Thus, we require that our algorithm should satisfy the principle of detailed balance and be ergodic. The problem with our ratio $$ \begin{equation*} \frac{A(j\rightarrow i)}{A(i\rightarrow j)}= \exp{(-\beta(E_i-E_j))}, \end{equation*} $$ is that we do not know the acceptance probability. This equation only specifies the ratio of pairs of probabilities. Normally we want an algorithm which is as efficient as possible and maximizes the number of accepted moves. Moreover, we know that the acceptance probability has \( 0 \) as its smallest value and \( 1 \) as its largest. If we assume that the largest possible acceptance probability is \( 1 \), we adjust thereafter the other acceptance probability to this constraint.