> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/0837-new-21-game.md).

# 0837. New 21 Game

<https://leetcode.com/problems/new-21-game>

## Description

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, maxPts]`, where `maxPts` is an integer. Each draw is independent and the outcomes have equal probabilities.

Alice stops drawing numbers when she gets `k` **or more points**.

Return the probability that Alice has `n` or fewer points.

Answers within `10-5` of the actual answer are considered accepted.

**Example 1:**

```
**Input:** n = 10, k = 1, maxPts = 10
**Output:** 1.00000
**Explanation:** Alice gets a single card, then stops.
```

**Example 2:**

```
**Input:** n = 6, k = 1, maxPts = 10
**Output:** 0.60000
**Explanation:** Alice gets a single card, then stops.
In 6 out of 10 possibilities, she is at or below 6 points.
```

**Example 3:**

```
**Input:** n = 21, k = 17, maxPts = 10
**Output:** 0.73278
```

**Constraints:**

* `0 <= k <= n <= 104`
* `1 <= maxPts <= 104`

## ac

```java
```