How to Play
Expert Croquet Tactics
Appendix By Keith F Wylie Second Edition 1991 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. Contents
Article 3: Establishing a Break: Style and Technique
For my parents, an inadequate explanation of time misspent. [Web Editors' note: the index has been expanded and numbered to assist with referencing.] Previous article: Article 4: The Opening AppendixFor 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:
It follows that
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= ¼q+ ½(1r) = ½¼ (2rq), 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),
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] BibliographyThis 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 postwar 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. [153] Postscript
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