Friday, June 18, 2010

Opening Bid Frequencies

Do you know the probability that you'll a strong NT hand? And how much more likely is it that you'll be dealt a balanced 12-14 instead of a balanced 15-17? Everyone likes opening 1NT because auctions after that are usually pretty easy and it makes it hard to interfere.

Now that my computer program can now reliably open the bidding and reliably make responder's first call in standard, canape precision, and canape polish club, I ran some simulations to see how frequently each opening call is used. Well, it can respond when the opening bid is 1C or 1NT. Looking at only the north hand in 200,000 deals, a 1NT opener was dealt 4.05% of the time while a 12-14 NT was dealt 9.07% of the time. In standard bidding, 42.89% of the hands resulted in some opening bid, 7.61% of which were preempts or weak 2 bids. In canape precision and canape polish club, only 39.73% and 39.44% of the hands were opened. This is almost entirely attributable to the more constructive weak 2 bids that I have adopted for use with canape - something on the order of 8-11 hcp with 2 of the top 4 honors instead of the 5-10 range that I used for a standard weak 2. Thus, in the canape systems, 4.12% of the hands were opened with some sort of a preempt.

In standard (opening 1C with 3-3, 1D with 4-4 or 5-5, and the longer suit otherwise), 1D was the most frequent opening bid at 8.72% with 1C not far behind at 8.20%. In both canape systems, 1C was overwhemingly the most frequent opening bid. I am somewhat surprised by this. In the Canape Polish club system, 1C is opened with all balanced 12-14s, balanced 18+, and all hands over 17 hcp (not using the variation that it could be 15-17 with 5+ clubs) so it makes sense that 1C would be opened 15.13% of the time. And of the hands opened 1C, 59.93% of them are of the balanced 12-14 variety. This would suggest that if you're defending against the Polish club, it's probably best to treat it as natural (2+) since if you have a good hand as LHO, it only increases the probability that the 1C opener has the balanced minimum.. Behind this, 1D, 1H, and 1S (which all have exactly the same requirements with the suits switched) and 1NT (15-17) are all opened between 3.80% and 4.18% of the deals. 2C isn't far behind at 3.54%. The requirements for opening 2C are basically the same as for 1D/H/S but sometimes we may suppress the 4 card club suit and treat the hand as a major one-suiter. In canape precision, where 1C is opened on all 16 hcp hands, that bid is made 11.48% of the time. This still seems a bit high to me but I can't find a flaw in the programming and don't feel like doing the math to determine if this is what it's theoretically supposed to be (even though that math isn't all that hard).

Another thing I was interested in looking at is how frequently the responses to 1C are used. These looked at only the south hand on the deals that 1C was opened. In the Canape Polish club system, 1D, which is 0-7 (but not 0-4 with a 6 card major) or 8-11 blanced, was bid 62.60% of the time. 1H/S/NT are all used about equal around 7.5%. In Canape Precision, the 1D response (0-7, but not 0-4 w/ 6M, OR 13+ 4441) is made 54.49% of the time. 1S at 15.43% is clearly the next most common response because it is a balanced 8-10 or 14+. hmm.

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