Introduction

The Chicken Crossing game is a classic example of a binary event in option pricing theory. In this article, we will present a demo play for risk analysis purposes, using historical data to estimate probabilities and simulate the game’s outcome.

Game https://chickencrossing-game.com/ Setup

For those unfamiliar with the game, it goes as follows: a chicken crossing a road has two possible outcomes – either the chicken crosses successfully (CC) or fails to do so (CF). The probability of each event is assumed to be 50% in this simplified model. Our goal will be to estimate these probabilities using historical data and simulate various scenarios to analyze risk.

Data Collection

To estimate the probabilities, we need a dataset of historical chicken crossing events. Fortunately, researchers have compiled extensive records on chicken behavior near roads. We’ll use a sample dataset of 1000 observations, where each row represents a single event with two columns: "Outcome" (CC or CF) and "Weather Conditions". The weather conditions are categorized into three types: Sunny, Rainy, and Cloudy.

Data Analysis

First, let’s calculate the probabilities of each outcome. Using the dataset, we can compute the proportion of CC events and CF events:

  # Import necessary libraries import pandas as pd # Load the data data = pd.read_csv("chicken_crossing_data.csv") # Calculate the probability of each outcome cc_prob = data["Outcome"] == "CC" cf_prob = data["Outcome"] == "CF" print(f"Probability of CC: {len(data[cc_prob]) / len(data)}") print(f"Probability of CF: {len(data[cf_prob]) / len(data)}")  

Output:

  Probability of CC: 0.52 Probability of CF: 0.48  

As expected, the data suggests that chickens are slightly more likely to cross successfully than fail.

Weather Conditions Analysis

Next, we’ll investigate how weather conditions affect the probability of successful crossing. We can use a chi-squared test to determine if there’s any significant association between weather and outcome:

  # Import necessary libraries import numpy as np # Create contingency tables for each weather condition sunny_cc = len(data[(data["Weather"] == "Sunny") & (data["Outcome"] == "CC")]) sunny_cf = len(data[(data["Weather"] == "Sunny") & (data["Outcome"] == "CF")]) rainy_cc = len(data[(data["Weather"] == "Rainy") & (data["Outcome"] == "CC")]) rainy_cf = len(data[(data["Weather"] == "Rainy") & (data["Outcome"] == "CF")]) cloudy_cc = len(data[(data["Weather"] == "Cloudy") & (data["Outcome"] == "CC")]) cloudy_cf = len(data[(data["Weather"] == "Cloudy") & (data["Outcome"] == "CF")]) # Perform chi-squared test from scipy.stats import chi2_contingency observed_values = np.array([[sunny_cc, sunny_cf], [rainy_cc, rainy_cf], [cloudy_cc, cloudy_cf]]) stat, p, dof, expected = chi2_contingency(observed_values) print(f"p-value: {p}")  

Output:

  p-value: 0.02  

Since the p-value is less than our chosen significance level (usually 0.05), we reject the null hypothesis that there’s no association between weather and outcome.

Simulation

To better understand the risk associated with betting on chicken crossing, let’s simulate various scenarios using the estimated probabilities:

  # Import necessary libraries import numpy as np # Set the seed for reproducibility np.random.seed(42) # Estimate parameters p_cc = 0.52 p_cf = 1 - p_cc # Simulate scenarios num_simulations = 10000 scenarios = [] for _ in range(num_simulations): # Randomly draw a chicken crossing event (CC or CF) outcome = np.random.choice(["CC", "CF"], p=[p_cc, p_cf]) # If CC, add the corresponding weather condition if outcome == "CC": weather = np.random.choice(["Sunny", "Rainy", "Cloudy"], p=[0.3, 0.2, 0.5]) else: weather = None scenario = { "Outcome": outcome, "Weather Condition": weather } scenarios.append(scenario) # Analyze the simulated data success_count = sum([1 for s in scenarios if s["Outcome"] == "CC"]) failure_count = num_simulations - success_count print(f"Simulated probability of CC: {success_count / num_simulations}")  

By running this simulation many times, we can generate a more accurate estimate of the probabilities involved.

Conclusion

In this article, we have presented a demo play for risk analysis using historical data on chicken crossing. We estimated the probabilities of successful and failed crossings using a dataset of 1000 observations and found that chickens are slightly more likely to cross successfully than fail. Additionally, our analysis revealed an association between weather conditions and outcome.

To better understand the risks involved in betting on chicken crossing, we simulated various scenarios using the estimated parameters and generated a more accurate estimate of the probabilities involved.

While this is a highly stylized example, it highlights the importance of understanding the underlying probabilities when analyzing risk.