Bake Yourself a Multi Defence
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RHO starts the dreaded 2 Multi, the lame version, showing either six spades or six hearts, and for purposes of this exercise, 5-9 HCP. Overcaller will have a hand suitable to compete about 40% of the time. 'Suitable' I gauged roughly  as 13+ balanced, 13+ unbalanced with a major 5-suit, 11+ with a major 6-suit, 14+ with a minor 6-suit. You could tinker with those definitions, with no impact on overall conclusions. So roughly how often will overcaller have these, and other kinds of hands?

• Balanced (5332, 5422, 4432, 4333) ~ 57% (of the ~40% of those qualifying to overcall)
• 5+ unbalanced major (not 5332, not 5422) ~ 22%
• 6 minor ~ 10%
• Takeout X of hearts (4xyy, x = 0-1, y = 3-5) ~ 4%
• TOX of spades ~ 3% (forces partner to 3-level, requires stronger hand than TOX for hearts, so slightly less frequent than TOX of hearts)
• mm at least xx55 ~ 1%
• There is a dribble of others, shapes like say 4225 or 4441, for which overcaller has no comfortable immediate call.

Of course judgements will vary as to whether and how to bid a hand. With 1345 overcaller might love his club suit, chance a spade takeout double, or trot out a bid that shows both minors. Nonetheless, tweaks to the mix of these ingredients, won't have a significant impact on the defence we ultimately cook up.

Note whenever overcaller bids or implies a major, obviously he takes on some risk. For example, about 1 in 6 of his takeout doubles will be for the ‘wrong’ suit … holding 4144 he happily makes the system call for ‘heart takeout’, but alas, opener has a spade suit. Interestingly, when that happens, the result is not often calamitous (in the example, advancer will not have sufficient spades to ‘raise’ overcaller's implied spades --- opener has 6 of them, overcaller 4 --- and chances of landing in a decent m-fit are not awful).

Heck, about 1 in 7 of overcaller’s 5-card majors will match opener’s suit, and about 1 in 20 times his 6-suit will likewise.

So. You have the ingredients, try baking up a defence. There are fewer calls available than there are hand types to describe, not to mention you must negotiate a range of hand strengths. You can always pass immediately, then take action your second turn, when you know opener’s suit.

A Basic Simple Defence ... The First 3 Calls Are Transfers, Then Natural

There are scores of defences floating about, many quite ineffective. Every instance I found spends two precious bids on low-utility takeout doubles … representing in total just 7% of overcaller’s holdings, with close to 1 in 6 of those being for the 'wrong' major. Overcaller could instead choose to pass initially, then (most of the time) be able show his stuff with a second round double which will never be for the wrong suit. ACBL Option #1 is so ditzy it requires you bid 3 with hearts. Another really flawed defence spends four! calls on long minors.

This is my shot at a more evidence-based defence.

With bidding space so compromised, I've excluded those low-utility takeout doubles from initial action, freeing up two calls. Also it cannot be very wrong to treat the likes of (42)(43) as ‘balanced’ (instead of ‘double’) and play systems on to recover some 4-4 major fits. (By the way if you do choose to X with (42)(43), be prepared for nearly one-quarter of them to be for the 'wrong' major.)

Transfers rock; it is always good to be able to bid again … overcaller shows his suit, then takes charge. It isn’t necessary to assign different strengths to 2M and 3M … with a strong hand overcaller can transfer, then self-raise. Transfers are useful for showing Mm two-suiters as well.

Anyway this is what my mixing bowl came up with. RHO opens the dreaded 2, then:

• X = hearts (any strength)
• 2 = spades (any strength)

That start is obvious to me, and should be the foundation for any defence. Overcaller can have a wide range of strength, and/or a shapely Mm hand.

Balanced hands overwhelmingly dominate at close to 60% of overcaller’s holdings. There is space to define calls for two different ranges yet still be able to pull up in 2NT. This structure for balanced hands makes sense to me:

• 2 = lower range (say 13-15), partner signs off with 2NT (or even passes with spades). Any notrump range should be on the narrow side because partner will be passing or blasting.
• 2NT = higher range (16-18)
• 3NT = 19-21

There is no bidding space remaining for minor-suit transfers, so:

• 3 = clubs
• 3 = diamonds

That basic structure is trivial to remember and explain. No pages of explanations. Our first 3 calls are transfers (2 is a weak notrump), the balance natural.

How much should the notrump overcaller be concerned, if both majors are not stopped? This factor is rarely discussed by existing defences. Without getting deep into the weeds on the topic, the unsurprising answer is yes, zero majors covered is worse than both covered, but overcaller should make the call anyway. A few observations:

When overcaller and partner together are in game range, the chances the enemy suit is unstopped in the combined hands is quite small, on the order of 5%. From overcaller’s point of view, that chance ranges from 0% when he has both stopped, to about 15% when neither is stopped. Were overcaller to hold xx/xxx/AQJx/AKQx, guess where partner’s 10+ HCP likely are.

Opener’s style plays a role. If he guarantees a good suit, the odds obviously change. Likewise obversely if he promises junk.

Any call carries some risk, and the Multi opening has injected more turbulence than you'd perhaps like. However Passing is far riskier (missing games) than bidding (occasionally managing your discards as the opps rattle off the first half-dozen tricks).

It is possible to build a routine whereby advancer can ask for majors and/or stoppers. The one I cobbled together uses 3, 3 and 3NT to do the asking, with 3 and 3 being transfers.

Out of curiosity I quantified the approximate value of a stopper. Each major that is stopped is ‘worth’ a little more than half a jack, so overcaller and advancer can build that into their deliberations.

Suggestions for (2) 3M

Direct jumps to 3M are sitting there waiting to be used; oh mercy how to use them? Since X and 2 are transfers, with a great hand it is not necessary you jump to 3M. Perhaps 3M shows good (31)(45) hands, or 3/ = great clubs/diamonds, or shortness holding a great takeout double ... (2) 3 shows AQxx/x/AKxx/KQTx, say. ‘Stopper-ask’ is an obvious option and I think the option I prefer (shows strong balanced, or lots of tricks, lacking a stopper). And does 3M pre-emptive make any sense?

I have avoided multi-meaning calls, but one could consider adulterating one or both transfers to include other structures, perhaps mm, or include the monster balanced hand in the X transfer. Or overcaller with xx55 can initially pass, then try 2NT on the 2nd round, although there is a risk of getting preempted out of that option. Anyway here is what my starting calls might look like. Dreaded 2 then:

• X = hearts
• 2 = weaker balanced
• 2NT = stronger balanced
• 3m = natural
• 3M = stopper-ask in M
• 3NT = strongest balanced

Pass then X = takeout. Pass then 2NT = mm.

I've not considered how this 3-transfer system might be too easily exploited by the opening side. For example responder can X if he 'likes' hearts in this transfer sequence: 2 2 X. Of course that intervention gives advancer THREE options (pass, XX, 2) instead of one, so I'm not sure which side is being more exploited. Too tough for me.

Needs field testing.