The Raven's Hat - Jonas Peters and Nicolai Meinshausen ***

This book promises something intriguing - 'a series of engaging games that seem unsolvable - but that can be solved when they are translated into mathematical terms.' Such a title succeeds or fails on two key aspects of that promise - are the games engaging and are the mathematical solutions comprehensible to the general reader.

Before getting into the detail, I must say that I loved the illustrations by Malte Meinshausen, featuring characters that are an endearing cross between a raven and the old 'Spy vs Spy' illustrations in Mad magazine. As will become clear, I do have some difficulty with the content as far as the general reader is concerned, though some will definitely find it interesting.

Are the games engaging? I'd say mostly not. The first, which features hat colour guessing, is the most so, as it's just about imaginable playing it as a real game. Similarly, there's a magic trick involving a pack of cards that feels as if it could just about be usable as a genuine card trick (even though it's a card trick where the magician is said to only have 84% chance of success, which seems a bit low to be truly successful.) Those apart, though, the game formats are so convoluted that they become abstractions rather anything that's imaginable as a game you would play.

How about the solutions? They are quite difficult to get your head around and aren't broken down well enough for the non-mathematician to really grasp them. They also generally seem too complex for anyone but a maths wizard to remember how to make use of in reality. And it can also be difficult to pick up on exactly what is meant. 

So, for example, in the hat colour game, players are given red or blue hats without seeing their own hats. They can't talk to each other, but after a few seconds, when asked, they have to hold up a sign with the answer to 'What colour is your hat?' of 'Red', 'Blue' or '?'. We are then asked the best strategy, which seems to involve the players deciding together what they should do - but we were told they can't talk to each other. When it comes to solutions of this game, we are told 'the key to success will be to "collect" the wrong answers in single instances of the game' as this will bundle 'the false guesses into the same game and spread out the correct guesses over as many games as possible.' But there was no suggestion up front the game was to be played multiple times - and the concept of bundling up false guesses feels wrong, so needs more explanation.

Similarly, for the card trick, the mechanism requires the pre-ordered pack to be riffle shuffled three times. I have never seen a real card trick, where the audience member is told a mechanism for shuffling - they are just asked to shuffle the cards (personally I would alternate overhand shuffles and riffle shuffles). As soon as the mechanism is forced on them, it immediately becomes suspect.

That all sounds a touch negative - but I would stress again that those who are deeply into the theory and mathematics of games will no doubt find this book extremely intriguing. It's just that there's an opportunity missed for it to reach a wider audience.

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Review by Brian Clegg