Calculus

{
  name: "Calculus",
  isFirstTurn: true,
  run(scores) {
    let ret = this.isFirstTurn ? 70 : (100 + (average(scores)) * 0.8) / 2;
    this.isFirstTurn = false;
    return ret;
  }
}

Assuming the average is constant and my score is higher than that, the maximum value of \$x(100-\left|0.8 \times avg - x\right|)\$ is reached at \$x=(100+0.8\times avg)\div 2\$. Deliberately ignores the first turn input (which is totally random and cannot be trusted for any purpose).