The Optimal Betting Method for Responsible Risk Management- Research Article #52
Balancing Probability and Profit in Games of Chance
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What if I offered you the chance of playing a coin flip game, with a coin that lands 60% of the time on heads?
Also, if it lands on heads, I’ll double your money.
How much would you bet?
A naive answer might be:
“Great, I’ll bet everything on heads.”
But are you sure that this is an optimal approach?
The concept we will talk about today applies not only to games of chance but also to our trading practices, which can also be a game of chance in many ways.
As traders we face the decision of how much to allocate to each trade, as it can be too much or too little.
If you bet too much, you can’t play anymore.
If you bet too little, you waste profit opportunity.
So how much do you bet?
That’s what we will find out today.
Let’s get into it!
Index
Introduction
Index
John Kelly’s Story
Understanding the Mathematics
Coin Flip Example
The Issue with Parameter Uncertainty
Trading Example
Implementation
Python Code Section
John Kelly’s Story
Imagine it's the 1950s.
The world is full of discoveries—everything from space exploration to stock market theories is booming.
Amid all this excitement is a young American mathematician named John Kelly Jr.
He sits quietly in his lab, working as a communications engineer at AT&T’s Bell Labs.
His research focuses on finding the most efficient ways to transmit data across telephone lines.
However, as he looked for solutions to this problem, he realized that the mathematics involved applied not only to telephone signals, but also to a much broader concept:
… the odds of winning in games of chance.
Imagine the earlier scenario where I give you an option to play a coin flip game against me, with a 60% chance of winning on heads.
Each time it lands on heads, I double your money.
Kelly recognized the risks involved.
If you lose even once, you could be completely out of the game.
If you bet too little, you miss out on maximizing your advantage from the positive expectation.
So, what should you do?