Sigi_BC84, on Feb 8 2006, 10:50 PM, said:
What I'm having in mind is to construct typical deals where Raptor and natural notrump overcalls would apply, and see which one loses or gains more and if it will average out in the end.
For what is worth, I did graduate work in game theory...
I also think that i have a passing knowledge regarding different bidding systems...
While I find discussions like this one an interesting way to pass time, I'd strongly recommend against trying to do any "serious" work in this field. The topic is WAY too complex to reach anything resembling a definitive answer...
Francis has already alluded to three of the key problems in formal analysis of bidding systems:
The first is the relationship between the "bidding game" and "card play" game. All the different bids that you make (or don't make) have an important impact on declarer play and defense.
Equally significant, you can't analyze individual bids in isolation. Case in point, you can't hope to analyze Ben's Misery preempts without also consider the impact on the major suit opening style.
Finally, you need to consider the opponent's best responses. Unfortunately, many people who vreate a new toy often have significant blind spot's regarding different ways to exploit the methods.
To this list, I'd add one other issue. From my perspective, this is the real deal-breaker in that it increases the complexity of the problem by a couple orders of magnitude. As I've noted in the past, we have no reason to suspect that bidding systems exhibit transitivity. Assume that
2/1 Game Force is a "better" system than Acol
In a similar fashion, Precision is better than 2/1 Game Force
If transitivity holds true, then Precision is better than Acol...
My gut says that transitivity assumptions are not warranted, in which case we aren't looking for an optimal bidding system, but rather, some a population consisiting of some optimal ratio of bidding systems. Throw in the potential for cyclical equilibria and you have a modelling problem that I wouldn't touch with a 10 foot pole (unless, of course, I was being paid by the hour)