The Power of Fits by GS Jade Barrett

Jul 3, 2013

We can easily determine what our minimum fit is based on what we learn from the auction and the opponents.

Hypothesis:  When they have a fit, we have a fit.

Rule #1:  When the opponents have an eight card fit our minimum fit is 7.

This rule is proven in the following manner:

The opponents have the following auction:

1     P       2     ?

The opponents have a minimum fit of 8 Spades. That leaves no more than 5 Spades for us. Since each of our hands has 13 cards for a total of 26 cards for the partnership, and we – as a partnership – hold no more than 5 Spades, 21 of our cards must be Hearts, Diamonds and Clubs, the 3 remaining suits. When we divide 21 by 3, the product is 7 – the number of cards that we could have as a partnership in each suit.

If you held Ax Axxx Kxxxx xx, the only instance in which your partnership would not have an 8 card fit is when your partner held 3 3 2 5.

This is represented in the following equation:  26 – (13 – their minimum fit)/3 = our minimum fit.

26: the total cards held by the partnership.

(13 – their minimum fit): the minimum number of cards held by us in their suit.

3: the number of the suits remaining.

Rule #2:  If the opponents have a nine card fit, we must have at least one eight card or longer fit.

1     P       3     ?

In this auction the opponents typically have 9 or more Spades.

Using the fit formula we can determine the following:  26 – (13 – 9)/3 = 7.333

26: the total cards held by the partnership

(13 – 9): their minimum fit subtracted from 13 (the total number of Spades)

3: the total number of suits remaining.

Since cards are always whole numbers (you cannot have 1/3 of a heart for example) we must have at least one 8 card fit.

An alternative way of expressing this rule follows:

Rule #2A: Whenever the partnership has fewer than 5 cards in any given suit, we must have at least one 8 card fit.

By the use of this formula we can also determine the following minimum fits:

When the opponents have a 10 card fit:

26 – (13-10)/3 = 7.666.   One 9+ fit, or two 8 card fits.

When the opponents have an 11 card fit:

26 – (13-11)/3 = 8. One 10+ fit, exactly one 9 AND one 8 card fit, or three 8 card fits.

When the opponents have a 12 card fit:

26 – (13-12)/1 = 8.333. One 11+ fit or exactly one 10 AND one 8+ card fit, or two 9 card fits.

When the opponents have a 13 card fit:

26 – (13-13)/3 = 8.666 one 12+ fit or exactly one 11 AND one 8+ card fit, or exactly one 10 AND one 9 card fit, or one 10 AND two 8 card fits, or exactly two 9 AND one 8 card fits.

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