Advanced Conventions and Concepts

Slam Conventions

Conventions for Contested Auctions

In contested auctions a whole level of bidding space is taken away and you lose the ability to differentiate between competitive/preemptive bids, constructive/invitational bids and game going bids. Many conventional bids have evolved to reduce the need to make your partner guess. 
A further refinement to standard Blackwood and Key-card Blackwood which enables the location of the trump queen to be found.
Partner has opened 1D, you have 7 points and 4 hearts, about to bid 1H, but pesky RHO bids 2C!!! Your side probably has the majority of the points. What now?? 

Other Conventions

Partner opens 1D and you have 13 points, 4 diamonds and a small doubleton or singleton. You have game points, maybe a slam, but is the best contract 3D, 3NT, 5D or 6D. How can you avoid a blind leap into 3NT or 5D. 
An opening bid of 2NT may contain a 5 card major.  If responder has three cards in that major the fit will not be found using standard Stayman. Puppet Stayman solves this problem
When partner opens a Weak 2 and you believe that game might be on if partner has the right sort of hand (point count and suit quality), the artificial 2NT enquiry (OGUST) asks partner to describe his/her hand. 
Popular in the UK. 
An alternative to Ogust. Preferred by most top players throughout the world.  Recommended by NoFear, Robson and others because it is easier to remember. 
Partner opens 1H and you are about to raise to 3H with 4 card support and 4 hearts, when RHO doubles for takeout. Now if you bid 3H partner will not know whether you are weak with support and trying to silence LHO and don't want partner to bid again, or whether you are inviting to game. How can you avoid making partner guess?
Your LHO opens 1H and partner overcalls 1S. If you are weak with 4 spades you may want to make a pre-emptive jump to 3S and not wanting partner to bid on.  But if you have 10-11 points and 3+ spades you may want to bid 3S inviting game if partner has 13+ HCP. How can you avoid making partner guess?

When you have to overcall at the 2 level it is often difficult to describe a hand with two long suits.

S KQ654  H KQ854   D 4  C 76  has just 10 HCP but has only 5 losers if a fit can be found in one of the long suits. 

The auction may get too high (or end too soon) for you to show both, or you may not have the strength or suit quality to bid either suit safely. 

Partner opens 1NT. You have q game going hand with five hearts but RHO bids 2S!! If you bid 3H how will partner know that you are not just competing for the part score? 
Suppose you showing your best suit means bidding at the 3 level. You have to respond with zero points, so how to you distinguish between a very weak hand, an invitational hand and a game going hand???? 
The opposition have overcalled. You have not found a fit but have game points. 3NT may be the best contract but you are worried about whether you have all suits stopped. 

Advanced Acol Bidding

A structured approach to  determining whether your hand is suitable for a pre-emptive opening bid, and at what level, taking into account your hand strength, suit quality and vulnerabilities of both sides. Using the Rule of 2-3-4 also helps partner to make an informed judgment when assessing whether a game contract has good prospects. 
After partner's 1NT opening bid, a jump in a suit is reserved for hands where game is practically certain but where slam may be possible if opener has the 'right' sort of 1NT hand. The jump bid asks opener's help. 
If your LHO opens in a suit at the 1-level followed by two passes, it is quite likely that the points are evenly divided. Your side might even have the majority of the points.  Partner could have an opening hand but no 5 card suit or no stop in opener's suit. Letting the opponents play in a 1-level suit contract is generally poor bridge - it rarely works out well for your side. All intermediate or higher level partnerships  'protect' in the pass-out seat (aka the 'cheat seat').  It is variously known as 'balancing', 'protecting', or 'borrowing a king'
 For more experienced players. Novices should play intermediate Jump Overcalls.
Modern experts are almost universal in their agreement that a single jump overcall (eg 1 ♣-2 ♠ or 1 ♥-3 ♦) should be disruptive, showing the same hand-type as a Weak two opener, ie 5-10 points and a six-card suit. When vulnerable or at the three-level use more caution - a seven card suit is advisable. Similar to all preemptive bids, the Weak Jump Overcaller does not bid again, his partner becoming Captain.
Strong jump overcalls  were standard 20 years ago but because such hands occur so infrequently the jump overcall is now most commonly used to show a hand that would be  suitable for a Weak 2 opening bid. To make a strong jump overcall you should double and, after partner's  forced response, bid your suit or No Trumps
Playing standard Jacoby Transfers, opener responds robotically and partner decides whether to pass (with 0-10 HCP) , invite game or bid game. However if opener has the 'right' sort of hand (e.g. 14 HCP and excellent support for partner's suit) game might be possible if responder has a moderate (9-10 HCP) hand. Breaking the Transfer / Super Acceptance is a way of involving opener in the decision. 

Partner has limited his hand (less than 12 points). If any side has 22+ points, it's your opponents. There is a greater than 50% probability that 4th seat will have a good hand. With 10-11 points you can open light, pre-emptively

In fourth position ALWAYS open if HCPs plus the number of spades in your hand = 15+. Spades is the master suit.  The high card points are very likely evenly divided between the two partnerships. Fourth Seat should open only with a Spade suit, thereby declaring that he does have the boss suit. Possessing the Spade suit inhibits intervention from the opponents. With 10 HCP and five spades, open 1♠.

The 2C opening bid is a 'last resort' forcing bid when you have a hand that can practically make game on its own but you are worried that partner might pass. It is a blunt instrument - you should adopt other methods where possible.  
In Standard Acol the NoTrump rebid ranges are:
15-16:  rebid No Trumps at the lowest available level
17-18: Jump rebid in No Trumps
19: Double Jump rebid in No Trumps
The double jump is very clumsy - there is no room to investigate alternative contracts. Most top players now play modern Acol rebid ranges.