Page 27 - ABF Newsletter June 2025

Letters to the editor
THE WEAK FREAK – ANALYSIS COMPLETED
Fred Whitaker’s question, about the probability of the hand his partner held in the Monday duplicate, was too much for me to pass up. The question was, what is the likelihood of holding an eight-high Yar- borough with a six-card suit.
I’m a bit rusty, but here are my calculations.
Board 15. Dealer South. North-South vulnerable.
]K9
[ J 10 3
} A 10 9 7 {KJ93
]AQJ3 ]876542 [AK765 [84 }KQJ }83
{4 {752
] 10 [Q92 }6542
{ A Q 10 8 6
Note: The exclamation mark means that you should multiply together all the numbers up to and including that number. For example, 4! = “Four factorial” = 1 x 2 x 3 x 4 = 24.
There are seven ways of having a six-card suit that is at most eight-high (876543, 876542, etc.), which can be in any of the four suits, which gives 4 x 7 = 28 such six-card suits.
There are seven other cards in your hand, and 21 other cards in the deck no higher than an eight. These seven cards can be ordered in 21! different ways. However, they don’t have to be in order, and there are 7! ways of ordering the cards that were
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in the given hand, and 14! ways of ordering the 14 cards that weren’t.
This gives ways of having seven other cards.
As this can be in any of the four suits, the number is therefore
= 3.3 million ways.
With similar reasoning to the above, the number of possible bridge hands is = 635 billion.
If we stop here, we get
= 1 in 195,000.
But we’ve left a few cases out ...
I’m assuming that a seven-card suit would also fit Fred’s conditions. There’s only one way to have a seven-card suit headed by the eight; similar to the above, the calculations are
= 217,056 such hands.
However, there’s a small amount of double counting here, as some hands have two six-card suits, or a six- and a seven-card suit. There are six combinations of two suits, each of them can be chosen in seven ways, and the final card can be any of the other 14 cards. That makes 6 x 7 x 7 x 14 = 4116 six-six hands, plus 4 x 3 x 1 x 7 = 84 seven-six hands.
So the number is
= 1 in 183,069.
Fraser Rew
Apology
The photos on page 1 and page 34 of our April edition should have been credited to Lauren Travis, rather than to the Gold Coast Congress. Lauren and Barbara Travis were the editors of this year’s Congress Daily Bulletins, and they also took on the role of photographer, after the retirement of long-time GCC photographer Anne Russell.
Australian Bridge Federation Ltd. Newsletter: June 2025
Page: 27