Pascal’s Wager: Definitive Edition High Stakes, Infinite Rewards, and the Mathematics of Faith
Expected Value=(Probability of Existence×∞)−(Probability of Non-existence×Finite Cost)Expected Value equals open paren Probability of Existence cross infinity close paren minus open paren Probability of Non-existence cross Finite Cost close paren Pascal's Wager: Definitive Edition
), the "Expected Value" of believing remains infinite. In the language of math: Pascal’s genius was moving the conversation away from
Most gamblers care about the probability of winning. Pascal argued that in this specific case, . The Math: Why the Odds Don't Matter As
Pascal’s genius was moving the conversation away from proofs (which he felt reason couldn't provide) and toward utility . He framed the existence of God as a coin toss you are to play simply by being alive. The logic follows a simple 2x2 grid: God Exists God Does Not Exist Wager for God Infinite Gain (Heaven) Finite Loss (Minor earthly restrictions) Wager Against Infinite Loss (Hell/Damnation) Finite Gain (Earthly autonomy) 2. The Math: Why the Odds Don't Matter
As long as the probability of God existing is greater than zero (
Can you actually force yourself to believe just for the reward? Critics argue that a God who is all-knowing would see right through a "mercenary" faith based on a spreadsheet.