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Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. At the start of the game, the two players agree on the length of the sequences to be generated. This length is usually taken to be three, but can be any larger number. Player A then selects a sequence of heads and tails of the required length, and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player whose sequence appears first wins. Provided sequences of at least length three are used, the second player (B) has an edge over the starting player (A). This is because the game is nontransitive such that for any given sequence of length three or longer one can find another sequence that has higher probability of occurring first. ==Analysis of the three-bit game== For the three-bit sequence game, the second player can optimise his odds by choosing sequences according to: An easy way to remember the sequence for using as a bar trick is for the second player to start with the opposite of the middle choice of the first player, then follow it with the first player's first two choices. :So for the first player's choice of 1-2-3 :the second player must choose (not-2)-1-2 where (not-2) is the opposite of the second choice of the first player.〔(Predicting a coin toss ) by Scam School (on YouTube)〕 An intuitive explanation for this result, is that in any case that the sequence is not immediately the first player's choice, the chances for the first player getting their sequence-beginning, the opening two choices, are usually the chance that the second player will be getting their full sequence. So the second player will most likely "finish before" the first player.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Penney's game」の詳細全文を読む スポンサード リンク
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