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Unusual NT - 5521 or 5530?

A player bids the unusual NT. What are the odds this player's hand is 5521 rather than 5530? Even though we are not talking about suit splits between two hands, the notion that a 2-1 suit split is more likely than a 3-0 suit split isn't a totally useless view.

 The ACBL Encyclopedia of Bridge, 7th Ed. provides two different tables where (in this case) the odds can be correctly determined to be 3.55 to 1 favoring the 5521 hand.

From Table 1, page 576, P[5521]/P[5530] = 3.1739%/0.8952% = 3.55. From Table 4, page 578, P[2-1 trump split]/P[3-0 trump split] = 78%/22% = 3.55. The odds are mathematically identical.

Considering 6421 and 6430 hands, we get P[6421]/P[6430] = 4.0721%/1.3262% = 3.55 also.

Caution is needed. Consider 7321 and 7330 hands. It is generally wrong to use suit split Table 4. Table 1 gives the correct answer P[7321]/P[7330]= 1.8808%/0.2652% = 7.09, not 3.55.

An observant reader might note that within roundoff, 7.09 = 2 * 3.55. The advantage in using odds is that even if the player bidding the unusual NT turned up to have 4432 distribution in the minor suits, the odds of 5521 over 5530 remain 3.55 to 1.

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