By John Cox
During this easy-to-read consultant, openings specialist John Cox is going again to fundamentals, learning the basic rules of Alekhine's Defence and its various adaptations. in the course of the booklet there are an abundance of notes, counsel, and warnings to lead bettering avid gamers, whereas key suggestions, principles, and strategies for each side are basically illustrated.
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Extra info for Alekhine's Defence (Starting Out)
Suppose, for the sake of argument, that black’s stones do not include a chain that connects the two black edges. Consider one ‘component’ of the black regions – all the black stones connected (by other black stones) to a black edge. Now look at the ‘boundary’ of this region – all the immediately adjacent white stones. Clearly, this set of white stones must connect the two white edges . . but why? Alternatively, we can prove that one player must have a winning strategy. Then the above claim easily follows.
As far as I know, these questions are wide open, even for relatively small values of x. JUMPING CHAMPIONS | 47 ANSWER Why do twin primes always have the same number of digits in decimal notation? It may seem obvious, but the proof reveals a potential loophole, which can occur in other number bases. Let the primes concerned be p and p + 2. In decimal notation, it is possible for p + 2 to have more digits than p. However, this happens only when p = 999. 98 or 999. 99. In the first case p is even (and at least 8) so cannot be prime.
Alternatively, we can prove that one player must have a winning strategy. Then the above claim easily follows. In fact, it can be proved that with proper play, the ﬁrst player should always win. The proof, found by Nash, uses a general technique called ‘strategy stealing’. Suppose, for the sake of argument, that white plays ﬁrst, and there is a strategy that guarantees a win for the second player, black. If so, then white can employ unbounded brainpower to work out what that strategy is. She can then use this alleged second-playerwins strategy to beat black, as follows.