In our last lab, we use MCMC method to simulate a walker walking in the phase space. Using the Metropolis method, a walker at its currect position will sample another point inside a cube (centered at the current position) with side length $\eta$ with equal probabilities. Then he accepts or rejects this attempted move by calculating the energy difference.
The instructor told us we should choose $\eta$ so that about 60% of the attempted move will be accepted.
He also stated that to reduce sequential correlation, we should add the sum not at every step, but after every $n$ steps (say $10$ steps).
My question is, why don't we just increase the step-size $\eta$, which will also reduce sequential correlation. The instructor's answer is that in that case most of the attempted move will be rejected and this reduces the efficiency. However, by sampling $10$ points and using only $1$ of them, we have also lost an efficiency of $90$%. I think that's no difference than making $\eta$ larger.
Am I missing something? Thanks!