Pascal wager1/7/2024 ![]() a game that is not too biased, believers imagine an immense net winning expectation. While the players to whom the wager is addressed expect a net winning expectation close to zero, i.e. What happens if the mathematical expectation of the net winning E of the game is non-zero? The formula to be considered is as follows: In this context, we can affirm that, when the winning tends towards infinity, the probability of winning tends towards 0. For example, if you bet 1 euro, it is a fair game to be able to win 1000 euros with a probability of 1/1000 in another game, if you bet 1 euro, it is a fair game to be able to win 1,000,000 euros with a probability of 1/1,000,000. In all games of chance, the more you aim for a high winning, the lower the probability of winning. ![]() Two variables remain: the winning and the probability of winning. In what follows, we assume it to be constant. In the context of Pascal's wager, the bet, which is the Christian commitment, is fixed, or at least capped. While the promises of charlatans can be invalidated by the absence of expected results, those of religious propagandists, being absolutely unverifiable, go further than charlatanism. The huckster is indifferent to true and false, for he is concerned only with pleasing, to his greatest advantage. The principle of Pascal's wager puts the gullible to sleep by the immediate comfort provided by the hope of a miraculous payoff. On the other hand, an "unverifiable hypothesis" loses its status as a hypothesis to become a fable or an ideology. Become my disciple, and your gain will be infinite!"Īn unverified hypothesis remains a hypothesis whose confirmation or rebuttal is postponed to the future. The Christian priest who speaks in the name of Jesus: " If you follow me, you will be rewarded with eternal happiness. Why not try, since there is so much to be gained?" It's worth betting on me: I'm counting on your vote!".Ī healer who asks to have faith in his powers: " If you trust me, your illness will disappear and you will be able to live a long time. Weigh the pros and cons, and don't hesitate to buy it!".Ī speech by a politician: " I'm going to improve the future of society, and you will be able to enjoy it at your leisure. If you give it up, you are depriving yourself of a great service. Its general formulation is: "The more wonderful the promise, the more justified it is to bet on it".Īn advertisement is displayed: " If you buy this product, you will be happier. Its versatility even allows its principle to be exploited far beyond the religious realm. But its central element - the possibility of a gigantic gain - is not specifically Christian and can be adapted to any doctrine that promises much. Initially, Pascal's wager was supposed to support the Catholic faith. Generalised formulation of Pascal's wager In other words, Pascal implicitly assumes the existence of God, which constitutes a vicious circle, a circular reasoning. To pronounce the "so on", one must admit that the supernatural exists. However, the earth's resources are limited. in a game with a zero bet, every time you try, you win a billion euros randomly every other time,.in a game with a zero bet, every time you try, you win a million euros randomly every other time.in a game with a zero bet, every time you try, you win a thousand euros randomly every other time.Consider for example the following suggested sequence: In mathematics, infinity appears as the limit of sequences. Secondly, it is prudent to examine what is covered by the term "infinite". First of all, in the object of the wager, there is not only the existence of God, but also that the Catholic religion would be true and that religious practice would lead to Paradise. However, one must be wary of hidden assumptions. If this is the case, one gains eternal life in Paradise, and the gain is infinite. Let us temporarily assume the value of one chance in two for the probability that God exists. The reasoning behind Pascal's wager is circular Wager, then, that He is, without hesitation.» Let us consider these two cases: if you win, you win everything if you lose, you lose nothing. ![]() « But your bliss? Let us weigh the winning and the loss, betting that God is.
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