论文标题
划界有限的投注策略
Betting strategies with bounded splits
论文作者
论文摘要
我们表明，如果以下两个条件中的任何一个中的任何一个都是如此： （i）有一个无限制的可计算函数$ g $，因此，当几乎所有$ \ ell $上的无限二进制序列上注时，两种投注策略在第一个$ \ ell-g（\ ell）$位置上都押注。 （ii）有一个均值函数$ g $，以便在几乎所有$ \ ell $上肯定在无限的二进制序列上进行投注时，在序列的第一个$ \ ell $位置中至少押注至少$ \ ell-g（\ ell）$位置。
We show that a pair of Kolmogorov-Loveland betting strategies cannot win on every non-Martin-Löf random sequence if either of the two following conditions is true: (I) There is an unbounded computable function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at most $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence. (II) There is a sublinear function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\ell$, bet on at least $\ell-g(\ell)$ positions among the first $\ell$ positions of the sequence.
