dsetzer · August 17, 2023 16:16 · Aug 17, 2023 · Aug 17, 2023
diff --git a/prob_using_coefficients.py b/prob_using_coefficients.py
@@ -7,7 +7,7 @@
 import numpy as np
 
 # Number of games to simulate (10 million)
-num_games_to_simulate = 10_000
+num_games_to_simulate = 10_000_000
 
 # Hash to generate from
 game_hash = 'a1f3e2d4c5b6a7f8d9e0a1f2b3c4d5e6f7a8b9c0d1e2f3a3b5c6d7e8f9a0b1c2'

diff --git a/prob_using_coefficients.py b/prob_using_coefficients.py
@@ -0,0 +1,101 @@
+import hmac
+import hashlib
+import binascii
+import math
+from collections import Counter
+from scipy.optimize import curve_fit
+import numpy as np
+
+# Number of games to simulate (10 million)
+num_games_to_simulate = 10_000
+
+# Hash to generate from
+game_hash = 'a1f3e2d4c5b6a7f8d9e0a1f2b3c4d5e6f7a8b9c0d1e2f3a3b5c6d7e8f9a0b1c2'
+
+# Target payouts to analyze
+target_payouts = [1.23, 1.48, 1.75, 2, 2.32, 3.25, 5.24, 7.59, 9.87]
+
+# Generate javascript code, if false will just outpit the coefficients
+generate_javascript_code = False
+
+def generate_multipliers(game_hash, num_games):
+
+    salt = '0000000000000000004d6ec16dafe9d8370958664c1dc422f452892264c59526'.encode()
+    hashobj = hmac.new(salt, binascii.unhexlify(game_hash), hashlib.sha256)
+    results = []
+    for i in range(num_games):
+        intversion = int(hashobj.hexdigest()[0:int(52/4)], 16)
+        X = 100 / (1 - (intversion / (2 ** 52)))  # Math.pow(2,52);
+        number = round(max(1, math.floor(X) / 101), 2) # Round to 2 decimal places
+        results.append(number)
+        game_hash = hashlib.sha256(game_hash.encode()).hexdigest()
+        hashobj = hmac.new(salt, binascii.unhexlify(game_hash), hashlib.sha256)
+    return results
+
+def calculate_probability(multipliers, counts, total_games):
+    """
+    Calculates the probability of a given multiplier occurring in a set of games
+    :param multipliers: A single multiplier or list of multipliers
+    :param counts: A Counter object with counts of each multiplier
+    :param total_games: The total number of games
+    """
+    if isinstance(multipliers, (int, float)):
+        multipliers = [multipliers]
+    probabilities = []
+    for multiplier in multipliers:
+        occurrences = counts.get(multiplier, 0)
+        probability = occurrences / total_games
+        probabilities.append(probability)
+    if len(probabilities) == 1:
+        return probabilities[0]
+    return probabilities
+
+# Generate multipliers for the given number of games
+print(f'Generating {num_games_to_simulate} results...')
+game_results = generate_multipliers(game_hash, num_games_to_simulate)
+result_count = Counter(game_results)
+
+# Calculate probability for exactly 2x multiplier
+print('Calculating probabilities...')
+probabilities = calculate_probability(target_payouts, result_count, num_games_to_simulate)
+
+# Print the probabilities for each target payout
+for target_payout, probability in zip(target_payouts, probabilities):
+    print(f'Probability of {target_payout}x: {probability}')
+
+# Given data points
+np_target_payouts = np.array(target_payouts)
+np_probabilities = np.array(probabilities)
+
+# Power-law function
+def power_law(x, a, b):
+    return a * x ** b
+
+# Fit the power-law function to the given data
+params, _ = curve_fit(power_law, np_target_payouts, np_probabilities)
+
+# Coefficients a and b
+a_coeff, b_coeff = params
+print(f'Power-law coefficients: a={a_coeff}, b={b_coeff}')
+
+# Generate javascript code for the power-law function
+if not generate_javascript_code:
+    print('Generating coefficients...\n')
+    print(f'const a_coeff = {a_coeff};')
+    print(f'const b_coeff = {b_coeff};')
+else:
+    print('Generating javascript code...\n')
+    print('function calculateProbability(multiplier) {')
+    print(f'    return {a_coeff} * Math.pow(multiplier, {b_coeff});')
+    print('}\n')
+    print('function cumulativeProbabilityForExactPayout(targetPayout, numberOfTrials) {')
+    print('    // Probability for the exact target payout in a single trial')
+    print(f'    const singleTrialProbability = {a_coeff} * Math.pow(targetPayout, {b_coeff});')
+    print('    // Cumulative probability after a given number of trials')
+    print('    return Math.pow(1 - singleTrialProbability, numberOfTrials - 1) * singleTrialProbability;')
+    print('}\n')
+    print('// Example usage:')
+    print('const targetPayout = 2.0;')
+    print('const numberOfTrials = 10;')
+    print('console.log(`Probability of exactly ${targetPayout}x occurring is ${calculateProbability(targetPayout)}`);')
+    print('console.log(`Cumulative probability for ${targetPayout}x after ${numberOfTrials} trials: ${cumulativeProbabilityForExactPayout(targetPayout, numberOfTrials)}`);')
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