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

Invoking strategy is basically a trade-off between the risk of getting nothing and waiting too long. The turns to wait after a successful #invoke versus probability of 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 rate 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. In the table, after waiting for "wait" turns, "chance" means the probability of a successful invoke, and "rate" is 100 times the expected rate of successful invokes per turn.

Consecutive failures beforehand	your level <=17			your level 18-20			your level 21-23			your level 24-26			your level 27-29			your level 30
	wait	chance	rate	wait	chance	rate	wait	chance	rate	wait	chance	rate	wait	chance	rate	wait	chance	rate
0	91	46.7	0.47	91	46.7	0.47	91	46.7	0.47	91	46.7	0.47	91	46.7	0.47	91	46.7	0.47
1	121	73.6	0.59	121	73.6	0.59	121	73.6	0.59	121	73.6	0.59	121	73.6	0.59	121	73.6	0.59
2	211	79.7	0.37	211	79.7	0.37	211	79.7	0.37	211	79.7	0.37	211	79.7	0.37	211	79.7	0.37
3	39	21.9	0.43	39	21.9	0.43	39	21.9	0.43	39	21.9	0.43	39	21.9	0.43	39	21.9	0.43
4	195	76.0	0.38	195	75.6	0.38	195	75.6	0.38	195	75.6	0.38	195	75.6	0.38	195	75.6	0.38
5	46	23.4	0.41	46	22.8	0.40	45	22.3	0.39	45	22.3	0.39	45	22.3	0.39	45	22.3	0.39
6	185	75.9	0.4	185	73.5	0.39	186	73.1	0.38	186	73.0	0.38	186	73.0	0.38	186	73.0	0.38
7	49	29.4	0.49	48	25.1	0.42	48	24.5	0.41	48	24.4	0.41	48	24.4	0.41	48	24.4	0.41
8	180	91.5	0.50	183	74.6	0.40	183	72.0	0.38	183	71.5	0.38	183	71.4	0.38	183	71.3	0.38
9	41	86.0	2.02	51	31.4	0.51	50	26.8	0.44	50	26.1	0.43	50	26.0	0.43	50	26.0	0.43
10	33	87.2	2.53	178	90.4	0.50	182	73.9	0.40	182	71.1	0.38	182	70.6	0.38	182	70.5	0.38
11	31	89.2	2.77	43	85.0	1.89	53	32.5	0.52	52	27.7	0.44	52	27.0	0.43	52	26.9	0.43
12	30	90.6	2.92	34	85.9	2.41	176	89.8	0.51	180	73.1	0.4	179	69.9	0.38	179	69.3	0.38
13	29	90.6	3.02	32	88.6	2.66	44	83.4	1.81	54	33.2	0.52	54	29.1	0.45	54	28.4	0.44
14	29	92.1	3.09	30	88.4	2.83	35	84.9	2.31	174	88.7	0.5	178	72.1	0.4	178	69.2	0.38
15	28	90.9	3.14	30	90.8	2.93	33	88.2	2.57	46	82.9	1.72	56	34.9	0.53	56	30.2	0.45
16	28	91.6	3.17	29	90.4	3.01	31	88.6	2.75	36	84.1	2.22	173	88.1	0.5	176	71.4	0.4
17	28	92.3	3.2	29	91.7	3.07	30	89.2	2.86	33	86.1	2.49	47	81.8	1.66	58	36.0	0.53
18	28	92.8	3.23	28	90.4	3.11	30	91.1	2.94	32	88.6	2.66	37	83.6	2.15	171	87.3	0.5
19	28	93.2	3.25	28	91.0	3.15	29	90.4	3.01	31	89.6	2.79	34	86.1	2.42	49	82.0	1.6
20	27	91.2	3.27	28	91.7	3.17	29	91.5	3.06	30	89.7	2.88	32	87.0	2.6	38	83.5	2.09

At level 17, the probability of 20 fails is 0.067%. On condition that outcome doesn't occur, the expected rate of successful #invokes is once every 101.35 turns.

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 the first #invoke attempt, we maximize the probability of successful invocation, times the expectation of one over the waiting time. This quantity * 100 is listed in the table as "rate". 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. Iteratively, the rate is again maximized and the conditional distribution updated. It isn't quite clear if each invocation attempt may indeed be optimized separately.

Robert Schneck gives a different invocation schedule in his ascension post of a liquid diet tourist:

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

Unfortunately, he does not justify these numbers. He only hints they could be the expected waiting time before the artifact regenerates on its own.

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.