One version of the Atheist's wager suggests that since a kind and loving god would reward good deeds – and that if no gods exist, good deeds would still leave a positive legacy – one should live a good life without religion.[2][3] Another formulation suggests that a god may reward honest disbelief and punish a dishonest belief in the divine.[4]
Explanation
Martin's wager states that if one were to analyze their options in regard to how to live their life, they would arrive at the following possibilities:[2][5]
You may live a good life and believe in a god, and a benevolent god exists, in which case you go to heaven: your gain is infinite.
You may live a good life without believing in a god, and a benevolent god exists, in which case you go to heaven: your gain is infinite.
You may live a good life and believe in a god, but no benevolent god exists, in which case you leave a positive legacy to the world; your gain is finite.
You may live a good life without believing in a god, and no benevolent god exists, in which case you leave a positive legacy to the world; your gain is finite.
You may live an evil life and believe in a god, and a benevolent god exists, in which case you go to hell: your loss is infinite.
You may live an evil life without believing in a god, and a benevolent god exists, in which case you go to hell: your loss is infinite.
You may live an evil life and believe in a god, but no benevolent god exists, in which case you leave a negative legacy to the world; your loss is finite.
You may live an evil life without believing in a god, and no benevolent god exists, in which case you leave a negative legacy to the world; your loss is finite.
The following table shows the values assigned to each possible outcome:
A benevolent god exists
No benevolent god exists
Belief in god (B)
No belief in god (¬B)
Belief in god (B)
No belief in god (¬B)
Good life (L)
+∞ (heaven)
+∞ (heaven)
+X (positive legacy)
+X (positive legacy)
Evil life (¬L)
−∞ (hell)
−∞ (hell)
−X (negative legacy)
−X (negative legacy)
Given these values, Martin argues that the option to live a good life clearly dominates the option of living an evil life, regardless of belief in a god. Whether one believes in god has no effect on the outcome.
References
^Oppy, Graham (2019). A Companion to Atheism and Philosophy (First ed.). Wiley. p. 221. ISBN978-1-119-11918-0.