Editing Pascal's wager (section)

=== Analysis with decision theory ===

The possibilities defined by Pascal's wager can be thought of as a [[decision theory#Choice under uncertainty|decision under uncertainty]] with the values of the following [[decision matrix]].

{| class="wikitable" style="margin:1em auto; text-align:center;width100%;"
|-
|
! God exists (G)
! God does not exist (¬G)
|-
! Belief (B)
| +∞ (infinite gain)
| −c (finite loss)
|-
! Disbelief (¬B)
| −∞ (infinite loss)
| +c (finite gain)
|}

Given these values, the option of living as if God exists (B) dominates the option of living as if God does not exist (¬B), as long as one assumes a positive probability that God exists. In other words, the expected value gained by choosing B is greater than or equal to that of choosing ¬B.

In fact, according to decision theory, the only value that matters in the above matrix is the +∞ (infinitely positive).  Any matrix of the following type (where f<sub>1</sub>, f<sub>2</sub>, and f<sub>3</sub> are all negative or finite positive numbers) results in (B) as being the only rational decision.<ref name="SEP entry" />

{| class="wikitable" style="margin:1em auto; text-align:center;"
|-
|
! God exists (G)
! God does not exist (¬G)
|-
! Belief (B)
| +∞
| f<sub>1</sub>
|-
! Disbelief (¬B)
| f<sub>2</sub>
| f<sub>3</sub>
|}