[RPG] Given one sending stone, how can I locate its mate

A few 5th level options

One of the best options is the 5th level spell Dream. With this spell, you can converse with a person known to you while they sleep, as long as they are on the same plane of existence as you. If you aren't trying to damage or impair them with this spell, the spell automatically works. And best of all...

The target recalls the dream perfectly upon waking. [PHB, p.236]

If the recipient of the message you intend to send is in a location with a permanent teleportation circle, (such as an academy of magic or a major temple of a powerful religion), then you could also use the 5th level spell Teleportation Circle. It can transport "creatures". You could find a mouse, tie your message to it, and have an ally toss it through the portal that the spell opens (you couldn't toss it yourself, since you already took your action to cast the spell, and the portal only lasts one round).

With some specific subclasses, there may be other options as well. As an example, a Wizard of the School of Illusion could cast Magic Mouth on the wall of the room of a minion, who is given instructions to stand in front of it and say a specific phrase every day at an appointed time. The mouth could be programmed to appear and say "nothing to report" over and over for 10 minutes when the minion says its trigger phrase. Then, when the Wizard wants to contact the minion, they could cast the 5th level spell Scrying on the location, and thus see the mouth activate. The Wizard could use their "Malleable Illusion" ability:

Starting at 6th level, when you cast an illusion spell that has a duration of 1 minute or longer, you can use your action to change the nature of that illusion (using the spell’s normal parameters for the illusion), provided that you can see the illusion. [PHB, p. 118]

With this, the Wizard could change the message every round, and thus send a long message over the 10 minutes that Scrying last. Since Magic Mouth lasts until it is dispelled, this could be done every day (though it would take up a 5th level spell slot to Scry on the location, in order to "see the illusion").

The highest average damage per round over three rounds that your tankard can deal is:

305.787

The Character

The character (let's call her Callie) to command the most dangerous tankard has the following classes:

• Wizard 11------------------------------- (for alter self, conjure minor elementals, haste, magic jar, and Tenser's transformation)
• Warlock (The Undying) 9 ------------ (for hold monster and death ward)

...and the following magic items:

• a twenty-two card deck of many things
• a robe of the archmagi
• a rod of the pact keeper
• an Ioun Stone of mastery
• a belt of storm giant strength
• a ring of air elemental command
• a scimitar of speed
• three javelins of lightning¹

¹ Credit to Medix2 for suggesting the javelins

Magic Jar

Firstly, Callie needs to be more proficient. A base proficiency bonus of +6 isn't good enough, so Callie has to take the body of a creature who is more generally proficient. This involves use of the magic jar spell, which lets her take the statistics of another humanoid, while keeping her class features.

She is looking for a humanoid of CR 21 or higher (to get a proficiency bonus of +7 or higher). Official options include:

• Halaster Blackcloak
• Quenthel Baenre
• any ancient metallic dragon who has used Change Shape to assume one such form

Spell Glyphs

Then, we need to create a number of Spell Glyphs using glyph of warding. To avoid the material component cost, Callie will cast glyph of warding using the wish spell, but she still needs to cast the stored spell as well.

To gain access to wish...

• Callie casts conjure minor elementals choosing 8 CR 1/4 or lower elementals (retrying if the spell summons chwinga since they can't speak).
• Callie commands an elemental to repeatedly declare that they want to draw one card from the deck of many things (while Callie carries it, so that the deck itself won't be desroyed if the elemental draws the Talons card.
• Eventually, the elemental will draw the The Fates card.
  • If the Donjon, Flames, Rogue, Skull, or The Void card is drawn, kill the elemental or let the elemental die and try again.
• Callie commands the elemental to use The Fates to reverse a draw of either the Donjon, Flames, Rogue, Skull, The Void, Ruin, or Talons card.
• Then, Callie repeatedly declares that she wants to draw one card from the deck of many things.
• Eventually, Callie will draw the Moon card
  • If the elemental reverses a bad draw, restart with a new elemental.
• Cast wish to replicate the effect of glyph of warding for a Spell Glyph with one of the following spells:
  • many counts of alter self
  • haste
  • Tenser's transformation
• Repeat the whole procedure until you have ample Spell Glyphs.

The Tiny Servant

Then, Callie's need the ideal Tiny Servant (we'll call him Tim). This involves the following procedure:

• Callie casts tiny servant on her tankard.
• Tim activates one of the alter self Spell Glyphs gaining the proper anatomy in order to speak.
• Tim repeatedly declares that he wants to draw one card from the deck of many things.
• Eventually, Tim will draw the Moon card for 3 castings of wish.
  • If the Donjon, Flames, Rogue, Skull, or the The Void card is drawn, kill Tim or let Tim die and try again.
  • Callie will have to make more alter self Spell Glyphs if she exhausts them all before a successful Tim.
• Tim attunes to the belt of storm giant strength, scimitar of speed, and ring of air elemental command
• Tim wields the scimitar of speed and a javelin of lightning.

Combat Preparation

Now that Tim is ready, it is time to prepare for combat:

• Callie casts death ward on Tim
• Tim casts wish replicating the effect of an 8th level delayed blast fireball so that it will be on it's last 6 seconds of duration during Round 1.
• Tim activates the haste, Tenser's transformation, and a new alter self Spell Glyph (in order to speak command words).

The Rounds

Round 1

Callie:

• Casts hold monster at 6th level on two targets that are nearby one another.
• Uses her bonus action each round to command Tim to take the listed actions.

Tim:

• Touches the delayed blast fireball (which will trigger death ward)
• Casts wish replicating the effect of an 8th level wall of fire placed in such a way that it will affect both targets, but not himself
• Attacks with the scimitar of speed as a bonus action.
• Hurls the javelin of lightning with the haste action so that it passes through one target to hit another.

Round 2:

• Tim draws a new javelin of lightning.
• Tim attacks with the scimitar of speed as a bonus action.
• Tim hurls the javelin of lightning with the haste action so that it passes through one target to hit another.
• Tim casts wish replicating the effect of an 8th level vitriolic sphere.

Round 3:

• Tim draws a new javelin of lightning.
• Tim attacks with the scimitar of speed as a bonus action.
• Tim hurls the javelin of lightning with the haste action so that it passes through one target to hit another.
• Tim casts chain lightning² with the ring of air elemental command.

² Credit to GcL for mentioning that chain lightning is superior to disintegrate against multiple targets

The Calculation

Hold Monster

To start with, it is impossible for any of the targets to succeed on the saving throw of hold monster.

• Callie's spell save DC is 31
  • 8 (base) + 8 (+7 proficiency bonus from magic jar statistics +1 from Ioun Stone of mastery) + 10 (Charisma) + 2 (robes of the archmagi) + 3 (rod of the pact keeper)

Round 1

• Delayed blast fireball deals 13d6 base damage and 10d6 ticking damage to both targets.
  • 23 * 3.5 * 2 = 161 fire damage
• Wall of fire deals 9d8 damage to both targets.
  • 9 * 4.5 * 2 = 81 fire damage
• Scimitar of speed deals 1d6 + 2d12 (Tenser's transformation) + 11 on a hit, or 2d6 + 4d12 + 11 on a critical hit.
  • 81.25% chance of a regular hit yields 11.78125 slashing damage and 10.5625 force damage.
  • 9.75% chance of a critical hit yields 1.755 slashing damage and 2.535 force damage.
• Javelin of lightning deals 4d6 damage to one target and 5d6 + 2d12 + 9 damage to the other on a hit, or 10d6 + 4d12 + 9 damage on a critical hit.
  • 4 * 3.5 = 14 lightning damage
  • 74.25% chance of a regular hit yields 9.28125 piercing damage, 9.6525 force damage, and 10.395 lightning damage.
  • 9.75% chance of a critical hit yields 1.56 piercing damage, 2.535 force damage, and 2.73 lightning damage.
• Wall of fire deals 9d8 damage to both targets.³
  • 9 * 4.5 * 2 = 81 fire damage

In Round 1, Tim deals an expected 323 fire damage, 13.53625 slashing damage, 25.285 force damage, 27.125 lightning damage, and 10.84125 piercing damage.

³ Credit to Medix2 for mentioning that wall of fire deals damage twice in Round 1 if Tim acts before the targets.

Round 2

• Wall of fire deals 9d8 damage to both targets.
  • 9 * 4.5 * 2 = 81 fire damage
• Scimitar of speed deals 1d6 + 2d12 (tenser's transformation) + 11 on a hit, or 2d6 + 4d12 + 11 on a critical hit.
  • 81.25% chance of a regular hit yields 11.78125 slashing damage and 10.5625 force damage.
  • 9.75% chance of a critical hit yields 1.755 slashing damage and 2.535 force damage.
• Javelin of lightning deals 4d6 damage to one target and 5d6 + 2d12 + 9 damage to the other on a hit, or 10d6 + 4d12 + 9 damage on a critical hit.
  • 4 * 3.5 = 14 lightning damage
  • 74.25% chance of a regular hit yields 9.28125 piercing damage, 9.6525 force damage, and 10.395 lightning damage.
  • 9.75% chance of a critical hit yields 1.56 piercing damage, 2.535 force damage, and 2.73 lightning damage.
• Vitriolic sphere deals 18d4 damage to both targets.
  • 18 * 2.5 * 2 = 90 acid damage

In Round 2, Tim deals an expected 81 fire damage, 13.53625 slashing damage, 25.285 force damage, 27.125 lightning damage, 10.84125 piercing damage, and 90 acid damage.

Round 3

• Vitriolic sphere deals 5d4 damage to both targets.
  • 5 * 2.5 * 2 = 25 acid damage
• Wall of fire deals 9d8 damage to both targets.
  • 9 * 4.5 * 2 = 81 fire damage
• Scimitar of speed deals 1d6 + 2d12 (tenser's transformation) + 11 on a hit, or 2d6 + 4d12 + 11 on a critical hit.
  • 81.25% chance of a regular hit yields 11.78125 slashing damage and 10.5625 force damage.
  • 9.75% chance of a critical hit yields 1.755 slashing damage and 2.535 force damage.
• Javelin of lightning deals 4d6 damage to one target and 5d6 + 2d12 + 9 damage to the other on a hit, or 10d6 + 4d12 + 9 damage on a critical hit.
  • 4 * 3.5 = 14 lightning damage
  • 74.25% chance of a regular hit yields 9.28125 piercing damage, 9.6525 force damage, and 10.395 lightning damage.
  • 9.75% chance of a critical hit yields 1.56 piercing damage, 2.535 force damage, and 2.73 lightning damage.
• Chain lightning deals 13d6 + 40 damage on both targets.
  • 10 * 4.5 * 2 = 90 lightning damage

In Round 3, Tim deals an expected 25 acid damage, 81 fire damage, 13.53625 slashing damage, 25.285 force damage, 117.125 lightning damage, and 10.84125 piercing damage.

The three round average DPR for Tim is 161.667 fire damage, 13.536 slashing damage, 24.285 force damage, 57.125 lightning damage, 10.841 piercing damage, and 38.333 acid damage, totaling 305.787 damage.