I have also summarized it for you so you don’t have to weed through a lot of historical and background material to get to the main argument.
If we look at things logically, then our one true God either exists or he doesn’t. I believe he does, but many others do not. To see if it is rational to believe in God, let’s calculate the various rewards for the situations where God either exists or he doesn’t versus whether we believe in God or not:
God exists and we choose to believe in him: after death our reward is going to heaven (reward is positive infinity)
God exists and we choose not to believe: after death our punishment is that we go to hell’s eternal damnation (reward is negative infinity).
If God doesn’t exist, then there is no reward after death whether we choose to believe in God or not and there is also no significant difference before death for either believing in God or not other than potentially the finite comfort one gets from the hope created by believing. (reward is basically zero).
Therefore, of the 3 situations, It makes the most rational sense to choose the infinitely positive reward of Situation 1. To do this all we have to do is choose to believe in God.
No rational person would consciously choose the infinite punishment of Situation 2, but God did give us free will.
Many people try to hedge their bets by thinking Situation 3 will save them from hell. Some of these folks may assume and/or argue that there is no God. Others may simply put off making a decision not realizing that their indecision is actually the same as choosing not to believe. The problem with Situation 3 for these people is that there is no upside if they are right, but if they are wrong, there is a huge downside (see Situation 2).
As a result of analyzing the three situations, it makes the most logical sense to actively choose to believe in God as per Situation 1 where there is no downside if one is wrong (see Situation 3), but there is a huge upside if one is right.