Pascal's Wager
The brilliant French mathematician and philosopher Blaise Pascal (1623 - 1662).conceived his Wager as an argument for belief in God rather than as an argument for the existence of God:
1.Either God exists or He does not.
2.If there is no God, whether you believe in God or not, then there is no afterlife.
3.If there is a God, and you believe in God, you go to Heaven.
4.If there is a God, but you do not believe in God, you go to Hell.
5. If you approach belief as a wager, betting on God's existence is a win-draw proposal: either you gain eternal bliss or end up with nothing .
6 Betting on God's nonexistence is a draw-lose proposal: either you end up with nothing, or you suffer eternal hellfire.
7. Belief is the best bet, by far.

Pascal's Wager depends on a God who doesn't mind gambling, who can't see through such devices.
Also, while Pascal did not adhere to the Orthodoxy of the day, he did not seem to understand the gods of other religions such as Hinduism and Islam.
Had he understood the ways of these gods, he probably would not have made such narrow statements as the if/than statements in his wager. Simple belief in Allah (the Muslim god) does not automatically earn someone infinite gain. This only works within the Christian paradigm. What if one of the gods that Pascal was unfamiliar with is the sovereign ruler of the universe?
Pascal's Wager does not allow for a specific god, only a god in general. If the wrong god is believed in, the true god would more than likely be rather upset. Further, the position of worshipping a non-existent god is costly. There are endless hours wasted in reverance, time spent in church and proselytizing, money given to church, etc.
Lastly, the desire to find truth is not based on "what if" type of questions. It is based on evidence. Pascal's Wager presents us with absolutely no evidence

Kant
Another attempted proof by Kant had to do with the expectation that the Good will be Rewarded and the Evil punished.
That does not happen in this life
Therefore there must be an afterlife
Therefore there must be a God.
This assumes a certain kind of afterlife, and a certain kind of God.

Gödel's existence proof

NOTE: Definition of God depends on a so-called "positivity predicate": some qualities are "positive", others are not. Godel introduces a set of axioms which put severe constraints concept of "positivity". God is then defined to have all properties which are positive, and no other properties.

Objections: (a) If at least one positivity predicate exists, there are bound to be more, and theologists can (and do) argue endlessly about which qualities are positive.
(b) What kind of God is defined?
If He is anything like the Judaeo-Christian one, he is supposed to have some power over what happens in the world. [Why, therefore does He not prevent the death of children, atrocities, genocides?]

Gödel'sl used modal logic, which allows one to make statements like "It is conceivable that..." or "It is necessarily true that...".
It is convenient to formulate modal logic in such a way that "It is conceivable that..." is equivalent to "There is a conceivable world in which..."
(This conceivable world may be ours, of course), and "It is necessarily true that..." is equivalent to "... is true in every conceivable world".

To prove the existence of God, Gödel needed to define what divinity is. For this he introduced a so-called positivity predicate for properties.
His positivity predicate satisfies the following requirements:
(A1) A property X is positive if and only if the property of not having the property X is not positive;
(A2) If a property X is positive and having this property also implies the property Y, then Y is also positive;
(A3) Divinity is a positive property;
(A4) If a property is positive, it is positive in any conceivable world;
(A5) Necessary existence is positive.

We need to define "divinity" and "necessary existence". We first define what it means for a property to be "essential" to an entity.
(D1) X is an essential property of an entity x if x has the property X and for any property Y this entity has, it is true for all entities that having the property X implies having the property Y.
(D2) An entity x necessarily exists if for any essential property of x, in every conceivable world there exists an entity y having this property.
(D3) An entity is divine if it has all positive properties.

Now we prove a few intermediate results:
Lemma 1. If some property X is positive, then there is a conceivable world in which at least one entity has this property.

Proof. Suppose the Lemma would be false. Then there would be a positive property X such that there is no conceivable world in which an entity has this property. Then we can say that in every conceivable world, having the property X implies not having the property X. Because of (A2) and the positivity of X, this would imply that not having the property X is a positive property, which contradicts (A1) and the positivity of X. Q.E.D.

Lemma 2. If an entity is divine, then any property it has is positive.

Proof. Suppose x is a divine entity having a property X which is not positive. Then because of (A1), the property of not having the property X is positive. (D3) then implies that x has the property of not having the property X. Contradiction. Q.E.D.

Lemma 3. If an entity is divine, then divinity is an essential property of this entity.

Proof. If x is divine, and it has some property Y, then Y is positive because of Lemma 2. Then from (A4) it follows that Y is positive in every conceivable world. So because of (D3), in every conceivable world it is true that if some entity z is divine, it has the property Y. This means that divinity is an essential property of x. Q.E.D.

Lemma 4. If the entity x is divine, then there exists a divine entity in every conceivable world.

Proof. (A5) says that necessary existence is positive, so x necessarily exists. According to Lemma 3, divinity is an essential property of x. >From (D2) we then get that there exists a divine entity in every conceivable world. Q.E.D.

We now come to the main Theorem:
Theorem. In every conceivable world there exists a divine entity.

Proof. From (A3) and Lemma 1, it follows that there is a conceivable world in which there exists a divine entity. From Lemma 4, it then follows that there exists a divine entity in every conceivable world. Q.E.D.