Monday, February 5, 2007

Cost-Benefit Analysis with Tools

A recent forum discussion on BBO brought up an issue that is worthy of analysis. One noted expert questioned whether an "Empathetic Splinter," for instance, might give up too much information to the opponents in a specifc auction.

The analysis of the cost-benefit to any slam move is a constant issue. Some times, resigning to a game when slam is remote may be the practical solution for a given hand, given event, given state-of-the-match. Of course.

However, knowledge of the tools necessary will help in the decision as to when to pounce, as events may suggest pouncing.

A simple example. After 1NT-P-2C-P-2H-P-3H, Opener holds AKx-KQxxx-Ax-xxx. Slam might make opposite Qxxxx-Axxx-xxx-x, right? The method to find the slam might be to use a cuebid of 3S, allowing 3NT from partner and 4D by you. (Empathetic splinters would be difficult here, because you cannot focus a suit and a hole, so cuebidding is used.) However, this might direct the defense to a club lead. So, you might forego the slam move for practical reasons.

However, studying this situation is useful. What if Opener's RHO had doubled 2C initially? Now, the cuebid may make sense for several reasons. First, a club lead is coming anyway, such that disclosure helps the opponents very little. Second, the chances of partner being stiff in clubs are higher, such that the possibility of the well-fitting slam increase. Third, a well-placed cue of 3S might occasionally help if the opponents happened to have been lurking and planning a sacrifice at 5C if you reach game, in which case your cuebid helps in the five-level (or slam) decision.

Of course, once 2C is doubled, empathetic splinters are more useful now, as the implied necessary shortness is known (clubs). Thus, 3S would imply five of seven keys, with spades and hearts being the focus suits and diamonds being the control suit. 4D, in contrast, would imply a similar hand, with diamonds-hearts focused and spades control-only.

A recap on empathetic splinter analysis. If the necessary shortness is established and known (their suit, or a previously-shown suit that might have caused improper discounting of reciprocal shortness value), the cue identifies the two-suit focus. If the necessary two-suit focus is established, the cue identifies the hole (where shortness would be of value). If neither is known, then normal cuebidding is used.

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