Reference
Mystery Tickets
The community nickname for this whole system is "gachapon" - the game's own flavor text leans into it too ("Sometimes monsters randomly drop gachapons!", and a line describing "a mysterious 'person' in spawn looking for gachapons"). The actual item is called a Mystery Ticket, and this page covers it exclusively. If you were looking for the unrelated item literally named Dye Gachapon, that's a much simpler random-Dye pull with its own entry on the Systems Glossary.
Neither this site nor the wiki has an exact drop-chance percentage for a Mystery Ticket from any specific monster, or odds for any individual reward inside the pool below. Re-checked directly against the wiki's own Mystery Tickets page while reworking this section: it still states the chance only qualitatively ("the higher a monster's level, the higher the chance"), with no percentages anywhere on the page. That's a real gap, not an oversight - no source anywhere states a number, so none is guessed at here.
Getting one, and redeeming it
The reward pool - 60 items
Categorized exactly as the wiki documents it. Named items are listed individually; where the wiki itself groups several color/recolor variants under one line (extra hat styles, dye-style shards and crystals, potion/food variety) that grouping is kept as-is here rather than guessed apart into individual names this project doesn't actually have.
| Cosmetics | Fireworks (Red, Blue, Yellow), Cat Ears, Wolf Ears, Bandana, Santa Hat, Goggles, and assorted other hats |
| Gems & Souls | Nurturing Gem, Mystic Gem, Calamity Gem, Energetic Soul, Turbulent Soul, Ambitious Soul, Chaotic Soul |
| Equipment | Ring of Power, Ring of Magic, Ring of Swiftness, Rock Pendant, Kunai, Spiky Shell, Dark Bullet-knife |
| Materials | Stone, Iron Ingot, Light Essence, Dark Essence, and assorted colored Shards & Crystals |
| Consumables | Assorted herbs, potions, and food/drink items |
| Crystals | Summoning Crystal, Return Crystal, Home Crystal |
Several of the named Souls above (Energetic, Ambitious, Chaotic, Turbulent) are also normal per-kill monster drops in their own right - see the Systems Glossary for that side of things. Energetic and Ambitious Soul additionally double as pet food - see Companion Pets.
The full 60-item reward pool and its categorization above come from the official community wiki's Mystery Tickets page - this isn't stored client-side in a form this project's own datamined files give access to, so the wiki's own compiled list is the source here. Cross-referenced on the Sources page.
See also: the Systems Glossary's own Mystery Tickets entry for the short version of this, and this project's source page directly.