If you want to know if you believe something look at the kinds of bets you are willing to take. If you are wearing an expensive suede suit that will be ruined by rain, and you don’t want it ruined, and you go outside without an umbrella, you believe it will not rain.
If you want to know how much you believe something look at how much you are willing to bet. If you go out in a cotton suit that will cost ten dollars to clean but you are unwilling to wear the suede suit you think there is a chance it will rain. If you won’t even go out in the cotton suit, you are much more sure of it.
A rational person changes his beliefs based upon the success of his bets. So for example if weather.com tells you when it will rain, and following weather.com helps you place successful bets — i.e. you take the umbrella when you need it and not when you don’t and you don’t ruin your suits too often — then you will trust weather.com. If believing the labels on your suits that say “safe even in rain” turns out to lead to your suits getting ruined, in the future, if you are rational, you will believe the labels less.
Sometimes we make decisions in which we bet our whole lives. These occur in two contexts, dramatic and undramatic. A religious Muslim who allows herself to be martyred rather than eat pork is betting that obeying the rules of Islam is more important than her life. That’s dramatic. But likewise someone who spends his whole life working at a boring job for a law firm in order to put money in his mutual fund is making an undramatic bet, namely that this is the best way for him to spend his life.
By the nature of things these bets cannot get adjusted in a rational fashion, because we only get one shot. We can’t try being Muslim once, die, then try being a kaffir once, die, and see how it worked out.
Maybe though Life or the Universe is the one making the bets, using our lives and decisions as the game pieces. The priest of Hera, Heracleitus, seems to have believed something like that when he said:
αἰὼν παῖς ἐστι παίζων, πεττεύων· παιδὸς ἡ βασιληίη.
A lifetime is a child playing, playing checkers; the kingdom belongs to a child.
Did he mean a game with perfect information, like checkers? Or something played with dice?