1597453020

# Cracking Blackjack : Setup + Simple Monte Carlo Simulations

Hi!

I am writing this “Cracking Blackjack” blog series as a way of consolidating the knowledge I have gained in the Reinforcement Learning space. I needed to combine the info of 30+ articles and blog posts when I was creating this Blackjack project, and I want to make it easier for the next person.

I am by no means an expert on this stuff. Please feel free to reach out if you have any questions or concerns about the information I am about to present! My contact info is at the bottom.

### Quick Summary of Blackjack

Blackjack is a card game played against a dealer. At the start of a round, both player and dealer are dealt 2 cards. The player can only see one of the dealer’s cards. The goal of the game is to get the value of our cards as close to 21 as possible, without crossing 21. The value of each card is listed below.

#reinforcement-learning #data-science #monte-carlo-method #cracking-blackjack #artificial-intelligence #deep learning

1597453020

## Cracking Blackjack : Setup + Simple Monte Carlo Simulations

Hi!

I am writing this “Cracking Blackjack” blog series as a way of consolidating the knowledge I have gained in the Reinforcement Learning space. I needed to combine the info of 30+ articles and blog posts when I was creating this Blackjack project, and I want to make it easier for the next person.

I am by no means an expert on this stuff. Please feel free to reach out if you have any questions or concerns about the information I am about to present! My contact info is at the bottom.

### Quick Summary of Blackjack

Blackjack is a card game played against a dealer. At the start of a round, both player and dealer are dealt 2 cards. The player can only see one of the dealer’s cards. The goal of the game is to get the value of our cards as close to 21 as possible, without crossing 21. The value of each card is listed below.

#reinforcement-learning #data-science #monte-carlo-method #cracking-blackjack #artificial-intelligence #deep learning

1625085120

## Monte Carlo Simulation and Variants with Python

### Your Guide to Monte Carlo Simulation and Must Know Statistical Sampling Techniques With Python Implementation

onte Carlo Simulation is based on repeated random sampling. The underlying concept of Monte Carlo is to use **randomness **to solve problems that might be deterministic in principle. Monte Carlo simulation is one of the most popular techniques to draw inferences about a population without knowing the true underlying population distribution. This sampling technique becomes handy especially when one doesn’t have the luxury to repeatedly sample from the original population. Applications of Monte Carlo Simulation range from solving problems in theoretical physics to predicting trends in financial investments.

Monte Carlo has 3 main usages: estimate parameters or statistical measures, examine the properties of the estimates, approximate integrals

This article is about these 3 usages of the Monte Carlo procedures and about 3 Monte Carlo variants, statistical sampling techniques, which can be used to generate independent random samples. The article will cover the following topics:

``````- Introduction to Monte Carlo Simulation
- MC Parameter Estimation
- MC Examining the Estimate Properties
- MC Integrals Approximation
- Importance Sampling
- Rejection Sampling
- Inverse Transform Sampling
``````

_This article is suited for readers who have prior Statistical knowledge since it will cover medium-level statistical concepts and examples. If you want to learn essential statistical concepts from scratch, you can check my previous article about _Fundamentals Of Statistics here.

#machine-learning #programming #monte-carlo #data-science #python #monte carlo simulation and variants with python

1597933800

## What is the Monte Carlo Simulation?

A Monte Carlo method is a technique that uses random numbers and probability to solve complex problems. The Monte Carlo simulation, or probability simulation, is a technique used to understand the impact of risk and uncertainty in financial sectors, project management, costs, and other forecasting machine learning models.

Risk analysis is part of almost every decision we make, as we constantly face uncertainty, ambiguity, and variability in our lives. Moreover, even though we have unprecedented access to information, we cannot accurately predict the future.

The Monte Carlo simulation allows us to see all the possible outcomes of our decisions and assess risk impact, in consequence allowing better decision making under uncertainty.

In this article, we will go through five different examples to understand the Monte Carlo Simulation method.

## a. Coin Flip Example:

The probability of head for a fair coin is 1/2. However, is there any way we can prove it experimentally? In this example, we are going to use the Monte-Carlo method to simulate the coin-flipping iteratively 5000 times to find out why the probability of a head or tail is always 1/2. If we repeat this coin flipping many, many more times, then we can achieve higher accuracy on an exact answer for our probability value.

#programming #monte-carlo-simulation #machine-learning #artificial-intelligence #mathematics

1597402620

## Cracking Blackjack — Finishing the First-Visit Monte Carlo Algorithm

Hi!

Image from Unsplash

• Learn how the `run_mc()` function facilitates the algorithm.
• Dive deep into Step 6 of the First-Visit MC algorithm, which is where the Q-table and Prob-table are updated after each episode.

## 10,000 ft Overview of First-Visit MC from Part 4

1. Initialize the Blackjack environment from Part 2.
2. Define the Q-table, Prob-table, alpha (α), epsilon (ε), ε-decay, ε-min, and gamma (γ) explained in Part 3.
3. Define how many episodes you would like your agent to learn from. More episodes usually yield a more profitable policy.
4. Play an episode. Record all of the (**state → action → reward) **tuples in the episode.
5. After the episode, apply ε-decay/ε-min to ε.
6. Then, update the Q-table and the Prob-table using (**state → action → reward) **tuples from Step 4 and the associated formulas.
7. Repeat Steps 4–6 for the number of episodes defined in Step 3.
8. After all episodes, the resulting Q-table and Prob-table represent the optimized policy for Blackjack that the AI agent just learned.

## How to Facilitate Steps 4–6

In Part 4, we learned how Step 4 is implemented in the `play_game()` function. Before diving into Steps 5 & 6 in the same level of detail, I would like introduce the `run_mc()` function, which allows Steps 4–6 to work together.

Skim the code below. I will be explaining it in detail below. View the code in its entirety here.

#reinforcement-learning #machine-learning #data-science #cracking-blackjack #artificial-intelligence #deep learning

1593362460

## The Joy of Simulation

Using Monte Carlo simulation to set test parameters and select algorithmic approaches

#testing #glengarry-glen-ross #data-science #simulation #monte-carlo