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Online training: An unexpected but reasonable ducking

HAHAHA, after one month off bridge, I'm back!!!

This deal happened in our weekly online training, Nov 5th, 2018.

First of all, I have to admit my mistake. Hahaha, to be honest, the training was quite boring. After 12 boards, the scores were still 2:2. Although I knew X was not allowed and I would be fined if 3♣X was brought home, I still couldn't help to doing that.

Board 13
Dealer: North
Vul: Both
North    East    South    West
 Pass     Pass      1♢         2♢*
  2♡*      2♠       Pass       Pass
  3♣         X         AP
2♢: Michael
2♡: ♣ suit, better than 3♣

Lead: ♡3 (if hasn't raised, count has a priority. That is to say, xxx lead the smallest card)
Table followed ♡9. Normally, you would play ♡Q causally. Would it be correct in this case?

Leading analysis: East seems to hold 3♡, unless East hold ♡32. In that case, North might not scramble for 3♣ under such vulnerability if North has 4 cards ♡.
Bidding analysis: There is no doubt that East doubled, depending on good trump. North scramble for the 3♣ which indicates that he hold at least 6 cards ♣ ,singleton ♠ and ♢A. Namely, ruffing ♢ was impossible. So winning 5 tricks in ♡ and ♣ was the only defense. East must hold two ♣ honors and some structures.
Structure analysis:
(1) ♣ suit
What  ♣ East becomes a serious problem.
(a) KQ9X Maybe he would not double.
(b) AQ9X At least he hold. Even better, such as AQ98 or KQ98
(2) ♡ suit
Does East hold ♡J? If North hold ♡J, there is no need for him to ruff the last ♡. That is to say, winning the first trick was meaningless. If East hold ♡J, playing Q and T is equivalent.
(3) Combination
Winning with ♡Q equals to give up the chance of trump promotion because ♡ is the only connection between you and your pn. So following ♡T seems to be crazy but reasonable.

Some readers may ask ducking would lead over one. Thinking deeply, South hold ♣T, if he ruff the last ♡, your pn would win 3♣ which has the same value in total tricks. In other words, if East hold ♣KQ9X without ♡J, the contract was icy. So you must assume that your pn must hold ♣KQ9X and ♡J at least and follow ♡T breezily.

The full deal
Board 13
Dealer: North
Vul: Both
Unluckily, being fined 1000 rmb was the end of the story.

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