In this paper we study a classical model concerning occurrence of?words in a random sequence of letters from an alphabet. The problem?can be studied as a game among $(m+1)$ words: the winning word in?this game is the one that occurs first. We prove that the knowledge?of the first $m$ words results in an advantage in the construction?of the last word, as it has been shown in the literature for the?cases $m=1$ and $m=2$ [CZ1,CZ2]. The last word can in fact be?constructed so that its probability of winning is strictly larger?than $1/(m+1)$. For the latter probability we will?give an explicit lower bound. Our method is based on rather general probabilistic arguments that allow us to consider an arbitrary cardinality for the alphabet, an arbitrary value for $m$ and different?mechanisms generating the random sequence of letters.
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机译：在本文中，我们研究了一个经典模型，该模型涉及字母表中字母的随机序列中单词的出现。可以将问题作为$（m + 1）$个单词之间的游戏来研究：该游戏中的获胜单词是第一个出现的单词。我们证明前$ m $个单词的知识会在构造最后一个单词方面带来优势，正如文献中针对$ m = 1 $和$ m = 2 $情况所证明的那样[ CZ1，CZ2]。实际上，可以构造最后一个词，以便使其获胜的概率严格大于$ 1 /（m + 1）$。对于后一种可能性，我们将给出一个明确的下限。我们的方法基于相当普遍的概率论据，这些论据使我们可以考虑字母的任意基数，$ m $的任意值以及生成随机字母序列的不同机制。
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