Invoke

The #invoke extended command allows you to activate certain objects. The only objects that can be activated this way are crystal balls and most quest artifacts.

Artifacts tire after you invoke them, and you cannot do so again for rnz(100) turns (averages 100; can be up to 2000, but 95% of the time it is less than 400). If you invoke again too soon, "You feel that the <artifact> is ignoring you" and 3d10 turns are tacked on to the wait time.

Optimum invocation schedule

When to invoke is basically a trade-off between the risk of getting nothing and waiting too long. The turns to wait versus confidence level success are graphed below (assuming your experience is <=17):

waiting time after successful #invoke versus probability of success of invocation

If you want to maximize the expected number of successful invocations per time, you should wait 91 turns after a successful invoke, 121 turns after one consecutive failure, 211 turns after two consecutive failures and so on:

Consecutive failures before	Turns to wait, XP<=17
0	91
1	121
2	211
3	39
4	195
5	46
6	185
7	49
8	180
9	41
10	33
11	31

These numbers were computed using the exact probability distribution of rnz(100). The relevant waiting time is the turns you actually wait plus the 3d10 penalty for early invokes. For each #invoke attempt, we maximize the expectation value of: probability of successful invocation divided by the waiting time. The waiting time for the next attempt is then computed with the conditional distribution of the remaining artifact timeout, including the penalty from the previous attempt. This algorithm likely gives the optimum result, but an expert on operations research, queueing theory and/or stopped Markov chains is needed to prove each invocation attempt may indeed be optimized separately.

List of possible invocations

• The Eye of the Aethiopica: branchport to another dungeon branch.
• The Eyes of the Overworld: provides enlightenment.
• The Staff of Aesculapius: heals half HP damage, cures sickness, unblinds, unslimes.
• The Orb of Detection: toggles invisibility on/off.
• The Sceptre of Might: toggles conflict on/off.
• The Magic Mirror of Merlin: gives random rumour, from the true file if blessed, the false file if cursed, or either if uncursed.
• The Mitre of Holiness: boost in spell energy.
• The Heart of Ahriman: levitation; you can stop this levitation with '>' at will, or by invoking the Heart again, providing no other levitation sources interfere.
• The Platinum Yendorian Express Card: charges objects like a scroll of charging with the same blessed/cursed status. Only Tourists can perform blessed charging.
• The Orb of Fate: level teleport.
• The Longbow of Diana: creates 7-16 uncursed arrows if uncursed, 7-21 blessed arrows if blessed, 6-11 cursed arrows if cursed.
• The Master Key of Thievery: untraps boxes and doors with 100% success.

Invoking a non-artifact crystal ball is exactly the same as applying it.

List of possible invocations for new SLASH'EM artifacts

• The Candle of Eternal Flame: summons a (tame) fire elemental.
• The Eye of the Beholder: reduces all non-undead monsters in eye's line of sight to 1/3 HP and reduces luck and alignment by 3 with luck above -9. Instadeath with luck below -9.
• The Gauntlets of Defense: toggles invisibility on/off.
• The Great Dagger of Glaurgnaa: boost in spell energy.
• The Hand of Vecna: summons 4-7 tame graveyard creatures and reduces alignment and luck by 3 with luck above -9. Does 5-24 damage to player with luck below -9.
• Holy Spear of Light: creates a lit field of a 12 square radius. This damages undead and demons in a 9 square radius.
• The Storm Whistle: summons a (tame) water elemental.