How to Solve New 21 Game Problem
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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 poi...
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Understanding the New 21 Game Problem
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Problem Statement
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.
New 21 Game
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Examples
n = 10, k = 1, maxPts = 10
1.00000
Alice gets a single card, then stops.
n = 6, k = 1, maxPts = 10
0.60000
Alice gets a single card, then stops. In 6 out of 10 possibilities, she is at or below 6 points.
n = 21, k = 17, maxPts = 10
0.73278
Constraints
0 <= k <= n <= 104
1 <= maxPts <= 104
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