# Convergence of Monte Carlo simulation

I am not sure if this is a valid question but here goes.

For the monte carlo method I know that estimation of the mean is also a random quantity and follows a normal distribution. The standard error of this distribution is proportional $\frac{1}{\sqrt{N}}$, where N is the number of Monte Carlo trials. So if i increase N, then the result will be more likely to be close to the true value of the mean.

I am wondering if there is a way to measure whether my Monte Carlo has reached some convergence criterion by simply looking at the Monte Carlo result as a function of N, without evaluating its standard error?

Thanks!