Theory of CDH

CDH is a our simple to use method aimed at competing against balanced 1NT openings.

Against a 12-14 NT the basic requirement is to hold 2 or more 4 card suits.

Of course a 5 card is good too! If NT is stronger, 15+, more length 5-4 becomes essential.

Vulnerable also requires more distribution - preferably 5-5.

12-14 on your right, leaves 27 around the other 3 players. Mathematical probabilities gives an expectation of 8 +/-1 HCP for the player on your left.

This leaves 19 combined expectation for you and your partner. Therefore intervention should be made from about 7-12HCP and this will be held at least 52% of the time; and of course a minimum of 2 or (3) 4 card suits or 5-4. The probability of holding this 2nd requirement is 49% of the time. This theory leads to at least 1 in 4 hands where CDH may be used in 2nd position after opponents open a balanced 12-14 1NT.

(Actually if the 1NT is more distributional e.g. 5332 then the it becomes more a little more likely that 20 HCP is shared with your partner.)

Expectation of results

In the 21-19 scenario: the declarer in 1NT is odds on to make 7 tricks 66% and possibly 8: 25% occasionally 6 9%.

While it is true that declarer has a natural advantage in planning the play, the defence has the advantage of the tempo from having the initial lead.

Given this, declarer left to his own devices will score 90 on average over time.

What can the CDH defence expect just from intervention initiated in 2nd position when non-vulnerable (opponents half the time Vulnerable)?

It all depends on the fit and the mathematics is complicated so i am using my experience with CDH to give this answer:

Probability of making a 2-level contract are about: 40% , down 1: 35%, down 2: 15% & +1 10%. Rarely been doubled for good or bad so leaving this out of the equation too. This gives average gain at about: 20 on intervention hands. When your partner instigates the defence the risk is higher and result tends to be more like -20. Intervention overall is about 50% of all hands. So we may expect to gain 2-3 Imps on average on half the frequency of a 1NT opening. This makes it very rewarding indeed.

My concern

Given this analysis one can see my concern when opponents bid 1N with a regular (not downgradable) 15 HCP as this seriously upsets the mathematics. With a known 13-15 an extra point is required etc.

CDH is used in three situations: Here's the summary:-

CDH overcalls 7-(13)HCP in 2nd position

2♣ Shows Clubs and 1 or 2 higher suits

2♦ Shows Diamonds and 1 or 2 higher suits

2♥ Shows both Hearts & Spades

2 Shows 5+ Spades

* Take-out 13+ HCP balanced asking partner for his longest/best suit.

If vulnerable more caution is required e.g 5-5 and/or 11+ HCP

In Protective position there is a change in the use of 2♥

2♣ Shows Clubs and 1 or 2 higher suits

2♦ Shows Diamonds and 1 or 2 higher suits

2♥ Shows 5+ Hearts - is now natural

2 Shows 5+ Spades

* Protective Double - again balanced - looking for partners longest suit.

Rubinsohl is not used

In the cases of 2♣ & 2 defence the 'wriggle' can follow!

If partner is short in the minor 0,1,or 2 cards an attempt is necessary to find a better fit.

The 'wriggle' operates by looking up the line selecting the next suit.

If partner cannot stand this he will move on up the line to his second suit

If you are short in this suit and have another suit 'up the line' - especially if it is 5 card - it should be bid.

Under no circumstances go on to the 3-level. 2NT can be bid if stronger and no 4-3 or better fit discovered.

In the case of 2H showing H+S responder is invited to show preference - that is either PASS or 2

###
See Rubinsohl transfers for more of our 1NT defence in 2nd position.

## Partner's 1NT opening is doubled by RHO

The nature of our 1NT opening is made use of with modified CDH

2♣ Shows Club preference - to be passed.

2 Shows Diamond preference to be passed.

** Shows equal length in minors - asking partner to choose his better minor (usually 4 or 5 card)

2♥ Shows both Hearts+Spade suits - at least 4-4

2 Shows 5+ Spades: To play.

PASS Shows 7-9(10) HCP

Again see Rubinsohl for further handling stronger hands with usually 5+ card suits.

Rubinsohl can also be used when opponents overcall partner's 1NT opening with a bid of 2 of a suit (whether genuine or indicating another suit).

Against a 12-14 NT the basic requirement is to hold 2 or more 4 card suits.

Of course a 5 card is good too! If NT is stronger, 15+, more length 5-4 becomes essential.

Vulnerable also requires more distribution - preferably 5-5.

12-14 on your right, leaves 27 around the other 3 players. Mathematical probabilities gives an expectation of 8 +/-1 HCP for the player on your left.

This leaves 19 combined expectation for you and your partner. Therefore intervention should be made from about 7-12HCP and this will be held at least 52% of the time; and of course a minimum of 2 or (3) 4 card suits or 5-4. The probability of holding this 2nd requirement is 49% of the time. This theory leads to at least 1 in 4 hands where CDH may be used in 2nd position after opponents open a balanced 12-14 1NT.

(Actually if the 1NT is more distributional e.g. 5332 then the it becomes more a little more likely that 20 HCP is shared with your partner.)

Expectation of results

In the 21-19 scenario: the declarer in 1NT is odds on to make 7 tricks 66% and possibly 8: 25% occasionally 6 9%.

While it is true that declarer has a natural advantage in planning the play, the defence has the advantage of the tempo from having the initial lead.

Given this, declarer left to his own devices will score 90 on average over time.

What can the CDH defence expect just from intervention initiated in 2nd position when non-vulnerable (opponents half the time Vulnerable)?

It all depends on the fit and the mathematics is complicated so i am using my experience with CDH to give this answer:

Probability of making a 2-level contract are about: 40% , down 1: 35%, down 2: 15% & +1 10%. Rarely been doubled for good or bad so leaving this out of the equation too. This gives average gain at about: 20 on intervention hands. When your partner instigates the defence the risk is higher and result tends to be more like -20. Intervention overall is about 50% of all hands. So we may expect to gain 2-3 Imps on average on half the frequency of a 1NT opening. This makes it very rewarding indeed.

My concern

Given this analysis one can see my concern when opponents bid 1N with a regular (not downgradable) 15 HCP as this seriously upsets the mathematics. With a known 13-15 an extra point is required etc.

CDH is used in three situations: Here's the summary:-

- Defending against an opposition 1NT opening in 2nd position ....CDH & S & Rubinsohl transfers (2NT, 3♣|♦|♥ transfers to 3♣♦|♥|♠
- Defending against an opposition 1NT opening in protected position (modified to ♣ ♦ & ♥ & ♠ )
- Handling your partner's 1NT opening and Doubled by opponent (modified ♣ &♦ (♥ ♠) to play & **(happy)

CDH overcalls 7-(13)HCP in 2nd position

2♣ Shows Clubs and 1 or 2 higher suits

2♦ Shows Diamonds and 1 or 2 higher suits

2♥ Shows both Hearts & Spades

2 Shows 5+ Spades

* Take-out 13+ HCP balanced asking partner for his longest/best suit.

If vulnerable more caution is required e.g 5-5 and/or 11+ HCP

In Protective position there is a change in the use of 2♥

2♣ Shows Clubs and 1 or 2 higher suits

2♦ Shows Diamonds and 1 or 2 higher suits

2♥ Shows 5+ Hearts - is now natural

2 Shows 5+ Spades

* Protective Double - again balanced - looking for partners longest suit.

Rubinsohl is not used

In the cases of 2♣ & 2 defence the 'wriggle' can follow!

If partner is short in the minor 0,1,or 2 cards an attempt is necessary to find a better fit.

The 'wriggle' operates by looking up the line selecting the next suit.

If partner cannot stand this he will move on up the line to his second suit

If you are short in this suit and have another suit 'up the line' - especially if it is 5 card - it should be bid.

Under no circumstances go on to the 3-level. 2NT can be bid if stronger and no 4-3 or better fit discovered.

In the case of 2H showing H+S responder is invited to show preference - that is either PASS or 2

2♣ Shows Club preference - to be passed.

2 Shows Diamond preference to be passed.

** Shows equal length in minors - asking partner to choose his better minor (usually 4 or 5 card)

2♥ Shows both Hearts+Spade suits - at least 4-4

2 Shows 5+ Spades: To play.

PASS Shows 7-9(10) HCP

Again see Rubinsohl for further handling stronger hands with usually 5+ card suits.

Rubinsohl can also be used when opponents overcall partner's 1NT opening with a bid of 2 of a suit (whether genuine or indicating another suit).