[bibleblack]

The prescribed solution appears to commit declarer to a 3–2 trump assumption, with the primary objective of safeguarding against a 5–1 diamond split. The drawback of this approach is that the contract fails whenever trumps are 4–1, despite that split being materially more common than the diamond break being protected against.

The Bridge Master line succeeds whenever trumps are 3–2 and diamonds are not 6–0, which occurs with probability

0.68×0.99=0.673

However, the combination of: trumps not 5–0 (3–2 or 4–1), and diamonds breaking 3–3 or 4–2, occurs with probability

(0.68+0.28)×(0.36+0.48)=0.806

Given this disparity, it seems more percentage-oriented to play the ♦A on the second round of diamonds, assuming East follows suit, and retain the duck (or allowance for an overruff) only when East shows a singleton diamond.

Unless the solution relies on an implicit vacant places inference not suggested by the auction or early play, the recommended line appears to favor a significantly less likely danger at the expense of a more common one. I would be interested to hear the intended reasoning. Comments appreciated. Thank you.

[AL78]

It only commits declarer to a 3-2 trump split if the diamonds break 5-1. If the second diamond is ducked and both follow, they are 4-2 or 3-3, declarer only needs to ruff once in dummy to be certain of establishing them, that cuts down the number of times declarer needs to ruff back to hand, so there are enough trumps to cope with a 4-1 split in these cases.

As it says in the solution, if you play the ace on the second round of diamonds and it is ruffed, the contract can no longer be made because firstly, one of your winners has been ruffed and secondly, West will return a trump which prevents you ruffing all your losing diamonds in dummy. If you duck, it does West no good to ruff as they are ruffing a loser.

If diamonds are 5-1, declarer needs to ruff their three diamond losers in dummy as the diamonds cannot be established. To do this, then need to ruff back to hand multiple times and shorten their trumps to the point where they need to break 3-2, but that is unavoidable.

If the diamonds are 5-1 and the trumps are 4-1, the contract cannot be made on best defence. The recommended line of play allows you to make the contract whenever it is possible.

[Stephen Tu]

The suggested solution only runs into trouble when both diamonds are 5-1 and spades are 4-1. If the diamonds split 4-2/3-1 there is no problem. The person you duck the second diamond to has to return a trump otherwise you can always just do a high cross-ruff. You ruff the third round of diamonds, if the diamonds have split you just draw trumps after ruffing one diamond and it's still fine if trumps are 4-1.

[bibleblack]

“It only commits declarer to a 3–2 trump split if the diamonds break 5–1.”

Indeed—that was the key point I had overlooked. I had initially thought the contract would go down on a 4–1 trump split, whereas in fact only one diamond ruff in dummy is required to make the contract provided diamonds are no worse than 4–2.

Apologies for the confusion, and thank you for the clarification.