New 21 Game

import { range } from '@algorithm/lib';
 
export function new21Game(n: number, k: number, maxPts: number): number {
  const dp = new Array(n + 1).fill(0);
  dp[0] = 1;
 
  for (const i of range(1, n + 1)) {
    for (const point of range(1, maxPts + 1)) {
      if (point <= i && i - point < k) {
        dp[i] += dp[i - point] / maxPts;
      }
    }
  }
 
  return dp.slice(k).reduce((acc, curr) => acc + curr, 0);
}