There is clearly a marked difference between the lawyer at the beginning of the story and the person who leaves the secluded hut moments before the bet is due to end. Note how impulsive the lawyer is at the beginning:
"If you mean that in earnest," said the young man, "I'll take the bet, but I would stay not five, but fifteen years."
He, of his own volition, is so proud and impulsive that he automatically triples the conditions of the bet for himself, so sure he is that he can fulfil what he has just proudly boasted.
However, the note that he leaves the banker at the end of the tale reveals a very different character. Having read and thought deeply about so many issues, he now realises how everything to do with mankind is "worthless, fleeting, illusory, and deceptive, like a mirage":
You may be proud, wise, and fine, but death will wipe you off the face of the earth as though you were no more than mice burrowing under the floor, and your posterity, your history, your immortal geniuses will burn or freeze together with the earthly globe.
Having started off as a figure defined by pride and arrogance, now the lawyer has eschewed these characteristics and realised the true humble position of man and how man could be wiped out at any second. The lawyer realises that life does have meaning, but misplaced values have effectively blinded people to that meaning. As a symbol of his new understanding, he deliberately breaks the terms of the bet to show how unimportant money is to him.