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After a simple opening, response and jump rebid, East made a cue bid of 4 Clubs that suggested slam interest to his partner. Note this only "suggests" interest, it does not force you to play in a slam. However... West visualised an easy slam. With a hand that contained possibly 5 Diamonds and 4 Clubs, why would East want to show these two suits when partner has shown a powerful Spade suit. The Cue Bid of 4 Clubs said simply 1: I like Spades; 2: I have the Ace of Clubs; 3: I may have the right cards for a slam if you are interested.
4NT was one of the popular versions of Roman Key-Card Blackwood (14-30) and the 5 Spade response showed 2 of the 5 Key cards AND most importantly, the Queen of trumps (Spades).
West visualised 6 potential Spades tricks, a good chance of 5 Diamonds (partner would only need say the Ace and Jack of Diamonds to make slam excellent) and two outside Aces to make 7NT. He check on Kings via 5NT (guaranteeing that all five Key cards were held) and the 6 Spade response showed none. East West were playing a popular response system where a bid at the 6 level would either show the King of the suit bid OR the other two Kings outside trumps.
At worst the Grand Slam may come down to a squeeze or a finnesse. 7NT made with ease when North led a Diamond and East West chalked up +1520. This translated to +11 IMPS when the board was only played in 6S+1 at the other table. East West were the only people in the room to bid 7NT. Two other pairs managed to bid 7 Spades.
TIP - 6 MAKE A CUE BID ON THE WAY TO GAME to suggest slam interest.