init

config.json

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+{
+    "probability_table": [
+        [1,0.008],
+        [73,0.008],
+        [90,1]
+    ],
+    "num_trials": 10000000
+}

main.py

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+import json
+import random
+import csv
+from tqdm import tqdm
+
+
+class ProbabilityTable:
+    def __init__(self, table):
+        self.table = table
+        self.maximum_draws = table[-1][0]
+
+    def get_probability(self, n):
+        for i in range(len(self.table) - 1):
+            if n < self.table[i + 1][0]:
+                return self.table[i][1] + (self.table[i + 1][1] - self.table[i][1]) * (
+                    n - self.table[i][0]
+                ) / (self.table[i + 1][0] - self.table[i][0])
+        return self.table[-1][1]
+
+
+class CardGame:
+    def __init__(self, probability_table):
+        self.probability_table = probability_table
+
+    def play(self):
+        n = 1
+        while True:
+            if n > self.probability_table.maximum_draws:
+                raise ValueError(
+                    "Reached maximum number of draws without finding a match"
+                )
+            r = random.random()
+            p = self.probability_table.get_probability(n)
+            if r < p:
+                return n
+            n += 1
+
+
+class Statistics:
+    def __init__(self, game, num_trials):
+        self.game = game
+        self.num_trials = num_trials
+
+    def run(self):
+        results = {}
+        maximum_draws = self.game.probability_table.maximum_draws
+        for n in range(1, maximum_draws + 1):
+            results[n] = {"count": 0, "samples": []}
+
+        with tqdm(total=self.num_trials, desc="Running simulations") as pbar:
+            for i in range(self.num_trials):
+                n = self.game.play()
+                results[n]["count"] += 1
+                results[n]["samples"].append(i + 1)
+                pbar.update()
+
+        with open("results_full.csv", "w", newline="") as f:
+            writer = csv.writer(f)
+            writer.writerow(["抽数", "该抽出金的概率", "刚好在该抽出金的概率", "该抽出金的样本数量", "该抽出金的样本号"])
+            for n in range(1, maximum_draws + 1):
+                p = self.game.probability_table.get_probability(n)
+                probability_of_exact_n = results[n]["count"] / self.num_trials
+                samples_str = ", ".join(str(s) for s in results[n]["samples"])
+                writer.writerow(
+                    [n, p, probability_of_exact_n, results[n]["count"], samples_str]
+                )
+
+        with open("results_no_samples.csv", "w", newline="") as f_no_samples:
+            writer_no_samples = csv.writer(f_no_samples)
+            writer_no_samples.writerow(["抽数", "该抽出金的概率", "刚好在该抽出金的概率", "该抽出金的样本数量"])
+            for n in range(1, maximum_draws + 1):
+                p = self.game.probability_table.get_probability(n)
+                probability_of_exact_n = results[n]["count"] / self.num_trials
+                writer_no_samples.writerow(
+                    [n, p, probability_of_exact_n, results[n]["count"]]
+                )
+
+
+with open("config.json", "r") as f:
+    config = json.load(f)
+
+table = ProbabilityTable(config["probability_table"])
+game = CardGame(table)
+statistics = Statistics(game, config["num_trials"])
+
+statistics.run()

requirements.txt

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+tqdm==4.66.1