A betting game establishes a sense in which confidence measures, confidence distributions in the form of probability measures, are the only reliable inferential probability distributions. In addition, because confidence measures are Kolmogorov probability distributions, they are as coherent as Bayesian posterior distributions in their avoidance of sure loss under the usual Dutch-book betting game.
Although a confidence measure can be computed without any prior, previous knowledge can be incorporated into confidence-based reasoning by combining the confidence measure from the observed data with one or more independent confidence measures representing previous agent opinion. The representation of subjective knowledge in terms of confidence measures rather than more general priors preserves approximate frequentist validity and thus reliability in the first game.