for the first sixteen duplicate boards:

I call this the BONE CHART.  Every combination of dealer and vulnerability occurs exactly once in the set.  The pattern is repeated for each subsequent group of sixteen boards (17-32, 33-48, etc.).  (Among other things, a mental image of this chart can serve as a quick reference for determining a board's vulnerability.)

Consider firstly the format of Chicago — a game of four-board segments featuring duplicate-style scoring.  Many players conveniently adopt the setup included with Boards #1-4.  From another perspective, those specs are as follows:

• 1 (N dlr) = none vul
• 2 (E dlr) = non-dealer vul
• 3 (S dlr) = non-dealer vul
• 4 (W dlr) = both vul

So the dealer is vulnerable only one time in four; and I ask you, "Is that equitable?"  I contend that it is not.

For example, an aggressive pair that is fond of light opening preempts when Non-Vul would be better-off sitting North-South, because there would be two opportunities to do their thing while the opponents would have just one.  Also, a pair playing Strong Notrumps Vul and Weak Notrumps Non-Vul also would benefit from sitting North-South on this set of boards, assuming that they would like to open with a Weak 1NT as much as possible (which is the whole idea, after all).

Many other Chicago players, who are not utilizing actual duplicate boards, commonly agree on a vulnerability rotation of 'None / Dealer / Dealer / Both'.  That pattern, however, clearly suffers from the same problem, but in reverse; for now the dealer is vulnerable three times in four.  In such a game, the more conservative pair would do best to sit North-South, forcing the opponents to start life vulnerable nearly every time.

The fairness issue regarding table positions could be resolved by starting each rotation of four boards at a different table-position; in other words, hands #1-4 begin with North as dealer, hands #5-8 with East the first dealer, etc.  That would not fix the overall bias of the session, however; for it still would favor the more conservative pair overall with the dealer being vulnerable three-fourths of the time.

Those players using duplicate boards could even the chances by playing sixteen hands.  Using another group of four consecutively numbered boards, however, would not resolve the matter; in fact, if you were to try Boards #4-7, you would find the dealer to be vulnerable on every hand! 

The solution to this problem, though, is elementary.  Simply adopt a vulnerability pattern of 'None / Dealer / Both / Non-dealer', or any rotation of that series including backwards.  Now, the dealer is vulnerable twice and non-vulnerable twice!  What a concept.

If using duplicate boards, this 'fix' can be implemented by rearranging the boards themselves.  The following groupings of four boards satisfy the requirements, while maintaining the four vulnerability patterns and enabling each player to deal a hand:

• 1 - 6 - 7 - 12
• 5 - 14 - 3 - 4
• 9 - 10 - 15 - 8
• 13 - 2 - 11 - 16

There are other workable matrices as well, but do you care?  If not, perhaps the next discussion will have some meaning for you.

Now we are down at the Swiss Teams, where it is common to play 7-board rounds.  Another chart is in order, showing the specs for the standard groupings of boards.  The highlighted boxes show the board numbers on which the dealer is vulnerable:

One anomaly of the configuration is that the set of Boards #8-14 will feature more overall 'action' in the long run due to increased opportunities for preempts as dealer.  So the next time your team needs to catch up to the leader in the late matches, it would be mathematically advantageous to be assigned tables with Boards #8-14 lying on them.  The likelihood of achieving the needed swing-results would be significantly better than if playing, say, Boards #1-7 or #15-21.

Granted, it is unlikely that this insight will change any director's behavior, and no League officials will lose any sleep over it either; but the next time you observe an event-contender skulking about just prior to the start of the last match with Boards #8-14 in his hand, you will know why.

In any case, you heard it here first — at Ted's World.