An o’ish relay is a forcing bid that is natural or has extra strength. Famous examples are Birthright (Kokish Relay, 2♣-2♦-2♥) and Polish Club (1♣), after which I name this treatment. I advocate playing a transfer o’ish relay instead, the relay that either transfers to the next suit or has extra strength. This method renders the negative response nonforcing and allows more descriptive rebids.

Basic structure

• TOR = transfer or extra
  • (R) = NF negative, accepts the transfer
• TOR + 1 = transfer back to the suit of TOR

Examples

Birthright (Kokish Relay)

A classical problem with the strong 2♣ opening is whether the auction is game-forcing. One solution is the Kokish Relay, where opener bids 2♥ to show hearts or a unilaterally game-forcing hand. This treatment potentially wastes space because opener hardly passes 2♥-2♠.

The rebids after 2♣-2♦ I propose are:

2♥

5+ spades or FG

2♠

NF, 5+ hearts

2NT to 3♦

NAT NF

After 2♥, the default 2♠ fits any hand that responder would pass natural 2♠. Other responses are game-forcing.

After 2♠, responder passes with weak long spades. The 3♥ response is to play. Whether 2NT is game-forcing is up to partnership agreement.

Polish Club with swapped minor suits

1♣

Polish Club with diamonds instead of clubs:

1. Balanced 12–14 HCP
2. 11–17 HCP, 5+ diamonds or 4441
3. 18+ HCP, any

1♦

11–17 HCP, 5+ clubs or (441)4

It took me almost one year to accept this idea until I realized that 1♣-1X-2♣ should retransfer to diamonds. The strength difference between natural diamonds (11+ HCP) and clubs (18+ HCP) is so large that opener should transfer twice. The odwrotka sequence of 1♣-1X-2♦ remains a power reverse.

Drawbacks

Responding to TOR + 1 is more complicated than TOR. You can no longer park at the negative relay (TOR + 1). Accepting the transfer (TOR + 5) becomes default and often meets a pass. Take 1♦ (showing clubs) for example:

• Pass: weak long diamonds
• 1NT: constructive natural, effectively 4+ diamonds
• 2♣: almost a signoff with 3–4 clubs
• 2♥♠: game try with 3+ clubs
• 2NT: preemptive raise with 4+ clubs
• 3♣: mixed raise with 4+ clubs

I’ve been with my girlfriend for 2+ months and finally found the red and blue mascots for my bridge bidding systems.

• Litten for Litten Polish Club
• Oshawott for Mijumaru Blue Club

Oshawott is my girlfriend’s favorite pokémon. She thinks that Litten is my pokémon since my fursona is an orange cat. These two pokémons fit the color stickers from WBF systems policy and also the Red Oni, Blue Oni trope.

By the way, recently I reached 1800+ Elo on Cuebids. I took a screenshot because I not only was proud of it but also thought it cannot last long.

I tested my bidding systems on Cuebids, a web app for pairs to practice bidding. All three accounts using my bidding systems made it to the top 10 this week. The following is the screenshot of the top 10 list when Mijumaru Blue Club (known as Bluepill (Canapé) Club then) just entered the list. My own account and Irene playing only Litten Polish Club were the top two.

We are still on top 5 as of this writing. We will try to stay on top 10 but not to be top 3 at the same time to keep the environment competitive.

My collection of bidding systems is available on GitHub. It contains aforementioned systems and a defensive system. Litten Polish Club is almost complete. Mijumaru Blue Club is still evolving. The defensive system is still in its infancy.

This collection is free software. You can use it for any purpose, including commercial purposes, at your own risk. I would appreciate it if you could share your experience with me.

Inspired by Thomas Andrews’ article on single hand evaluators, I want to check out how good such an evaluator NLTC is. Since LTCs need an established trump fit, we only consider suit offense tricks, i.e. the most tricks a partnership can take in any suit contract.

Thomas built his data with Matt Ginsberg’s (GIB) double dummy library containing 700K+ deals. However, available sources of that library are long gone. To achieve similar statistical power, I would have to solve about 1M deals. Thanks to DDS, the well known double dummy solver in C++, along with modern computer architecture, we can solve 1M deals within one day.

I generated all data in this article with my bridge utility. It took 8 hours to solve 1M deals for only suit contracts. The following is the correlation coefficient matrix of various evaluations.

Tricks	HCP+	BUM-RAP+	LTC	NLTC	ALTC
1	0.508270	0.512822	-0.482577	-0.521692	-0.516951
	1	0.987782	-0.861016	-0.927226	-0.903264
		1	-0.831184	-0.943001	-0.915663
			1	0.919761	0.935646
				1	0.979818
					1

The plus sign stands for short-suit points in GIB bid descriptions. As BUM-RAP gives fractional points, I made such an adjustment more rigorous.

• S = (void = 3, singleton = 2, doubleton = 1)
• X+ = max(X, S, X + S − 1) for each suit

As for how this adjustment is slightly better than max(X, S) and X + S, there will be a separate article.

ALTC is what Jeff Rubens suggested. Adjust −0.5 losers for each held ace and +0.5 for each guarded queen. NLTC bears this in mind but adjusts for missing aces and queens instead.

Things are different when we add up evaluations in each partnership. LTCs are less additive than HCP+. I think this phenomenon arises from counting values twice. A classic example is that a long suit in one hand and the corresponding doubleton in another are both counted as values a priori.

Tricks	HCP+	BUM-RAP+	LTC	NLTC	ALTC
1	0.861012	0.870637	-0.749171	-0.839970	-0.813800
	1	0.987937	-0.832577	-0.910715	-0.880367
		1	-0.804589	-0.924311	-0.890025
			1	0.922495	0.940156
				1	0.974347
					1

Using NLTC in bidding

NLTC is more a single hand evaluator than an additive one. It is good to use NLTC for suit-oriented initial actions like preemptive openings and overcalls. Consider using additive point counts to assess supports.

The exact ranges of NLTC for preemptive openings are up to partnership agreement. I’d still like to point out some problems if you try to migrate from LTC to NLTC.

Don’t directly apply the rule of 2, 3, 4

With the plain LTC, we estimate the minimum playing tricks to be 13 − LTC. However, NLTC counts more losers than LTC, especially in single suiters. NLTC counts x and xx as 1.5 and 2.5 losers respectively, i.e. each 0.5 more than LTC. Single suiters are rich in singletons and doubletons. Besides, it is discouraged to preempt with a void. In general, NLTC intrinsically counts 1–1.5 more losers than LTC for single suiters. I am still not sure how to map NLTC to preemptive bids. There is going to be an update if I finally figure it out.

My favorite defense to strong 1♣ is Psycho Suction. I filled in 2NT and the 1-level as per the useful space principle. This defense is so flexible that it also applies to small 1♣, strong 1♦, and over the forced responder, e.g. (1♣)-(1♦).

X	Takeout double or stolen bid
1x	Natural or lead-directing
1NT	Non-touching pairs (♠ ♦ or ♥ ♣)
2♣	Clubs or red suits
2♦	Diamonds or majors
2♥	Hearts or black suits
2♠	Spades or minors (supplement to 2NT)
2NT	Minors

Psycho Suction is an extension to the natural defense. It is a superset of the weak twos. The two suiters increase the probabilities of the 2-bids and unanchor them. Psycho Suction establishes a pass-or-correct system where the 2x overcalls are also pass-or-correct. The word “psycho” reflects the risk of playing an undoubled misfit like psychic bids.

Paradox advances

The paradox principle in a pass-or-correct system is to bypass underbids. For example, hearing (1♣)-2♦, we hold

♠ J98
♥ KJ1032
♦ Q98
♣ Q2

Option	Advance
Diamonds	3♦
Majors	4♥

Bid 3♦. Besides diamond support, this bid also shows that we can also raise either major. Underbidding 2♥ conveys too little information and takes away too little space.

The paradox lies in that we do not bid our favorite strain. We have to make the cheapest call of the conjectured advances. Resultantly, we usually bid for the worst case.

Comparison with defenses to 1NT

Similarities

The most common subtype of strong 1♣ is a strong notrump. The opener is so strong that we are unlikely to have a game, so our main goal is to compete with partscores. Our cuebid strain is notrump because opponents have shown strength but no suit.

A common way to devise a defense to 1♣ is using our defense to 1NT. Suction is originally a defense to 1NT. Such a defense to 1NT with no anchor suit is banned in the ACBL Basic+ chart.¹ However, artificial defenses to an artifical opening are generally allowed.² Therefore, we can derive a defense to 1♣ from such an exotic defense to 1NT.

Differences

An obvious difference is that we can access 1-level overcalls. Beware of the lowest 2 overcalls as they give out bidding space.

X	Gives 2 steps (P, XX)
1♦	Gives 1 step (P)
1♥	Neither gives nor takes
1♠	Takes 1 step
1NT	Takes 2 steps

X and 1♦ are better constructive to make bidding space useful to everyone. Natural 1♥ and 1♠ are fine. Try to increase the probability of 2-level overcalls, which take considerable space.

Another difference is that 1NT is limited and descriptive. The opener does not have much to say even if given a second chance to bid. The probability that the opener has a major is also lower. These reasons make major-oriented overcalls effective, e.g. Multi-Landy.

On the other hand, a strong artificial opening is usually unlimited. Forcing overcalls are less effective since they let the opener pass at ease. Thus, a natural defense to 1♣ is stronger than to 1NT. Besides, Inverted Psycho Suction may work for 1NT, but Psycho Suction works better for 1♣.

Discussions

5=4 two suiters

I include some 5=4 two suiters to increase the probabilities of Psycho Suction bids. The rest can be easily expressed with a simple major overcall, where the 4-card suit is lower than the 5-card major.

1♥	5+ hearts
1♠	5+ spades
1NT	4+ spades 5+ diamonds or 4+ hearts 5+ clubs
2♣	6+ clubs or 4+ hearts 5+ diamonds
2♦	6+ diamonds or 4+ spades 5+ hearts
2♥	6+ hearts or 4+ spades 5+ clubs
2♠	6+ spades or 4+ diamonds 5+ clubs
2NT	5+ diamonds 4+ clubs

I believe 5=4 is the sweet spot of two suiters. The original 5-5 is too infrequent to make these overcalls different from weak twos. The 5-4 pattern is as frequent as the single-suited, putting the pass at higher risk. Moreover, 5-4 bids are better guided with an extra step showing equal preference. For example, Landy shows 5-4 in majors, and the 2♦ advance indicates equal preference. Nevertheless, this additional step bears a suit we deny, so it lets opponents come in cheaply.

Strength of X and 1♦

The strength to double is opening values. The double is a two-way call that is either a takeout double or a stolen opening bid with 5+ cards.

The 1♦ overcall is slightly stronger than 1♥ and 1♠ because it gives space yet exhibits no major. I suggest near average strength, i.e. 10+ total points in which there are 8+ HCP. I even recommend this approach to natural 1♣ since 1♦ leaks information without taking space.

Overcalls with 16+ HCP

Congratulations on holding yet another strong club! A comeback after passing the first round definitely reveals 16+ HCP. There are also situations where an initial double is better. To decide the best overcall, we have to investigate their pros and cons.

The pass is better when coming back is easy. The following qualities suggest a pass.

• Single suiter
• 5-card major
• Balanced

The takeout double is made for three suiters. It lets our partner decide the strain. If our partner bids our shortness, we can bid 1NT to provide choices again.

Two suiters fall between these scenarios. First, try to bid 1NT and 2NT since they are forcing. Next, hide a 4-card minor with a pass because introducing the longest suit is often enough. Then, we are left with the following two suiters to double.

• Majors
• 4=5 or more in same-colored suits

When a fit is not found yet, we can easily run to the cheaper suit. This strategy happens to spare 2♣, our rebid to show a regular opener with clubs.

Advance	Majors	Black	Red
1♦	1♥	1♠
1♥		1♠
1♠			2♦

---

Responder’s direct cuebid is a disputed and under-discussed topic. There are two popular usages of this bid:

• Limit raise or better
• Generic game force

I suggest different approaches to major and minor openings.

After a major opening

The cuebid is a limit raise or better. From the pigeonhole principle, you have either of these:

• 3-card support
• 5-card unbid suit
• 4-4 unbid suits
• 4-card adverse suit

The promise of a fit clears the way for finding a game. Other calls better describe game-forcing hands without 3-card support.

• 5-card unbid suit: free bid
• 4-4 unbid: negative double
• 4-card adverse suit: 3NT

After a minor opening

We make the cuebid a versatile tool to combine the advantages of popular treatments.

According to the previous section, you can have an embarrassing strong hand with no 4-card support, no biddable side suit, and no stopper in the adverse suit. Imagine holding the following hand at 1♣-(1♠)-?

♠ xxx
♥ Axx
♦ Axxx
♣ Axx

You could have bid 3NT if RHO did not overcall, but you cannot now because there is no spade stopper. You are wary of passing because 3NT is still playable if your partner has a spade stopper. Ask for one with 2♠.

Besides, we can keep the limit raise. Your partner is eager to show a stopper as notrump games score more than minor games. Including the limit raise in the cuebid does not affect the bidding structure.

I have been researching on Wbridge5, a prominent bridge program. I used to be confused that it disables inverted minors by default. Recently I came up with a conclusion.

Wbridge5 opens strong notrump by default, so this treatment is disabled. Wbridge5 still includes inverted minors because weak notrump is a choice.

Inverted minors originated from Kaplan–Sheinwold. It is popular in East and Southeast Asia because of Precision Club, a bidding system based on K-S with the strong club that inherits the weak notrump opening.

Nowadays, many players open strong notrump according to something American. However, some of them still employ inverted minors. It has pros easily found by searching “inverted minors.” Hence, I list its cons as a balance report.

Garbage 1NT response

The weakness of inverted minors is not on itself but the 1NT response adjusted by the inverted minors. The 1NT response shows either of the following:

Constructive 1NT

Expected 6+ tricks if both minimum.

Garbage 1NT

Expected only 5 tricks if both minimum.

When the partner opens 1♠, 1♥, or 1♦, not to miss a probable game, the garbage 1NT is on. Overcalls invalidate inverted minors, so their counteractions fall out of the topic.

Without inverted minors, a 1NT response to 1♣ is always constructive. Respond 2♣ with a weak 3-3-3-4 because the opener often has 4+ clubs.

If 1♣ ensures 3+ clubs

With minimum strength, the probability of mere 3 clubs is 21.5%.

If 1♣ can be 4-4-3-2

With minimum strength, the probability of mere 3 clubs is 20.4%, 4-4-3-2 5.19%.

Weak 4-card support dumped as garbage

Express 5-card support as 3 level preempts. Nevertheless, 1NT with weak 4-card support is much less preemptive. Is there so much difference between 2 of a minor and 1NT, as 1NT is just one or two bids lower? Let’s consider the following.

W	N	E	S
	1♣	-	1NT
X1	-	-2	?

The point is not whether to escape, but the positive pass. Notrump is awful for the declarer, with 6.06 tricks taken on average. 1NTxS−3 is more tragic than 3NTE= without favorable vulnerability. Besides, the total notrump tricks may be less than 13.

If we responded 2♣ instead, east must have clubs to pass, and the lowest positive advance becomes 2NT. Preemption is force opponents to bid strong hands high. Although 2♣ is only one bid higher than 1NT, it pushes pass and cuebid onto 2NT.

1. Takeout double ↩

2. Convert to business double ↩