When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided that you are testing by betting and do not risk more capital than initially committed. Standard statistical theory uses Cournot's principle, which does not allow such optional continuation. Cournot's principle can be extended to allow optional continuation when testing is carried out by multiplying likelihood ratios, but the extension lacks the simplicity and generality of testing by betting. Game-theoretic probability can also help us with descriptive data analysis. To obtain a purely and honestly descriptive analysis using competing probability distributions, we have them bet against each other using the Kelly principle. The place of confidence intervals is then taken by a sets of distributions that do relatively well in the competition. In the simplest implementation, these sets coincide with R. A. Fisher's likelihood intervals.

翻译：当检验统计假设时，是否允许根据初始数据决定是否以及如何收集更多数据？博弈概率论基于"赌注检验"的基本原理给出肯定回答，前提是采用赌注检验方式且不冒超出初始承诺资本的风险。标准统计理论运用库尔诺原则，该原则不允许此类选择性延续。通过似然比乘积进行检验时，库尔诺原则可扩展允许选择性延续，但这种扩展缺乏赌注检验的简洁性与普适性。博弈概率论同样有助于描述性数据分析。为使用竞争性概率分布获得纯粹且诚实的描述性分析，我们运用凯利原则让这些分布相互博弈。此时置信区间被竞赛中表现较优的分布集合所取代。在最简实现中，这些分布集合与R.A.费舍尔的似然区间完全一致。