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How to Play
Expert Croquet Tactics
Appendix

By Keith F Wylie

Second Edition 1991
Published by The Croquet Association, 2014

ALL RIGHTS RESERVED. No part of this publication maybe reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system without permission in writing from the publishers.

Text Copyright © The Croquet Association, 2014. Typesetting & diagrams © Dr Ian Plummer, 2014.
Electronic copy prepared by Stuart Lawrence & Dr Ian Plummer.

Contents (Full Contents)


Article 1: The Triple Peel

Part I General

1.I.1 Introduction

1.I.2 A Quiz

1.I.3 Simple break organisation

1.I.4 Priorities

1.I.5 Jawsing and hugging

1.I.6 In my end is my beginning

1.I.7 A haunted hoop

1.I.8 Pull

1.I.9 An answer is not always required

1.I.10 Experto crede

Part II: The 4-Back Peel

1.II.1 The 4b peel before 3

1.II.2 The 4b peel after 3

1.II.3 Jawsing after 3: how to continue

1.II.4 The 4b peel before 5

1.II.5 The 4b peel before 6

1.II.6 The 4b peel after 6

1.II.7 Jawsing before 6: how to continue

1.II.8 The 4b peel before 1b

1.II.9 Jawsing before 1b: how to continue

1.II.10 Peeling 4b after 1b

1.II.11 Peeling 4b before 2b or 3b

Part III: The Penult Peel

1.III.1 The penult peel after 6 or before 1b

1.III.2 Jawsing (or not quite jawsing) the penult peel before 1b: how to continue

1.III.3 The penult peel after 1b

1.III.4 Continuation after doing the 4b peel before 1b

1.III.5 The penult peel before 2b or 3b

1.III.6 The penult peel before 4b, and how to continue after jawsing

1.III.7 The straight penult peel (except in the straight triple)

Part IV: The Rover Peel and Peg-Out

1.IV.1 The rover peel before 3b

1.IV.2 The rover peel after 3b

1.IV.3 Jawsing before or after 3b: how to continue

1.IV.4 The rover peel before 4b or before penult

1.IV.5 The straight rover peel (other than a straight double or triple)

1.IV.6 The peg-out

Part V: The Straight Triple, The Three-Ball Triple and Some Leaves

1.V.1 The straight triple

1.V.2 Four tips on doing straight peels

1.V.3 The three-ball triple

1.V.4 Some leaves

Part VI: Epideixis

1.VI.1 Promotion of peeled ball with escape ball

1.VI.2 Promotion of peeled ball with other ball

1.VI.3 Promotion of escape ball with peeled ball

1.VI.4 Promotion of escape ball with other ball

1.VI.5 Promotion of other ball with peeled ball

1.VI.6 Promotion of other ball with escape ball

1.VI.7 Promotion of other ball with other ball

1.VI.8 Some other cannons

1.VI.9 Peeling two balls

1.VI.10 Faster and furiouser

1.VI.11 Index to the Quiz

 

For my parents, an inadequate explanation of time misspent.
I shall teach no longer in riddles

[Web Editors' note: the index has been expanded and numbered to assist with referencing.]

Previous article: Article 4: The Opening


Appendix

For many people, mathematical analysis in this context is somewhat tiresome. I set it out only because it seems to demonstrate definite conclusions which readers might be slow to accept without it.

I assume that K shoots at R and does not leave a worthwhile double target. Probabilities are in the range of 0 (no chance) to 1 (certainty). Let:-

p = probability of hitting tice (same for K and Y);
q = probability of K hitting on the 5th turn after K and Y have missed;
r = probability of Y hitting after K has hit.

It follows that

s = probability of UK getting first innings
   = (probability that K misses) * (probability that thereafter Y misses)
                                             * (probability that thereafter K hits)
       + (probability that K hits) x (probability that thereafter Y misses)
   = (1-p)(1-p)q +p(1-r).

This does not take account of the likelihood that Y will shoot at the tice from an angle and thus from further away; but since my eventual conclusion is that the opening favours UK, I prefer to make any simplifying assumptions in RY’s favour. I now apply that formula.

(a) Chance of UK winning the first innings after a critical distance tice.

By definition p = ½, so that s= q+ ½(1-r) = ½- (2r-q), which is less than 50% if 2r exceeds q which it does. How much UK’s chances are below ½ depends on your evaluation of q and r.

(b) Change in UK’s chance as tice shortens. If p≥ ½ (i.e. tice of critical distance or less),

ds/dp = -2(1-p)q+(1-p)(1-p)dq/dp + (1-r)
         = 1-(q + r)+(2p-1)q+(1-p)(1-p)dq/dp
         ≥ 1-(q+r)-(-dq/dp) (NB dq/dp<0).

From inspection, (-dq/dp) < 1 - quite easily - so that, taking sensible values for q and r, I deduce that ds/dp > 0, i.e. UK’s chance increases as the tice gets shorter. [152]


Bibliography

This is a list of the works mentioned in this book and the sources of my quotations. The books by Cotter, Prichard and Solomon should be in any serious croquet library. It might have been more scholarly of me to have made similar reference to the other post-war books on croquet which, like those by Cotter and Solomon, bring the reader up to the point from which this book starts. That I have not done so implies no criticism of those works. The books by Cotter and Solomon are important not so much because they are good books as because the opinions expressed in them have far greater authority than any other book can claim. Those opinions cannot be ignored, and when I have differed from them I have felt it necessary to draw attention to the fact and to explain myself.

Aeschylus, Agamemnon (line 1183), 

Alexander, C.B.O’D. and others, Fischer v. Spassky, Reykjavik 1972, (Penguin Books 1972)

Campbell, P., The P-P-Penguin Patrick Campbell, (Penguin Books 1965)

Cotter, E.P.C., Tackle Croquet This Way, (Stanley Paul 1960)

Erasmus, D. (translated by H.H. Hudson), Moriae Encomium, (Princeton University Press 1941)

Ibsen, H. (translated by R. Farquharson Sharp), Peer Gynt, (J.M. Dent & Sons Ltd 1921)

Prichard, D.M.C., The History of Croquet, (Cassell 1981)

Solomon, J.W., Croquet, (Batsford 1966)

Tollemache, Lord, Modern Croquet - Tips and Practice, (Strange the Printer 1947)

Wittgenstein, L. von, Tractatus Logico-Philosophicus,  

Wyclif, Select English Works, (The Early English Text Society 1869 - 71)

The Australian Croquet Gazette, (The Australian Croquet Council)

The Croquet Gazette (otherwise known as Croquet), (The Croquet Association)

[153]

Postscript

Let Erasmus, in the persona of Folly, have the last word:

“The ones who write learnedly for the verdict of a few scholars ... seem to me more pitiable than happy, since they continually torture themselves: they add, they alter, they blot something out, they put it back in, they do their work over, they recast it, they show it to friends, they keep it for nine years; yet they never satisfy themselves ... The scholar considers himself compensated ... when he wins the approbation of one or two other weak-eyed scholars.”

Previous article: Article 4: The Opening

Author: Keith Wylie
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