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What is the friction of the secret library floor? Or what speed is needed to reach the breakpoints?

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They have a friction value of 150. An easy way to figure out these values for tiles is through the client's minimap which stores the current friction of the explored tiles inside the WaypointCost files as a greyscale colour, so by opening these files inside an image editor you can get the a tile's friction by looking at one of its RGB colour components.

For the character speed required to reach the breakpoints I refer to the following table:Source: https://www.reddit.com/r/TibiaMMO/comments/7qn9sf/list_of_all_available_speed_boosts/