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As a previous commentator has noted, the words 'believe' and 'faith' inherently imply ascribing to a set of concepts for which there is no evidence of absolute TRUTH!
It appears to me that you have chosen a game theory model in an attempt to rationalize 'belief'. This approach is insufficient to resolve the question that is of primary concern i.e., is it it rational to KNOW absolutely that there is a Gd?
The latter question is very simply answered by observation. The observations that the sun rises each day, that you wake up each morning refreshed in mind and body and the observation that I can correspond with you and others by tapping away on my iPhone right NOW are direct revelations of (what you name) a 'SB'.... I am thusly content to KNOW ( not 'believe') that there is a Gd...Game theory and mathematics are unnecessary in my argument. It is elementary my dear Watson!!