An ordinary person has to make up to 35,000 trivial decisions every day. Two hundred twenty-seven of them are about food alone. If you make the wrong choice, it is not a significant event in your life if it comes to your coffee; you make a face and move on. What about your decision to choose your soul mate, health, or work? Errors in decision-making lead you in the wrong directions. Your choices can irreversibly impact not only that day but also the years after.
Some choices can be easier than others. Let’s say there is a bicycle behind one door and an expensive car behind the other. Before asking you which door you would choose, you also know which door the bicycle is behind and which door the car is behind. There is a bicycle at door A and the car door is B. Now let's ask our question: Which door would you choose? A or B? The answer is pretty obvious: of course, you would choose door B.
Let's make the decision a little harder: things might not be as they seem. We have doors A and B again. There is a possibility that there is a bicycle behind door A and a car behind door B. There may or may not be a bicycle and a car behind doors. I don't think your choice will change. In the end, the chance of them existing or not existing is the same, but because the car’s worth outweighs the bicycle’s worth, it is the most sensible decision.
We can prove what we said by calculating the expected value in probability. First considering door A: there is either a bicycle behind it or there is nothing. The chance of getting a bicycle is ½, and let’s say the bicycle is worth $100; the profit will be $100. If there is no bike behind door A, the probability of this happening is ½ again, but there is no profit this time. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values. So, expected value in this scenario is calculated as:
E(A) = $100 x (1/2) + $0 x (1/2) = $50.
The expected value of door A is $50. The expected value for door B is also considered and calculated in the same way. Let's say the price of the car here is $100,000. From the same formula:
E(B) = $100,000 x (1/2) + $0 x (1/2) = $50,000.
The expected value of door B is a thousand times that of door A. If a choice is to be made between two doors, the wise choice will undoubtedly be door B.
Pascal's stake is very similar to this game of chance. Blaise Pascal was a scientist and mathematician who lived in the 17th century and developed his own theory of probability. His theory was quite successful. Using his own approach, he showed the existence of God and the necessity of believing in God. Instead of the door metaphor we used, he used two people, one who believed in God and one that didn’t believe in God. We assume that there is a fifty percent chance of God's existence—that God either exists or he doesn’t. People that believe in God would pass through door B, similar to the example above. Under these conditions, if a person believes in God and God doesn’t exist, they lose or gain nothing. If God does exist, the believers go to Heaven and achieve infinite happiness. When we formulate this situation, we find out that the expected value of believing in God is infinite. We consider the probability of not believing in God is fifty percent, and there is no gain if it is true. On the other side, the existence of God is also fifty percent, and one gains infinity of happiness. Therefore, the expected value of believing in God, E(Believing), is calculated as above in the car/bicycle example:
E(Believing)= 0 x (1/2) + ∞ . (1/2) = ∞
Remember that half of infinity is also infinite.
So, even if God doesn’t exist, the faith that the believer has is priceless.
For those people who choose door A (not believing in God), there is nothing so beneficial for them. Even if they are correct, there is no gain for them in the end. If there is no God, then there is no afterlife. They receive finite pleasure from this life: choosing the bicycle still has some value but choosing the car is way more sensible. What if the other possibility happens? If a person does not believe in God and God exists, they will be deprived of all believers will get. When we think of the second option, that is door A, we formulate the expected value of not believing as:
E(not Believing)= 0 x (1/2) + (-∞) x (1/2) = -∞
Not believing in God also has infinite value but in the opposite way. You are in debt, bankrupt.
One of our choices is God existing, which is fifty percent. Someone may say that it is a high probability. So, despite all the evidence to believe in God, what if we reduce the probability of His existence to one in a thousand? Then the chance that God does not exist is 999/1000. In this case:
Probability of God not existing: 999/1000 and no gain.
Probability of God exists: 1/1000 and the gain is infinite.
E(Believing)= 0 x (999/1000) + (∞) x (1/1000) = ∞
As can be seen, the expected values do not change. Likewise, an atheist will get the same negative infinity. According to possibility calculations, belief in God means an infinite gain in any case. According to mathematics, believing in God, even if the likelihood is one in a googolplex, is still profitable. This topic leaves no room for choice. The chance to gain infinite value is infinite, and the value you lose is finite or, more likely, non-existent. There is no doubt that you have to give everything in this game of life that you are obliged to play. There is no other way to end it than to risk your finite life to win eternal life. Preferring the other option is like resigning from one’s mind.
On the other hand, you may say that the profit is uncertain, and everything is left to luck. But when considering the infinite distance between the certainty of the misery endured and the uncertainty of gain, it makes no sense to argue that the finite life we have should be used to endanger the infinite gain. Everyone who enters a game of chance tries their luck by putting in something sure, but it is always doubtful whether they will win. He puts something limited and negligible in danger without offending the mind. As Pascal states, “Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.”
The following story is related to Pascal’s argument. Someone came to Ali, the Caliph. The man denied resurrection, reckoning in the hereafter, heaven, and hell. He asked Ali:
"Ali, you believe in hereafter; we don't. You worship, spend a lot of money, and go through the trouble to be saved from hell and enter heaven. Is it worth it? And how do you know that there will be a resurrection after death?"
Ali (R.A.) listened to the man calmly, then gave him the following answer:
"Let's first assume that what you say is true. If there is no afterlife, we are in the same situation as you. We are even, and there is no gain for you or us. In the meantime, our prayers, good deeds, good morals, and charity we give for the sake of God will not harm us. On the contrary, it will be beneficial for improving the community. But what if there is an afterlife, and what we say turns out to be true? What will you do?"