kenrexford, on Aug 19 2009, 03:46 PM, said:
Cascade, on Aug 18 2009, 07:54 PM, said:
I gave one hand a specific game going 5=1=4=3 opposite any Balanced hand.
The standard deviation for tricks in spades was 0.955707068
Second i started with a specific 3=4=3=3 opposite a random 5=1=4=3.
The standard deviation was then 0.829442584
Not surprisingly lower since 5=1=4=3 is more specific than any Balanced hand.
Next I looked at 5 spades and 1 heart and any minor distribution (which happens to mimic our system).
The standard deviation was 0.906209689 - still lower than the distributional hand judging.
Surprisingly I generalized a bit more to 5+ spades and 0-1 heart (0 only with exactly five spades) and the standard deviation was 0.864081015.
While the responder most certainly needs to be the captain for the initial decision - part-score, invite game, game, invite slam, slam. It seems that most definitely that opener is better placed to make the final decision.
I also tried crunching some numbers on this. I took the standard deviation ratio of the inverse of the par 0.50000, multiplied by the ratio of the number of cards in spades in the average deal where 1♠ is the opening, divided by the number of side suits expected to split 2-3 or 3-2 because of a secondary, but unknown, fit.
Using this figure, I then extrapolated the likelihood of a stiff emerging against each of the three top honors, and then combinations of the same, with an averaged deviation expectancy for the unknown values of lesser honors (using 8, 9, 10, and J at a surrogate value of .25, .33, .50, and 1 respectively), plus or minus from an average expectation of 3.33 (the average length of a suit when esponder has 4-3-3-3 and 3-card spade support) times the average spread of these cards that is expected (each suit having honors, or no honors, respectively).
I then cross-checked these figures to corroborate the valuations, discerning that ties to higher honors were less likely than originally inspected, in a sense because the high honors take a "space" in the grid of calculated occurrences.
This final figure was then tweaked by 0.125% off base, to gain a more realistic view of what is actually happening.
I then did the same process in reverse, to account for Opener-directed inquiry, as opposed to Responder-directed inquiry, alternatively Opener-show versus Responder-show (a term I think fits). Comparing these two results yielded interesting insights.
Primarily, I determined that Winston has no clue how to bid bridge hands and that Cascade is out of his mind.
I hope that doesn't mean i am in your mind.

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