When trying to work out the theme of a story, we need to remember that the theme is the overall meaning of a work of literature that usually expresses a view or comment on life. Writers rarely state their theme directly; the reader must consider the complex interplay of all of the elements of the story in order to piece together the possible meanings of the work as a whole. Discerning themes always requires a tolerance for ambiguity - especially in an open-ended story like "The Bet" that raises more questions than it answers.
Considering this, there appear to be a number of possible themes that we could apply to this intriguing short story. One central idea seems to be concerning the value of earthly possessions and knowledge. Remember how the lawyer chooses to renounce the money he would gain by winning the bet, because he realises that all earthly treasures are ephemeral and will pass away:
"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 describes human learning and culture as being "worthless, fleeting, illusory, and deceptive, like a mirage." In his opinion, these things blind us to the ultimate reality of death that will "wipe [us] of the face of the earth as though [we were] no more than mice burrowing under the floor..." Surely this must lie at the heart of the message of this short story - the lawyer, through his time of reflection and study in solitary confinement, has realised and understood the true insignificance of man and the superiority of death in the face of all of our supposed achievements. This story thus cries out for man to not think too highly of himself and to realise his proper position in the order of things.