Probability Monte Carlo Simulation
This article provides an overview of Monte Carlo simulation. As an application example, it considers how to estimate the probability of winning in Texas Hold'em using Monte Carlo simulation.
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Probability Texas Hold’em
This article is a simple explanation of the rules of the game Texas Hold'em. It may be used as a subject for explaining probability calculations and Monte Carlo simulations in the future.
Probability Regression Analysis Like Machine Learning
This article shows what happens when stochastic gradient descent, a method often used in machine learning, is applied to parameter estimation in regression analysis.
Probability Normal Distribution of Complex Numbers
We consider the probability density function of the normal distribution when the random variable is a complex number. We also briefly touch upon Brownian motion of complex numbers.
Probability Probability Distribution on the Sphere
This article consider a probability distribution that is uniformly distributed on a sphere. In the case of a two-dimensional sphere, the probability distribution of each coordinate has a uniform distribution, and has some interesting properties.
Probability How Machine Learning Works
Although it may seem a little late to be saying this, I feel like I've finally come to understand what makes machine learning different from other data analysis methods such as regression analysis and how it works, so I'll give a brief explanation here.
Probability The Kelly Criterion in Gambling: Implementation
Some readers may want to try using the Kelly Criterion, so I have included the source code in VBA and python. This will probably be the last in "The Kelly Criterion in Gambling" series.
Probability The Probability Distribution of Composites of Normal Random Numbers
For two random numbers that follow a normal distribution, the probability distribution that their sum, product, ratio, etc. follow is shown.
Probability Extension of the Kelly Criterion in Gambling: Mean-Variance Utility Function
As another variant of the Kelly criterion, we define the utility function in terms of the mean and variance of the assets and consider the problem of maximizing it.
Economics Extension of the Kelly Criterion in Gambling: CRRA-type Utility Function
In this article, we extend the Kelly criterion to a more general utility function (CRRA-type utility function) and explain how to determine a betting portfolio based on a gambler's risk aversion.