In Christian writings, pride is one of the most basic and important sins, the one has been getting humans in hot water ever since Adam and Eve. As the proverb says, pride goeth before the fall. While it's not clear exactly why the Mariner shoots the albatross in The Rime of the Ancient Mariner, the answer has something to do with pride. He obviously didn't intend to bring about drought and death to the crew, but he thought they could do without this bird whose arrival happened to coincide with a lot of good luck. The poem takes elements from the stories of Adam and Eve and the crucifixion of Christ and weaves them into an entirely original take on man's pride.
The Rime of the Ancient Mariner retells the central stories of the Book of Genesis and the New Testament: the fall of Adam and Eve and the crucifixion of Jesus Christ.
The dice game between Death and Life-and-Death is an appropriate part of the Mariner's punishment because, when he killed the albatross, he expressed a belief that the world is guided by luck and chaos.