Optimal quest artifact invocation strategy

[Robert R Schneck]

"You feel that the Platinum Yendorian Express Card is ignoring you."

The question has arisen for me, what is the optimal strategy for
invoking a quest artifact? Optimal could mean a number of things, but I
think in most cases a reasonably good goal is obtaining the shortest
expected wait time between successful invocations.

I have calculated and can now report that:

Waiting 100 turns between invocations yields an expected wait
of 186.48 turns.

Waiting 80 turns between invocations yields an expected wait
of 181.08 turns.

Waiting 78 turns between invocations yields an expected wait
of 180.83 turns. This is the best such simple strategy.

There is a *best* strategy, of course; it follows the sequence

82; 81; 68; 81; 88; 67; 54; 96; 78; 62; 88; 81; 65; 63; 81; 65; 49; 38...

and yields an expected wait of 180.2354 turns. What you do in the 1 in
50000 chance you are still failing after following the sequence that far
won't affect the expected wait within that precision, as long as each
subsequent wait is between 31 and 41 turns. Note that intervals close
to 30 cause a large longest possible wait (which, when your experience
level is 17 or less, is 999 + 30 * the number of failed invocations).

The calculations for the simple one-number strategies surprisingly don't
depend on your experience level; the best strategy is only correct up to
experience level 17, but is not far off even after that.

Robert

[Sam Dennis]

Robert R Schneck wrote:
> [Artifact invocation waits]

> The calculations for the simple one-number strategies surprisingly don't
> depend on your experience level; the best strategy is only correct up to
> experience level 17, but is not far off even after that.

I'm pretty sure that no source diver would be surprised by this, as the
experience level factor in rne(), referenced by rnz(), only varies with
every third level after 15 (18, 21, ...) and not much, at that.

--
++acr@,ka"