Purpose of trace-decay parameter in eligibility traces
The beauty of eligibility trace lies in the fact that it generalizes and unifies TD and Monte-Carlo methods.

When lambda=0, only the present state will get updated, because for the other states eligibility trace will be 0 and they will not be updated. This will be a TD update.

For larger values of 0 &lt; lambda &lt; 1, more of the preceding states are changed, but each state which is more temporally distant is changed less due to decaying property of eligibility traces.

When lambda=1, the preceding states with positive eligibility traces will be updated. This allows us to achieve monte-carlo updation method by backward view. Eligibility trace allows us to look backward and perform updated to the preceding states. Here, the decay parameter is used to achieve the discounted reward setting for the monte-carlo updates. This property of eligibility trace will also allow us to use monte-carlo approaches for continuing tasks.