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What should it mean for an agent t o k n o w or believe an assertion is true with probability :99? Di erent papers FH88, FZ88, HMT88] give di erent answers, choosing to use quite di erent probability spaces when computing the probability a n a g e n t assigns to an event. We s h o w that each c hoice can be understood in terms of a betting game, and that each c hoice corresponds to betting against a di erent opponent. We consider three types of adversaries. The rst selects the outcome of alldoi:10.1145/72981.72988 dblp:conf/podc/HalpernT89 fatcat:tv336ivegjbaxlnlzf7w5mkt6i