2♦ . Your partner opens 1♠ and South doubles for take-out. The double changes most of the meanings of responder’s bids. Redouble is used for all the strong hands (9+) so all 2-level changes of suit show weaker hands: 5-8 HCP, 6+-card suit, non-forcing. This is a distinct change from without a double, when the two-level bids would be 10+ and forcing. The key is the use of the redouble to show the stronger hands. Here, you bid 2♦ , expecting your partner to pass, as he should

East Hand ♠ AK753 ♥ A82 ♦ K3 ♣ 632

6NT. Your partner rebids 2NT which, in modern Acol, shows 18-19 points. You have a balanced hand, with no major suit fit, so you aim for a no-trump contract. Adding your 15 to partner’s points gives 33-34, which is enough for slam. There is no need for any shilly-shallying: bid 6NT. The number of aces and kings is not important in no-trumps because the queens and jacks are just as important. For 7NT you need closer to 37 points unless you have a strong and long suit, which is not the case here.

East Hand ♠ A7 ♥ A943 ♦ KQJ4 ♣ AT2

3NT. When a minor is supported, then both members of the partnership should have aspirations towards no-trumps and all their bids will be directed in that direction until they get to the 4-level (above 3NT). Your partner’s 3♠ bid is not an attempt to play in spades, rather it is a try for no-trumps – he is showing strength in spades. Just as important as his spade strength is his implied heart weakness (he missed that suit out). Have you got a stop in the heart suit? It may not be very strong, but as long as you are playing 3NT, your ♥ K constitutes a stopper. The lead will come towards you and if they lead a heart, you will definitely make a trick. Therefore, you bid 3NT and reach the right contract. You have nine top tricks with a tenth trick available on a heart lead (unless diamonds break 4-0)

East Hand ♠ AK5 ♥ 987 ♦ A8765 ♣ T98

2♥ . When your partner shows two suits and you have a weak hand, you do not have too many options. Generally, you give preference to one of his suits, favouring the first suit if there is any doubt. You rebid your own suit only if you are sure it will make the best partscore contract, which means you must be willing to play opposite a singleton in your partner’s hand (a good six-card suit or better). Your spades are not good enough to rebid on this hand so it is a choice between diamonds and hearts. You should give false preference to hearts. When the first suit is a major and the second a minor, if you have one fewer card in support for the major with a weak hand, you should generally go back to the major suit. 2♥  is the most comfortable part-score. With two weakish hands, it is your job to find the safest part-score contract. 

East Hand ♠ 6 ♥  AK753 ♦ AK43 ♣ T98