human
What is a the probability that she has N or less points given the following:
Solve in Python:
Alice plays the following game, loosely based on the card game "21".
Alice starts with 0 points, and draws numbers while she has less than K points.  During each draw, she gains an integer number of points randomly from the range [1, W], where W is an integer.  Each draw is independent and the outcomes have equal probabilities.
Alice stops drawing numbers when she gets K or more points.  What is the probability that she has N or less points?
Example 1:
Input: N = 10, K = 1, W = 10
Output: 1.00000
Explanation:  Alice gets a single card, then stops.

Example 2:
Input: N = 6, K = 1, W = 10
Output: 0.60000
Explanation:  Alice gets a single card, then stops.
In 6 out of W = 10 possibilities, she is at or below N = 6 points.

Example 3:
Input: N = 21, K = 17, W = 10
Output: 0.73278
Note:

0 <= K <= N <= 10000
1 <= W <= 10000
Answers will be accepted as correct if they are within 10^-5 of the correct answer.
The judging time limit has been reduced for this question.
assistant
#Here is the probability that she has N or less points.

class Solution:
    def new21Game(self, N: int, K: int, W: int) -> float:
        if K == 0:
            return 1
        dp = [0] * (W + K)
        dp[0] = 1
        sliding_sum = 1
        for i in range(1, K+W):
            # print(sliding_sum)
            # constant = dp[i] / W
            # for j in range(i+1, i+W+1):
            #     dp[j] += constant
            # dp[i] = 0
            dp[i] = sliding_sum / W
            if i < K:
                sliding_sum += dp[i]
            if i-W >= 0:
                sliding_sum -= dp[i-W]
                dp[i-W] = 0
        # print(dp)
        return sum(dp[K:N+1])/ sum(dp)