Spikes

From Simplex

Motivation: Simplicity

It has long bugged me that bridge players are expected to learn many different forms of hand evaluation, e.g.

• HCP (e.g. to determine which level to raise partner to), losers (e.g. to decide whether to overcall 1NT),
• suit length (e.g. to determine the best trump suit),
• stoppers (e.g. to investigate the possibility of a 3NT contract),
• Rule of 19 etc totals of HCP + length of two longest suits (to test compliance with the EBU Orange Book),
• Suit Quality Test (e.g. to evaluate the possibility of an overcall), and
• counts of aces and kings (e.g. to assess the possibility of slam).

It would be very helpful to beginnners and others if this list could be reduced, even if it means introducing a new valuation method. It would also be helpful if a single numerical valuation could describe the hand, accounting for both high-card strength and suit length, in particular.

The Valuation

We devised the simplest possible measure which takes into account both strength and suit length: HCP + suit length. This basis, or variations thereof, must have used countless times before. Fr example, Klinger proposes that, until a suit fit is found, bidders should value a hand by adding length points to HCP, where a length point is each card beyond four in a suit.

Naming

The last thing the bridge community is another meaning to the word 'points'. It is already confusing enough for beginners that points are used both for scoring and hand evaluation. The most appropriate monosyllabic synonym I could find was 'spike'. So

Spikes = HCP + suit length

So the spike count of your hand is just 13 more than your HCP. No insight there. The real insight comes from looking at the distribution of spikes across all four hands within each suit. As there are 10 HCP and 13 cards in a suit, there are 23 spikes in each suit across the four hands, and therefore 92 spikes in the full pack.

Notation

An important decision is how to portray the distribution of spikes in anyone suit across the four hands. As anyone who has typeset a maths text knows, it is relatively very time-consuming to depict any expression which could simply be typed linearly from a typewriter. So a compass depiction of N, S, E and W would cumulatively add much cost to the spike distribution analysis. A simple vector expression — e.g. (4, 3, 9, 7) — does not indicate the back-to-the beginning rotation. Instead we use superscripts and subscripts to give some indication of a squashed and rotated bridge table:

_W^N_S^E ♥(₆¹⁰₃⁷)

Note the use of rounded brackets and the ordering (W, N, E, S) as per the standard bidding record. As we become familiar with the notation, the W N E S prefix can be omitted for brevity.

Findings

Stoppers

Any suit holding of 5+ spikes constitutes a stopper — A or K-x or Q-x-x or J-x-x-x or x-x-x-x-x.

A corollary is that if a partnership has 9+ spikes between them, they have the suit stopped.

Likely Tricks in a Suit

At the extreme ends of the 23-spike scale, the spike-count gives a good estimate of the number of tricks to be obtained from that suit.

Likely Partnership Tricks in a Suit
Total Spikes in Suit held by Partnership	Spikes in Suit in One Hand	Spikes in Suit in Partner's Hand	Likely Tricks	Sources
19	10	9	5	T101#16
18	17	1	7	T101#13
18	16	2	5	T101#12
16	15	1	4	T101#12
16	10	6	3	T101#13
16	9	7	3	T101#15
15	12	3	3	T101#12
15	9	6	4	T101#11
14	12	2	5	T101#14
14	11	3	3-5	T101#16
14	8	6	2-4	T101#11, T101#15
14	7	7	3	T101#16
13	11	2	2	T101#14
13	10	3	1	T101#15
13	8	5	3	T101#12, T101#13
13	7	6	3	T101#16
12	10	2	2	T101#14
12	9	3	1-2	T101#14, T101#15
12	8	4	1	T101#11
12	7	5	2	T101#11
11	10	1	3	T101#11, T101#14
11	9	2	2	T101#14
11	7	4	2-3	T101#11, T101#15
10	9	1	3	T101#15
10	8	2	2	T101#13
10	5	5	1-2	T101#14, T101#16
9	7	2	1	T101#15
9	6	3	0	T101#16
9	5	4	1	T101#11
8	7	1	1	T101#12, T101#11
7	5	2	1	T101#15

Likely Suit Layouts

Likely Layouts in a Suit up to seven cards
Spikes in Suit	Likely Layout
17	A-K-Q-J-x-x-x
16	A-K-Q-J-x-x, A-K-Q-x-x-x-x
15	A-K-Q-J-x, A-K-Q-x-x-x, A-K-J-x-x-x-x
14	A-K-Q-J, A-K-Q-x-x, A-K-J-x-x-x, A-Q-J-x-x-x-x
13	A-K-Q-x, A-K-J-x-x, A-K-x-x-x-x, A-Q-J-x-x-x, A-Q-x-x-x-x-x
12	A-K-Q, A-K-J-x, A-K-x-x-x, A-Q-J-x-x, A-Q-x-x-x-x, A-J-x-x-x-x-x, K-Q-J-x-x-x, K-Q-x-x-x-x-x
11	A-K-J, A-K-x-x, A-Q-x-x-x, A-Q-J-x, A-J-x-x-x-x, A-x-x-x-x-x-x, K-Q-J-x-x, K-Q-x-x-x-x, K-J-x-x-x-x-x
10	A-K-x, A-Q-J, A-Q-x-x, A-J-x-x-x, A-x-x-x-x-x, K-Q-J-x, K-Q-x-x-x
9	A-K, A-Q-x, A-J-x-x, A-x-x-x-x, K-Q-J, K-Q-x-x, K-J-x-x-x, K-x-x-x-x, Q-J-x-x-x-x, Q-x-x-x-x-x-x
8	A-Q, A-J-x, A-x-x-x, K-Q-x, K-J-x-x, K-x-x-x-x, Q-J-x-x-x
7	A-x-x, K-Q, K-J-x, K-x-x-x, Q-J-x-x, Q-x-x-x-x,
6	A-x, K-x-x, Q-x-x-x, Q-J-x, J-x-x-x-x, x-x-x-x-x-x
5	K-x, Q-x-x, J-x-x-x, x-x-x-x-x
4	K, Q-x, J-x-x, x-x-x-x
3	J-x, x-x-x
2	x-x
1	x

Examples

T101#12

The configuration is:

• _W^N_S^E
• ♠( ₂ ⁵ ₈ ⁸ )
• ♥( ₇ ³ ₁₂ ¹ )
• ♦( ₁ ⁷ ₀ ¹⁵ )
• ♣( ₁₆ ⁰ ₅ ² )

Commentary

The layout of the clubs and diamonds is critical: lots of top tricks for E-W, but lousy breaks in both suits. If, for example, E-W were to choose clubs as trumps, North need only lead a diamond, simultaneously obtaining a ruff from South and removing declarer's only entry into East's wonderful diamonds. Luckily E-W have the majors stopped, so 3NT is on. West's 16 spikes in clubs should gain five tricks, and East's 15 spikes in diamonds should gain another four. Winning the stopper in one of the majors will enable declarer to cash all or almost all of his minors. (Note that E has no entry in spades, but does have the suit stopped.). So it is up to N-S to sacrifice in 4♥X-1 for -200.

T101#13

The hand's spike distribution is: _W^N_S^E ♠( ₈ ⁸ ₂ ⁵ ) ♥( ₁ ¹ ₉ ¹²) ♦( ₄ ⁶ ₁₀ ³ ) ♣( ₄ ¹⁷ ₁ ¹ )

Commentary

The first step in analysing any deal is to look for the highest spike count , and here it is North's 17 in clubs, which will yield 7 tricks off the top. Assuming that suit is going to be trumps, then, using the Likely Tricks table above, estimate your tricks in the other suits. The two tricks in spades (because the king is likely to be onside in West's 8-spike holding) and the likely three in diamonds, coupled with the single loser in hearts, means that small slams in clubs and NT are on.

T101#11

The hand's spike distribution is: _W^N_S^E ♠( ₁ ⁸ ₄ ¹⁰ ) ♥( ₄ ⁸ ₆ ⁵ ) ♦( ₉ ⁷ ₁ ⁶ ) ♣( ₇ ⁴ ₇ ⁵ )

Commentary

If the highest individual spike count is less than 15, the second step is to identify the highest partnership spike count in a suit, and here it is E-W's combined 15 in diamonds, which the table says should generate four tricks, assuming it becomes trumps. Added to the three in spades, one in hearts and two in clubs, and 10 tricks in diamonds appear to be the limit of E-W's ambition. If interested in game, the next step is for the pair to work out their total spike count. With a combined total of only 47 spikes — i.e. 21 HCP — E-W do not have enough high-card strength for 3NT.

T101#14

The hand's spike distribution is: _W^N_S^E ♠( ₁₀ ³ ₉ ¹ ) ♥( ₂ ⁶ ₃ ¹² ) ♦( ₂ ¹⁰ ₂ ⁹ ) ♣( ₁₁ ⁵ ₅ ² )

Commentary

The highest individual spike-count is East's 12 in hearts, and the highest partnership's score is E-W's 14 spikes, again in hearts. North's six spikes in the suit, versus South's three, suggest that two finesses in hearts will work. So with five tricks in hearts, two in clubs, and at least one in each of spades and diamonds, and at least 11 spikes in every suit, 3NT looks a good contract.

T101#15

The hand's spike distribution is: _W^N_S^E ♠( ₂ ⁶ ₈ ⁷ ) ♥( ₁₀ ⁹ ₁ ³ ) ♦( ₇ ² ₅ ⁹ ) ♣( ₃ ⁴ ₇ ⁹ )

Commentary

The highest individual spike-count is West's 10 in hearts, and the highest partnership score is E-W's 16 spikes in diamonds. NT is a possible contract for E-W, but their 7-2 spike count in spades is a concern. Diamonds as trumps look a better bet because of their high spike-count; one trick in spades, hopefully two in hearts, three in diamonds and one in clubs, making a total of seven suggest that this will be a difficult contract to bring in. With so many broken honour holdings, both pairs will want the other pair to be on lead.

T101#16

The hand's spike distribution is: _W^N_S^E ♠( ₆ ⁵ ₅ ⁷ ) ♥( ₅ ¹¹ ₃ ⁴ ) ♦( ₇ ⁶ ₃ ⁷ ) ♣( ₀ ¹⁰ ₉ ⁴ )

By partnership, these add up to: ^N-S_E-W ♠( ¹⁰ ₁₃ ) ♥( ¹⁴ ₉ ) ♦( ⁹ ₁₄) ♣( ¹⁹ ₄ )

Commentary

What dominates this configuration is N-S's 19 spikes in clubs. This suit will give the pair five tricks. However the pair will lose the first three diamonds tricks. So 5♣ is not a feasible contract. And in NT, N-S can only hope for one trick in spades and two in hearts. 2NT and 4♣ must be the limit of N-S's ambitions.

• 1♥:1♠, 3NT or
• 1♥:2♣, 4♣ or
• 1♥:1NT, 3♣:4♣

A Suitable Bidding System

Opening

1x

• Opener should open his highest-spike suit, at the 1-level with 26-? spikes.

1NT

• Opener needs at least 4 spikes and less than 9 in each suit to bid 1NT. A total of 27 spikes should be OK.

2x

Responding

After 1x

Responder needs 20+ spikes to respond to a 1-level suit bid.

• He should respond with 1 of his cheapest 5+ spike suit.
• 1NT probably means around 20 spikes and little support for partner and unable to bid a senior suit.
• He can respond at the 2-level with an 8+ spike suit.

After 1NT

• Responder needs 8+ spikes in a suit to take out.
• An 18 spike hand is insufficient to raise.

Opener's Rebid

After 1x:1y

• Raise to 2 with 9-spike support and 28 spikes in total.

After 1x:2y

• Raise to 3 with 6-spike support and 26 spikes in total.

Responder's Rebid

After 1x:1y, 2y

• Pass on 22 spikes.

Overcalling 1NT

The partnership should look for a 15+ spike fit in one suit.

• Double in the direct seat could say: "I have 25+ spikes, and each suit contains 5+ spikes. The only 10+ spike suit I could have is spades. Please bid your cheapest 9+ spike suit."
• A suit bid in the direct seat would show a single-suiter, denying tolerance in at least one of the other suits.