As the name implies, Lottery Paths are simply a choice of paths where only one will lead to the next room, while the others will send the player back to the initial choice; or perhaps even further back, depending on the location of the last checkpoint. The player cannot tell which path is correct, due to the limited field of vision in the game, and must choose one at random much like in a lottery. There is technically no skill involved in this puzzle type, since it's purely based on luck (unless a poor design allows the player to use the minimap to determine the correct choice). Now you can disable minimap off and try that if possible.
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