The major irony of the story "the Bet" comes from the financial situation of the two men (the banker and the lawyer) between the beginning of the story and the end of it. In the beginning, when the bet is conceived of, the banker is rolling in the dough: "The banker, spoilt and frivolous, with millions beyond his reckoning, was delighted at the bet." It doesn't really say about the lawyer's finances, but we get thge impression that they are nowhere near as "large and in charge" as the banker's.
Ironically, by the end of the story, there is a reversal in fortunes. The lawyer stands ready to win the bet (and receive the two million dollars) while the banker is nearly broke: "Fifteen years before, his millions had been beyond his reckoning; now he was afraid to ask himself which were greater, his debts or his assets."
That's one example, but I think there are others. I find it ironic that at the end of the story the banker contemplates smothering the lawyer with his own pillow (perhaps an impulse shared by others in our modern world!) "And I have only to take this half-dead man, throw him on the bed, stifle him a little with the pillow, and the most conscientious expert would find no sign of a violent death." This comes from the man who at the beginning of the story had stated that it would be more humane to kill a man than to keep him in jail for life...ironic, here, because he chooses to consider smothering the man after he has already spent the 15 years "imprisoned."
A third irony is the idea that at the beginning of the story both the lawyer and the banker consider the idea of imprisonment as a horrible thing...the banker would rather be dead and the lawyer simply says it would be better to carry on living in some fashion (even a horrible one) than to be killed outright. By the end of the story, though, it is the time "imprisoned" that has transformed the lawyer to be a greater person than he was before; prison actually helped him. Freedom, on the other hand, has only given the banker time to ruin himself financially. By the end of the story his freedom has only given himself the ability to screw up his life.
According to me, the greatest irony is that of the occupations of both men. Of course as other people stated, their answers are valid as well, but when you go to think of the two men's occupations, they play great ironical roles in the story. The lawyer, being somebody who saves people from prison, at the court, here himself is in prison. And as far as the banker is concerned, they usually know how to handle money, unlike here as the banker here is frivolous with his money. This is the great irony of Anton Chekhov's, The Bet.
I find it Ironic, that the Lawyer, whose original reason for agreeing to the imprisonment was to receive 2 million dollars from the banker, but in the end decided against this. What is Ironic is that he decided he doesn't want the money only after 15 years of self imprisonment just to get it.