path-to-one

Path-to-One is a mathematical roguelike game based on the Collatz conjecture (the 3n+1 problem).

Choose a "curse number" and navigate the dark labyrinth. Odd-numbered rooms are dangerous — the curse grows at 3n+1, dealing damage. Even-numbered rooms offer a brief respite — the curse weakens at n÷2. Goal: Reach 1 and break the curse.

Strategic Battle
Odd-numbered rooms present choices: direct action (3n+1), detour (n+1) to acquire cards, use magic cards, or escape. Passing through consecutive odd-numbered rooms accumulates the curse, doubling the damage multiplier.

Magic Cards (Single Use)
Start with 6 cards. 7 types: Halve, Barrier, Heal, Clairvoyance, Acceleration, Purify. Choosing the same card as a reward upgrades it to an enhanced version.

7 Stages of Enemy Characters
Enemies range from cursed slimes to gods of the apocalypse, with the difficulty varying according to the number. Unleash your strategic power with unique abilities like Dark Mist, Pierce, and Despair.

6 Builds & 4 Difficulty Levels
Choose from Guardian Mage, Accelerator Mage, Sorcerer, Clairvoyant Mage, Contract Mage, and Overlord Mage. Rewards and risks vary across the 4 difficulty levels: Normal, Abyss, End, and Pit.

Daily Challenge
Attempt a daily challenge with a unique number of attempts each day. Completing a challenge grants a 1.5x score bonus and 2x currency bonus.

Combo System
Each consecutive unscathed room clears increases your combo count. Earn up to a 100-point score bonus.

Replayability Features
- 19 Achievements
- Grimoire: Encyclopedia of enemies, magic, and events
- Unlock builds and difficulty levels with curse marks
- D-S rank scoring system
- Review past playthroughs with Adventure Log
- Unlock 4 derivative events under certain conditions

Random Events
Healing Fountain, Cursed Trap, Treasure Chest, Dark Merchant — Further conditions unlock enhanced versions of events (Blessed Fountain, Curse Lab, Black Market, Sealed Box).

Can you escape the curse with the power of mathematics?