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Speed & Fuel

Players can influence their movement speed by depositing $ASTRO tokens into the map contract using the deposit() and withdraw() methods.

speed and tokens visualization

How Speed Works

The speed calculation depends on 3 factors from the map configuration:

  1. s0\textcolor{blue}{s_0} = base speed of the map
  2. fb\textcolor{red}{f_b} = burning factor (multiplier for burned tokens)
  3. fh\textcolor{green}{f_h} = holding factor (multiplier for held tokens)

The Speed Formula

speed=s0+fb⋅ln⁡(1+b)+fh⋅log⁡2(1+h)\text{speed} = \textcolor{blue}{s_0} + \textcolor{red}{f_b} \cdot \ln(1 + b) + \textcolor{green}{f_h} \cdot \log_2(1 + h)

Where:
  • hh = amount of tokens staked by the player
  • bb = amount of tokens burned by the player (for a single move)

Strategy

This design encourages both long-term holding and active burning while keeping the system simple, fair and strategic.

speed formula image

Token Mechanics

  • Holding tokens gives you a passive speed bonus that scales logarithmically
  • Burning tokens gives you an immediate speed boost for that specific move with diminishing returns
  • No speed cap - more burn = more speed (just less efficient over time)
  • Strategic depth - players must balance between holding for passive benefits and burning for immediate gains