Why does the banker think he will win the bet?

The banker believed that the fact the lawyer had the choice to leave his imprisonment would win out.... that staying in imprisonment voluntarily would be a far worse state than being in enforced incarceration.

"Two millions are nothing to me, but you stand to lose three or four of the best years of your life. I say three or four, because you'll never stick it out any longer. Don't forget either, you unhappy man, that voluntary is much heavier than enforced imprisonment. The idea that you have the right to free yourself at any moment will poison the whole of your life in the cell. I pity you."