Standard 1NT opener. 

East is probably best doubling for penalties with 15-18 HCPs. South now needs to escape. The most popular defence is known as wriggle - Re-double for ♣ s and use transfers for other suits.

West can wait to see what East will do after the transfer. When East bids 3Cs West can see game values and has probably a ♥ stop so bids 3NTs.

To see what contracts can be made - click on the "play it again" tab, then choose "Bridge Solver Online" and then click analyse.

West opens 1NT with balanced 12-14.

After 2 passes South could bid 2♥ s or a double would be for penalties and after two passes East would try to escape to ♣ s then South could bid ♥ s with a similar result. This works here as North can invite to game which South can go to game with his 5 loser hand. The use of losing tricks is a useful tool. 

After 3 passes East can open 1♦ .

As South has passed he could overcall 1♥ .

West can bid 3♦  as a weak supporting hand. With a strong hand West could bid 2♥  to show good hand with ♦ s.

North may have a free bid to show ♥ s and a reasonable hand. 

The difficult decision for East is whether to bid 5♦ s or double 3♥ s for penalties.

West cannot bid over the 1♥ opener by South.

North with a 4333 hand bids 1NT.

East has a borderline 2♦ overcall which is ok NV.

As North may often have ♣ s for his NT bid so 3♣ s is probably better than 2♥ s.

After 1♦ by South, West can overcall with 1♠  (some might consider a weak 2♠ as a reasonable 5 card suit).

North is probably best to pass. 

East can bid 2♦ as a good (for a passed hand) raise in ♠ s.

West has a weak overcall so converts to 2♠ s.

South opens 1♣ .

North cannot double as they cannot support ♥ s so has to pass.

East bids 1♦  

West can bid 1♠ which is not a reverse.

East can see game, but if West is strong there may be a slam. Best is 2♥  which is fourth suit forcing. If West can bid ♦ s there may be a slam.

However West bids 2NT to show a ♥ stop.

East raised to 3NT

Many possible contracts.

East opens with 1♣.

South overcalls 1♠ 

West can double to show 8+ HCPs and support for other suits.

North can make it difficult for East by bidding 2♠ s that is weak. To show a stronger hand with support he could bid 2♣ s.

East with support for other suits, but without 4♥ s can double showing ♣ ♦  and probably 3s♥  without a ♠ stop.

West then has to choose between 3♣ or 3♥ s.

East opens 1♣ 

West should bid 1♠ which is far more important than 1♦ . If an opportunity ♦ s can be bid later.

East bids 1NT showing balanced 15-16 HCPs.

West can then bid a quantitative 4NTs which says bid 6NT if you are maximum or have a good source of tricks.

East has a good hand and can bid 6NT

A difficult hand to bid due to the voids.

North bids 1♦ 

South bids 1♥ 

North bids 1♠ 

Now how can South explore a slam?

Normal 4NT Roman Keycard will not tell you which of the 5 Aces North has? 

As South can see a minimum 30 HCPs and has control of ♦ ♣ ♥  and 4 card support, the gamble of 6♠ s is reasonable.

East can open a weak 2♦ .

South has difficult decision whether to pass or overcall 2♥  The vulnerability might suggest a pass. However competing is the best decision here.

West should pass as no game values and East is unlikely to have 4♠ s.

North has a strong support for a passed hand so should probably bid an unassuming cue bid with 3♦ , 3♥  would be a weaker bid. South being minimum or subminimum will pass this.