CROQUET — credits, sources, and everything this game reconstructed rather than sourced ====================================================================================== WHAT THIS IS ------------ An independent reimplementation of ASSOCIATION CROQUET, played in the browser in true 3D. Croquet has no author. The modern game was codified in England in the 1860s — the first widely used rules were published by John Jaques II in 1864 and the All England Croquet Club (which later became the All England Lawn Tennis and Croquet Club) held the first championship at Wimbledon in 1868. Since 1989 the Laws have been the responsibility of the WORLD CROQUET FEDERATION. The rules implemented here are the WCF's LAWS OF ASSOCIATION CROQUET, SEVENTH EDITION, approved by the WCF Council on 24 January 2021, together with two WCF regulations that narrow them for championship play. Those documents are: Laws of Association Croquet, 7th Edition — World Croquet Federation, 24 January 2021 https://worldcroquet.org/wp-content/uploads/2021/02/Laws-7th-Edition-master-new.pdf WCF Equipment Regulations v6.4, effective 24 December 2023 https://worldcroquet.org/wp-content/uploads/2023/12/WCFEquipmentRegulations_v6.4published.pdf WCF Sports Regulations v9.6, effective 4 August 2025 https://worldcroquet.org/wp-content/uploads/2025/08/WCF-Sports-Regulations-v9.6-Final.pdf The Croquet Association — which now trades as CROQUET ENGLAND — adopted the 7th Edition verbatim on 30 January 2021 and publishes it in full at croquet.org.uk. The Laws are a WCF document, not a CA one; national associations adopt them. THIS GAME IS NOT PUBLISHED BY, ENDORSED BY, OR AFFILIATED WITH the World Croquet Federation, Croquet England, or any other croquet body. It is an independent work built from their public documents. All rules text quoted in the source comments is quoted for identification and accuracy. WHAT IS FAITHFUL, AND TO WHICH LAW ---------------------------------- Every dimension on the court is the Laws' own number and is asserted against it in this app's test suite: Court 28 x 35 yards, tolerance +/- 6 in L4.1.1, L4.1.2 Yard-line one yard in; corner spots where its sides meet Glossary Baulk-lines A and B, the halves of the south and north yard-line Glossary Peg central; inner hoops 7 yd N and S of it; outer hoops 7 yd from each adjacent boundary L4.4.1, L4.4.2 Peg 18 in high, 1.5 in in diameter, white to 6 in, bands blue / red / black / yellow descending L5.1.1, L5.1.2 Hoops 12 in high, uprights 15.9 to 19.1 mm, inner surfaces not less than 94 mm nor more than 102 mm apart, first hoop's crown blue and the rover's red L5.2.1.1-3, L5.2.2 Championship hoop separation 93.7 mm +/- 1.2 mm EQ Appendix 3, 5.1 Ball 92 mm +/- 0.8 mm, 454 g +/- 7 g L5.3.1 Ball rebound 30 to 45 in from a 60 in drop onto steel Appendix A2.1 Hoop/ball clearance not less than 0.8 mm; 0.4 mm in easy conditions; up to 1.6 mm in difficult ones SR 8.1.2 The order and direction of all twelve hoop points Diagram 1 and L2.4 and every rule of play the game turns on: The objective, 26 points a side L1.1 The opening four turns from a baulk-line L11.1, L11.2 Free choice of either ball at the start of a turn L12.1, L2.6.1 Roquet, and the limits on it L17.1, L17.2 The croquet stroke: placement in contact, and the requirement to move or shake the croqueted ball L18.3, L18.5 The croqueted ball becomes dead immediately L18.6 A ball off the court in a croquet stroke ends the turn L18.7 The continuation stroke, and that it cannot accumulate L19.1, L19.2, L19.3 Starting, completing, and scoring a hoop point, with the retractions if the ball comes back L20.1, L20.2, L20.3 Borderline decisions go in the striker's favour L20.6.1, L20.6.2 Hoop and roquet in the same stroke, all four cases L21.2, L21.3, L21.4 The peg point and the three-ball ending L22, L7.3.1 Live and dead balls, and their revival on a hoop point L9.5, L2.6.10 A ball leaves the court when ANY PART of it would touch the boundary; replacement on the yard-line L13.1.1, L15.1, L15.2 The striker's ball stays in the yard-line AREA until the end of the turn — every other ball is drawn in every stroke L14.1, L14.2 Wiring, including a ball in the jaws L16.3.1-4 The advanced-play lifts after 1-back and 4-back, and the contact after both L39.1-39.5 The fault of failing to move the croqueted ball, and its remedy L29.1.13, L29.3.1 Turn-ending events L7.6 THE PHYSICS, AND WHOSE MEASUREMENTS IT USES ------------------------------------------- The Laws fix exactly ONE dynamical quantity — Appendix A2.1's rebound test — and no surface property, no mallet property, and no stroke taxonomy at all. Rather than invent the rest, the croquet stroke is calibrated against published MEASUREMENTS: Don Gugan (Department of Physics, University of Bristol), "Croquet Drives, Pass-Rolls, Stop-Shots and Scatter-Shots", Oxford Croquet technical archive, updated 27 January 2018. NOTE: oxfordcroquet.com no longer serves the archive — the domain now returns a hosting control panel. Read via the Internet Archive: https://web.archive.org/web/20190323073845/http://oxfordcroquet.com/tech/gugan5/index.asp From it this game takes, as data rather than as inspiration: the ratio of the distance the croqueted ball travels to the distance the striker's ball travels in a straight croquet stroke — stop shot 5.64, drive 4.12 (4.23 measured over twelve strokes), full roll 1.24, pass roll 0.94; the ball restitution 0.772, measured on a Dawson 'International' match ball; and the mechanism: a croquet stroke is three successive two-body impulses, not one collision, and "for straight croquet drives ... 90% of the energy and distance of the striker's ball comes from the double-tap" as the mallet catches it up again. That is why the momentum split in this engine is near two thirds and not the 0.886 a single collision would give. David Appleton, "Hitting In: A Probabilistic Approach", 31 May 2011 (same archive; the paper is also at https://www.scottishcroquet.org.uk/roquet/roquet.pdf). The opponent's accuracy is his model exactly: one number, P(13,1), the chance of hitting a single ball at 13 yards, fixes the chance at every distance and every target width through Phi(d,k) = Phi(13,1)^(13k/d). This app's test suite reproduces his published table cell for cell. Dr Ian Plummer, Oxford Croquet "Intermediate Coaching Notes" (same archive), and the Croquet Association Coaches' Manual (https://www.croquet.org.uk/?d=3150), for the four-ball break: the pioneer, the pivot and the reception ball, and the five-step recipe the opponent follows stroke for stroke. Plummer's note on hoop running independently derives the same closed form used here and prints 13.73 degrees for a 3 3/4 inch hoop and 6.927 degrees for a 1/32 inch clearance; this engine's formula gives 13.7291 and 6.9269. RECONSTRUCTED — every number here is this app's own, and no source fixes it -------------------------------------------------------------------------- 1. GRASS. Rolling resistance 0.060 and sliding friction 0.55 of a croquet ball on a lawn. No governing document fixes any surface property; SR 8.1.4 only asks that hoops be set in ground "that is level and flat". 0.060 makes a firmly struck ball cross the court, which is what a firmly struck ball does. 2. THE MALLET. Mass 1.15 kg and a maximum head speed of 10 m/s. Law 5.5 fixes the geometry — a rigid head, two identical parallel end-faces, a shaft at right angles to its mid-point for the bottom 12 inches, no aiming devices — and NOTHING else. There is no WCF mallet specification of any kind: the Equipment Regulations cover balls and hoops only. The 10 m/s cap is set by what the game needs, not by comfort: a four-ball break has to load a pioneer from hoop 1 to hoop 3, the full 21-yard diagonal, and below about 9.5 m/s that is geometrically impossible. 3. BALL-BALL RESTITUTION taken equal to Gugan's measured ball-on-steel 0.772. Appendix A2.1 measures ball against steel, not ball against ball; hoop uprights ARE steel (L5.2.1.1 "solid metal"), so for those the figure is used for exactly what it measures. 4. BALL-BALL SURFACE FRICTION 0.06, which produces "pull" — the croqueted ball leaving a shade off the line of centres, towards the striker's ball. Every source consulted describes pull and none quantifies it; one states plainly that its magnitude has not been measured. 5. THE ROLL CONTROL. The Laws describe no stroke type whatever: "stop shot", "drive", "roll" and "pass roll" are coaching vocabulary. The mapping from the player's roll control to the spin the striker's ball receives is this app's, and the momentum split that goes with it is SOLVED at load time from Gugan's four measured ratios rather than hard-coded. 6. THE FAULT THRESHOLD. L18.5 requires the croqueted ball to be "moved or shaken" and sets no threshold; half a millimetre of travel is used here. 7. THE OPPONENT's shot selection, its break plan's tolerances, and how it chooses which ball to go for. Its ACCURACY is Appleton's, but what it decides to do is this app's. 8. THE PIONEER'S PLACE. Plummer's rule is "between the peg and the hoop, say 1 yard or less from the hoop". That is written for the hoops whose playing side faces the peg and is geometrically impossible for the others — hoop 1 is run northward from a position 7 yards north of the south boundary, so a pioneer literally between the peg and the hoop would sit on the far side from where the striker has to arrive. This app places the pioneer one yard from the hoop on the PLAYING side, drawn a third of a yard sideways towards the peg, which is what the rule is for. 9. Every colour on the court except the four balls, the peg's bands, the corner flags and the blue and red crowns. WHAT DIFFERS FROM THE LAWS, deliberately ---------------------------------------- * Level SINGLES only. Bisques and handicap play (Laws 42-44) and doubles (Laws 45-50) are not implemented. * The errors and interferences of Laws 23-38 are not implemented, because a single-player game has nobody to forestall play or to choose rectification. The one exception is the fault the croquet stroke turns on, L29.1.13. * The wiring lift of Law 16 is OFFERED rather than adjudicated by a referee, and the advanced lifts of Law 39 likewise. * No ball ever leaves the ground, so there are no jump shots and no cannons (L18.4). * A stroke is aimed with a pointer rather than swung, so the faults of Laws 29.1.1 to 29.1.12 cannot arise. LICENCE ------- This reimplementation is released under the MIT licence — see LICENSE.txt. It contains no code, art, text or data from any croquet body, and no third-party library: the renderer, the physics and the rule engine are all written for this app.