In his summary of my book Nature and Nature’s God for the Review of Metaphysics, Caleb Estep writes that I hold that in infinite time all possibilities will be realized. This is not quite what I claim. As I explain in the book, what I hold is that all possibilities that approach arbitrarily close to 1 over time will be realized. In infinite time even something with a small probability of occurring, in any given finite duration, may become nearly certain to occur. This will be the case unless the probability of its occurring diminishes continually such that the sum-total of its probability over infinite time (technically the integral of its probability density from t=zero to t=infinity) is still significantly less than one.
For example, if there is a 1/2 probability of getting heads on a first coin flip, then there is only a 1/4 chance of not getting heads at all on two flips. After three flips there is only a 1/8 chance of not getting heads at all, and so on. However, in some cases the odds decrease so rapidly that there is very little chance of ever getting the desired result. For example, if there is a 1/100 chance of getting result X on the first go, and then a 1/10,000 chance of getting it on the next go, and then a 1/1,000,000 chance of getting it on the third go, and so on, then the odds are against ever getting the result.