## README ¶

### 837. New 21 Game

#### 题目

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 probabilitythat 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.

#### 解题思路

见程序注释

## Documentation ¶

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