# 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
```
