Randomness is inherently imprecise

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into study randomness. In particular, we define several notions randomness associated with interval, rather than precise, forecasting systems, and their properties. The richer mathematical structure that thus arises lets us, amongst other things, better understand place existing results for precise limit. When focus on constant interval forecasts, find every sequence binary outcomes has an filter intervals it is random for. It may happen none these precise—a single real number—which justifies title this paper. illustrate by showing non-stationary systems can be captured a forecast, which must then less precise: gain in model simplicity paid loss precision. But imprecise can't always explained away as result oversimplification: show there are sequences but never any computable (more) system. also set non-vacuous system meagre, systems.