Bidding the Odds - can we do better than Kokish Relay?
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KOKISH RELAY AFTER 2

If anyone needs a refresher, it is:

2 - 2;

2

asks partner to bid 2, then you bid 2NT with a hand too strong to bid 2NT the first time, otherwise rebid something else if you had hearts.

At first glance this appears to be an improvement, as it allows very strong balanced hands to show at 2NT allowing methods.  When you have hearts how much does that round of bidding cost?

So lets give us hearts and diamonds and a good hand.

A AKxxx AKQxx Kx.

Fair enough, right?

2 - 2;

2 - 2 (art)

3 (normal rebid)

Now it is partner's turn.  Is 3 a preference, possibly false, in order to keep NT from the correct side in the picture?  How many spades need he have to bid 3 - if that is a probe for 3NT, can you recover spades ever?

The fact that partner was deprived of the opportunity to FREELY raise hearts has a very tangible cost.  Lets not pretend otherwise.  Not to mention that partner couldn't bid anything else over 2.  Like a splinter.  Maybe you bid 2 on AKx AKQxxx Axx x and partner was going to splinter to 4 over 2. But since you had to rebid 3, partner no longer can do so.  Will you still get to slam opposite Qxxx xxx x xxxxx?

Putting in hands with no singletons and no 6+ card suits gives us these frequencies for occurence:

22 HCP:  .14%

23 HCP:  .08%

24 HCP:  .04%

25 HCP: .02%

26 HCP:  .01%

27+ HCP: .01%

So of the hands that would open 2 and rebid in NT, the higher range (if played as 25+) occurs just over 13% of the time.  If played as 24+, then close to 27% of the time.

The frequency of a strong 2 in hearts occuring is about .18% (depending on how many HCP you require when distributional)

So when the auction starts:

2 - 2;

2

and you are playing Kokish, you will have hearts about 82% of the time that you start your strong hands at 25.

You will have hearts about 69% of the time you start at 24.  So if your experience is that the 2 rebid usually has hearts, thats because it does.  And that's a lot of heart auctions to be screwing up.

Is the next step is to compare how much worse off you are if you must jump to 3NT with the higher point range (or risk a pass of 2NT)?

The loss there is real as well - but hard to compare.  I guess the REAL next step is to ask "Can we do better?"

YES!

Here are the things we'd like to show after opening a strong 2:

1) A strong but not quite GF balanced hand

2) A strong GF balanced hand

3) A strong 2 in a major

4) A strong 2 in a minor

I note than there are several efficiencies available with different types of inversions.  One initial thought I had was that you could bundle the 3 and 3 rebids into 2 and remove the strong heart hands.  This takes no room at all on the 3m bids, since you end in the same spot.  That would mean you'd have to move the hands into the direct 3-level rather than through the relay.  Unfortunately, that does no better than break even.

My second thought on optimization was to have 2 GUARANTEE a balanced hand of some strength.  And I think I have something there...

And it comes up.  A lot more than a natural 2 call - remember, you'd have 20+ HCP and an unbalanced heart hand about .18% of the time.  You'll have 22+ balanced about .30% of the time.

So 2 - 2; 2 = balanced 22+

responses:

2NT: 5-5 majors or three kings (pick one meaning - you don't want to bid 2NT when it might wrongside NT)

3/3: Natural, 6-card suit (super-efficient here, as we get to start our minor slam auctions a level lower!)

3/3: (I recommend 3 be a minor suit slam try and 3 be a transfer to 3NT for now, although I haven't thought it through)

2 - 2;

2 - 2;

Now, with the maxes we have to untangle puppet directly, and we'll do it as natural as possible.  We lose mss though.

2NT = min

3 = max with at least one 4-card major

3D = stayman

3M = transfer to the other major

3 = max, no 4-card major

3M = 5-cards in the other major

3 = max; 5 hearts

All of this to free up the 2NT (and 3NT) rebids for the 2 opener.  2NT has to show hearts.  While less efficient than 2 (as we lose 2) partner wasn't going to be bidding 2NT to wrongside the NT very often (unless you're clever and would have used 2NT to show a fit.)

Over

2 - 2;

2NT (hearts)

hearts haven't been named yet.  We need a negative as well.

So...

this might shock you, but I propose that an unfitted disaster hand negative just pass 2NT.  If partner has game in hand, he needs to rebid 3 or 3NT instead (or take this risk)

3 = fitted, positive

3 = fitted negative (a transfer)

3 = unfitted slammish positive - 1 and 2 suited minor hands start here as well.

3NT = game

4m = splinter

Yeah, its not as good as having the auction start at 2, but it is very close and it has logical structure (you're playing Jacoby transfers and essentially MSS, so memory shouldn't be hard - Stayman, the call you don't need is the one that has a special meaning.)

Compare:

In Kokish, if you have hearts, you are making 2-bids in a row, the second ending 3 or higher - getting no information from partner.  You'll often have no room for a negative and fit agreement is awkward.

With this inversion, if you have hearts, you are bidding them the first time at 2NT.  You have cheap artificial positive and negative suit agreement available below 3.  You don't get your second bid in on a 2-suiter at 3m - but that is a mixed curse, as it crams the auction as well.   If you need to be completely efficient, you're better off switching to big club anyways.