1. Hand Evaluation

• Balanced shapes: 4-3-3-3, 4-4-3-2 and 5-3-3-2. A five-card heart or spade suit is still balanced when there is no four-card side suit. Weak 1NT is fundamentally 12–14 actual HCP: a genuinely balanced 12–14 HCP hand opens 1NT even if positive hand-evaluation adjustments take the evaluated total above 14. Evaluation may also bring a borderline hand, such as a poor 15-count, into the weak-NT range. 2NT is 20–22 evaluated points. A 5-3-3-2 hand with a five-card major in the 1NT range opens 1NT rather than the major.
• Balanced-hand evaluation (“Goodies and Baddies”): deduct 1 for 4-3-3-3; add ½ for a five-card suit (1 for a good-quality five-card suit); add ½ for supported honours; add ½ for each 10 or 9 supporting an honour; deduct ½ for an isolated honour; add ½ for an honour in a suit bid naturally by partner. These adjustments are used only on balanced hands for NT/opening/rebid/invitational decisions. For automation, a “good-quality five-card suit” means two of the top three honours (A/K/Q) or three of the top five honours (A/K/Q/J/10).

2. Opening Bids

• Weak twos: 2♦, 2♥ or 2♠ with a six-card suit and roughly 6–10 HCP. 2♣ remains the strong opening.
• Pre-empts: a seven-card suit may open at the three level; an eight-card suit may open at the four level, normally with a weak hand.
• Otherwise a one-level suit opening is used from normal opening strength, with four-card majors recognised.
• Third seat — “borrow a king”: after two passes, add 3 points for opening judgement. This is a judgement aid, not extra HCP: the hand must still satisfy the EBU Level 2 minimum for a one-level suit opening — 11+ HCP, or 8+ HCP with Rule of 19.
• Fourth seat — Rule of 15: after three passes, add HCP to the number of spades held. With 15 or more, consider opening; below 15, pass the board out. A one-level suit opening must still satisfy the EBU Level 2 minimum — 11+ HCP, or 8+ HCP with Rule of 19.

3. Responses

• Responder with support — use the better of points or LTC. For a major-suit fit with four or more trumps, compare the point-count raise (6–9 → 2-level, 10–12 → 3-level, 13+ → game) with the Losing Trick Count raise (9 losers → 2-level, 8 → 3-level, 7 or fewer → game) and make the higher bid. If the known combined trump holding is more than eight cards, deduct one loser before applying LTC. This allows distribution and a nine-card-or-better fit to upgrade the hand. With exactly three-card support, a marginal 9-loser hand may still make the simple raise to 2 of opener’s suit.
• A four-card major is not suppressed when a one-level response is available. With 6–9 HCP and no three-card fit or better one-level suit response, 1NT remains the fallback response.
• Stayman and transfers are completed: over 1NT, 2♣ is Stayman and 2♦/2♥ transfer to hearts/spades. Opener answers/completes; responder then signs off, invites or offers game. Over 2NT, 3♦/3♥ are transfers and 3♣ is Puppet Stayman, allowing opener to show a five-card major, a four-card major, or no major.
• Strong 2♣: the auction is not allowed to die after the first response. With more than 4 HCP and an Ace, responder shows an Ace-control suit; 2♦ remains the waiting/negative response, so a diamond Ace control is encoded as 3♦ in this teaching version. Opener then rebids shape/NT and the partnership continues.
• Negative doubles are used by responder after partner opens one of a suit and the next hand makes a natural suit overcall: normally 6+ HCP at the one level, 8+ at the two level, showing the unbid major(s).

4. Rebids & Continuations

• Stay low after a weak 1NT response: responder’s 1NT shows about 6–9 HCP. Opener does not rebid 2NT merely to describe a balanced hand. If even 9 opposite leaves the partnership below 25 HCP, pass 1NT; invite only when game is possible opposite the top of the range.
• Fourth-suit forcing: once the partnership has naturally shown three suits, a game-going responder may bid the fourth suit artificially to keep the auction alive and ask opener for a stopper, delayed support or further shape.
• Auction memory: a change of suit by responder is forcing for one round; fourth-suit forcing is forcing to game. The engine retains the strength promised by raises, negative doubles and NT rebids instead of judging each later call in isolation.
• Slam tools: 4NT is quantitative in NT auctions, not Blackwood. Gerber is the slam-investigation convention: 4♣ asks for Aces (4♦ = 0/4, 4♥ = 1, 4♠ = 2, 4NT = 3); 5♣ asks for Kings with the same step pattern.
• Suit-slam trigger: after a trump fit is established, opener compares their actual LTC with the assumed 7-loser opening hand. With 5 losers or fewer, combine opener's losers with the losers shown by responder's raise. If 18 minus that combined loser count suggests at least the five level, and 4♣ is still legally available, opener starts Gerber. LTC decides whether to investigate; Gerber decides whether enough top controls exist. Control cue-bidding is not used for slam investigation.

5. Competitive Bidding

• Competitive actions include natural one- and two-level overcalls, a 15–17 1NT overcall with a stopper, CRO (Colour–Rank–Other) for suitable 5-5 two-suiters over an opponent's one-level suit opening, take-out doubles, negative doubles, penalty doubles, redoubles, responses to doubles, competitive raises and descriptive rebids. Over an opponent's 1NT opening, natural suit overcalls use the Rule of 8: add the lengths of the two longest suits, subtract Losing Trick Count; with at least 6 HCP, enter when the result is 2 or more. A natural overcall still requires a five-card or longer suit in this teaching engine.
• CRO: with at least 5-5 in two of the three unbid suits and useful values concentrated in those suits: cue-bid opener's suit = the two suits of the same Colour; 2NT = the two suits of the same Rank (majors or minors); 3♣ = the Other two suits. Partner chooses between the two explicitly shown suits; the artificial CRO denomination is not treated as a natural suit.
• Law of Total Trumps in competition: once a fit is known, compete approximately to the level of the partnership trump count — 8 trumps → 2-level, 9 → 3-level, 10 → 4-level, 11+ → 5-level in this teaching engine. Do not bid above that Law level merely because the opponents have pushed the auction higher.
• Pender–Flint after 1NT X: weak responder escapes by transferring so the 1NT opener remains declarer: XX → clubs, 2♣ → diamonds, 2♦ → hearts, 2♥ → spades. With no useful five-card escape suit, stay in 1NT X.
• A double of a weak 1NT is penalty with about 15+ HCP. Penalty doubles of suit contracts are reserved for higher-level contracts where the hand has real defensive values and/or a trump stack.
• A redouble after an opponent's take-out double shows roughly 10+ HCP and strength; a redouble of a penalty double is used only with substantial confidence in the contract.

6. Leads

• Paramount lead rule — choose the suit first, then the card. Against NT, partner's natural suit gets first consideration; otherwise choose from the auction and length. A sequence does not choose the suit — it only chooses the card after the suit has been selected.

• NT — card from the selected suit: top of a sequence of three honours (or a near-sequence, e.g. AQJ); top of an internal sequence of three (or near-sequence, e.g. KJ108 → J); otherwise fourth from an honour when there is an entry to establish and cash the suit.
• NT — small holdings: Middle-Up-Down from three small cards; top from a doubleton; the singleton from a singleton. The purpose of the long-suit lead is to drive out declarer's high cards, so an entry back to the hand matters.

• Suit contract — “Should I lead a trump?” uses only the auction and the opening leader's own hand. Positive clues include delayed/reluctant trump agreement, a jump or competitive raise suggesting distribution, the declaring side bidding several suits before settling in trumps, outside honours sitting over a side suit they bid, and unattractive side-suit alternatives. Partner's clearly bid side suit, the other unbid major against an established major fit, or a useful singleton count against a trump lead. The test never looks at unseen dummy shape or the opponents' actual HCP.
• If those clues do not justify a trump, choose the side suit first from the auction. Partner's suit has priority; when the opponents have found a fit in one major, prefer the other unbid major when available; then consider a useful shortage or another unbid/safe suit. Only after the suit is chosen does the engine apply sequence, A-K, doubleton or low-card rules. From three small cards in a safe suit, lead Middle-Up-Down (MUD): the middle card first.

7. System Diagnostics

• Minor-suit versus NT preference: when game values are present and a minor fit is known, prefer 3NT to 5♣/5♦ whenever 3NT is legally available and the auction does not reveal an unstopped opponent suit. At invitational level, a balanced hand also prefers NT to committing to a minor. A minor contract remains the choice when NT is unsafe or unavailable.
• Double-dummy audit: after the Acol auction, DD is used only as a diagnostic. It can flag a contract that is down, or a possible missed game/slam, but it never replaces the information available to the bidders. “Sound” means the auction is consistent with the DD result; “Review” is a one-step warning; “Check bidding logic” is a larger discrepancy.