In Life of Pi, how does Pi's faith contribute to his survival?
On a superficial level, Pi's faith contributes to his survival by providing daily ritual. On a deeper level, Pi's faith contributes to his survival through answered prayers.
Let's explore Pi's survival on the physical level first. If you look closely at chapter 63, you will see that exactly how much keeping busy with daily rituals contributes to Pi's survival. This chapter contains Pi's daily agenda. In regards to your specific question, what is the most interesting is the number of times Pi has recorded the word "prayers." Pi prays more than he does anything else on the raft. He prays no less than five times every day. Pi considers these prayers just as important as any other physical, survival preparations: "I kept myself busy. That was one key to my survival."
Now let's explore Pi's survival on a spiritual level. As a scholar of the religions of the world, I am going to suggest a deeper meaning here. Keep in mind that the deeper meaning I suggest is purely subjective (and not necessarily the opinion of the author). This is because I believe that Pi actually survives because of the deity/deities in which he calls upon. There are two instances where Pi (probably even subconsciously) calls upon these deities from the three major world religions of which he has combined: Christianity, Islam, and Hinduism. Both of these instances involve life or death situations.
Interestingly enough, the first instance involves Richard Parker's survival and the second instance involves Pi's survival (spared FROM Richard Parker).
I could see [Richard Parker's] head. He was struggling to stay at the surface of the water. "Jesus, Mary, Muhammad and Vishnu, how good to see you, Richard Parker! Don't give up, please. Come to the lifeboat! ... Swim, swim!"
Here, Pi is absolutely ecstatic to see Richard Parker. They knew each other from the zoo, of course. Pi is happy to have any creature survive with him. (In reality, even after almost a year at sea, Pi will admit that this kinship with the tiger is the very thing that kept Pi from death.) Pi's prayer is answered when Richard Parker enters the lifeboat.
The next prayer is a bit different, to say the least:
My heart stopped and then beat triple speed. I turned. "Jesus, Mary, Muhammad and Vishnu!" I saw a sight that will stay with me for the rest of my days. Richard Parker had risen and emerged. He was not fifteen feet from me. Oh, the size of him! The hyena's end had come, and mine.
Here it is Pi who is on the point of death. Richard Parker, a deadly animal, could have easily killed Pi. However, due to Pi's prayer, Pi is saved. A miraculous rat "appeared out of nowhere" that Pi is able to fling at Richard Parker who, already a bit hesitant to leap on the less than firm tarpaulin, accepts the rat as an "offering" and flops back down on the bottom of the lifeboat.
Since Pi practices faith in three major religions, he draws upon all of them to pull him through his suffering on the lifeboat. Not only does his commitment to three different religions show that Pi bears great love and faith within himself, it also proves to be the foundation from which he draws the strength and the desire to survive his ordeal. During times when Pi wants to give up hope, he prays or remembers a story from one of the religions he knows so well. He is strengthened to keep on fighting for his life. In chapter 60, Pi wakes up in the middle of the night and is overwhelmed with feelings of insignificance. He remembers a Hindu story of a character named Markandeya:
I felt like the sage Markandeya, who fell out of Vishnu's mouth while Vishnu was sleeping and so beheld the entire universe, everything that there is. Before the sage could die of fright, Vishnu awoke and took him back into his mouth (177).
Vishnu saves the sage in this story, and Pi awakes in the morning revitalized to continue fighting for his life. He says, "I mumbled words of Muslim prayer," which shows how he also draws strength from mixing religious prayers and practices. Furthermore, in chapter 63, Pi's daily schedule is listed, and his prayers and rituals play a vital role in giving him something to do. By having religious practices to accomplish each day, he keeps his mind active and his hope alive. In chapter 74, Pi explains how his religious practices bring him comfort:
At such moments I tried to elevate myself. I would touch the turban I had made with the remnants of my shirt and I would say aloud, "This is God's hat!" . . . Despair was a heavy blackness that let no light in or out. It was hell beyond expression. I thank God it always passed (209).