The original post was:
Matchpoint pairs, Unfavorable Vulnerability, you have this hand in third seat:
S: KQJ
H: QT8
D: 762
C: AKQ8
You play a 2/1 system, where after a 2/1 game forcing bid a rebid by opener of his major suit promises six cards (Larry Cohen style).
The auction goes:
1S (P) 2C (P)
2D (P) ?
-----------------
On the certificate of the Society of Actuaries (yes, I'm a retired actuary) is a motto -- a quote from Ruskin, who lived during the 19th Century.
"The work of science is to substitute facts for appearances and demonstrations for impressions.”
I thought I'd apply that quote to the problem presented in this thread, with such passionate, emotional, but ultimately wrong-headed advice, from several parties.
The painstakingly time-consuming demonstration was done this way:
-- I purchased the program GIB (Ginsberg's Intelligent Bridge Player), which is the Robot player on Bridge Base Online. The Convention Card I chose for GIB was a Two over One system, 15-17 1N, with RKC.
-- Fixing the hand in question to be that in the original post, I generated random partner hands with 5+ spades and 4+ diamonds, using Lorne's Bridge Analyzer. I selected the first 100 random hands in which the GIB program would open 1S and respond 2D to my game forcing 2C bid.
-- After 1S-2C-2D, I forced the fourth bid three ways. I bid 2S, 3S, and 3N, according to the suggestions that have been made. After the fourth bid, the bidding was entirely done by the GIB program. I then recorded the ultimate contract.
-- For each of the 100 hands and for the ultimate contracts that resulted from the 2S, 3S, and 3N candidate fourth bids, I used Lorne's simulator to generate 1,000 random hands for the opponents. Lorne's simulator then compares the DD pairwise result of the final contracts on both an average matchpoint and average IMP basis. I recorded the results of Lorne's simulator in a spreadsheet.
-- The entire spreadsheet, with each of the 100 partner hands, with each GIB auction, and with the Lorne simulator comparison of matchpoint and IMP results is viewable in a Google spreadsheet by copying the following link into your browser.
https://docs.google.com/spreadsheets/d/16C2NVy_srn_N6qKbHiAvFRopV4dWpHyGtMMfsQ-a-lU/edit?usp=sharing
The final results of this painstaking proof were:
At matchpoints, a fourth bid of 3N scores 65.5% versus a fourth bid of 2S.
At matchpoints, a fourth bid of 3N scores 62.1% versus a fourth bid of 3S.
At matchpoints, a fourth bid of 3S scores 50.1% versus a fourth bid of 2S.
At IMPs, a fourth bid of 3N (surprisingly!) scores +.08 IMPs versus 2S.
At IMPs, a fourth bid of 3N scores +.22 IMPs versus 3S.
At IMPs, a fourth bid of 2S scores +.10 IMPs versus 3S.
Statistically, the IMP result is not compelling in favor of any fourth bid. However, I originally expected 2S or 3S to strong favorites versus 3N at IMPs...so it's interesting to see otherwise.
Statistically, at matchpoints, there is no question at all that 3N is the right fourth bid to get the best results if you're playing with GIB as a partner. The results are so compelling, that I'd conclude this is true with any partner not just GIB.
You can look at the spreadsheet yourself, but some interesting things that I note:
-- Once 2S or 3S is bid as a fourth bid, GIB never found its way back into a notrump contract EXCEPT the grand slam in notrump on the appropriate hands.
-- With six spades and a singleton heart that is not the HA or HK, GIB will almost always correct to spades after the fourth 3N bid.
-- The category of the lowest scoring hands at matchpoints for the 3N bid were those that had exactly five spades and a void or singleton in hearts that was not the HA or HK. 16% of the hands fell in this category, and the average matchpoint score for the 3N bid was 22% for this category.
Let me know if anyone can not access the spreadsheet for some reason. I can send it to you by email, or can give you specific access through Google.