Clearly one central piece of situational irony is the fact that the lawyer decides to lose the bet and forsake his wealth, even though he is literally moments away from winning and he has lived almost the entire time in solitude, according to the bet. This is the premise that this short story is based around - the lawyer through his time of solitude has obviously learned far more about the world and life than the other characters in the novel. Consider what he writes in his letter:
"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...
To prove to you in action how I despise all that you live by, I renounce the two million of which I once dreamed as of paradise and which now I despise."
The lawyer has learnt the truth of the illusions that we try to project to protect ourselves from the reality of our own fragility, and above all he has learnt the false promise of wealth and paradise that money gives.
How ironic therefore that the banker has obviously not learned this lesson. Note how he responds to reading the letter:
At no other time, even when he had lost heavily on the Stock Exchange, had he felt so great a contempt for himself. When he got home, he lay on his bed, but his tears and emotion kept him for hours from sleeping.
Clearly the words of the lawyer and his resolution to forsake the bet impact the banker deeply at an emotional and fundamental level. Yet note how in the last paragraph, we are told that the banker took the letter which recorded the renunciation of the bet and stored it safely away, in case the lawyer should change his mind. The author ironically shows us that, whilst the lawyer has definitely developed and moved on in his humanity, the banker is just as greedy and doubtful as he ever was, showing, ironically, that whilst the lawyer has overtly lost the bet, it is the banker who is the real loser, because he has not been able to learn from the lawyer and develop in his character.