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+# 837. New 21 Game
+
+"""
+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 range
+'[1, maxPts]', where 'maxPts' is an integer. each draw is independent and
+the outcomes have equal posibilities. 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
+"""
+
+
+class Solution(object):
+ def new21Game(self, n, k, maxPts):
+ """
+ :type n: int
+ :type k: int
+ :type maxPts: int
+ :rtype: float
+ """
+ if k == 0 or n >= k + maxPts:
+ return 1
+ dp = [1.0] + [0.0] * n
+ sum = 1.0
+ for i in range(1, n + 1):
+ dp[i] = sum / maxPts
+ if i < k:
+ sum += dp[i]
+ if i - maxPts >= 0:
+ sum -= dp[i - maxPts]
+ return sum(dp[k:])
+
+
+if __name__ == "__main__":
+ obj = Solution()
+ print(obj.new21Game(n=10, k=1, maxPts=10))
+ print(obj.new21Game(n=6, k=1, maxPts=10))
+ print(obj.new21Game(n=21, k=17, maxPts=10))