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A matter of statistics

After opening 1N (weak or strong) many play 4M if they find an 8-crd-fit in M and 3N if not. Some consider that not all 8-crd-fits must play in 4M. The opposite however is equally true: not all 7-crd-fits must play 3N. With a singleton opposite three small, opps have 9 with all the high cards and are very likely to find the correct lead. 4M in a 5-2- or 4-3-fit or even 5m in an 8-9-crd fit is probably better. We are currently thinking about an NT-structure taking this into account. In the discussion an interesting statistical aspect came up in comparing WNT to SNT.

Partner: the problem is less likely to occur with SNT because opener has in total more high cards to make up a stopper.

Me: WNT or SNT, if we have a total of 26 hcp in 26 cards, the probability of a stopper in the singleton is independent of how the 26 hcp are devided.

Your opinion?

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