Trader’s Guide 3.3- Probability, Expectancy, and Kelly Criterion
Probability: the magic wand of the gambling and trading world. It's the secret ingredient that separates amateurs from professionals. Whether you're sitting at a poker table, trying to decide if you should hit on 16 or stand, or standing in front of a stock market ticker, trying to decide if you should buy or sell, probability is the key to making informed decisions.
Imagine you're at a poker table, with a hand full of cards that you're convinced will win you the pot. But then, your opponent looks at you with a smirk and says, "I'll see your bet and raise you, because the probability of you winning this hand is only 30%." Ouch. That's a hard pill to swallow, but it's a cold hard reality of the game. Professional poker players use their knowledge of probability to make informed decisions about which cards to play and when to bet. They use their knowledge of the odds to determine the likelihood of winning a hand and make decisions based on that information. In other words, they use math to beat the house.
Now, let's jump to the blackjack table. You're sitting there, trying to decide whether you should hit or stand. You're holding a 12 and the dealer is showing a 4. What do you do? A novice player might just go with their gut feeling, but a professional knows that the probability of busting is much higher if they hit, as opposed to standing. So, they make the decision to stand, increasing their chances of winning.
Probability also plays a huge role in trading financial instruments. Imagine you're a trader, staring at a stock market ticker, trying to decide if you should buy or sell. You could just go with your gut feeling, but that's not a smart move. Instead, a professional trader uses their knowledge of probability to make informed decisions about which trades to make and when to enter and exit the market. They use their knowledge of the odds to determine the likelihood of a stock going up or down and make decisions based on that information.
But it's not just about the probability of winning or losing, it's also about the risk and reward. Imagine you're about to make a trade and you have the choice between two options: Option A has a 50% chance of winning and will earn you a profit of $1000, but if you lose, you'll lose $500. Option B has a 30% chance of winning, but if you win, you'll earn $2000. Which option do you choose? A novice trader might choose option A because it has a higher probability of winning, but a professional trader knows that option B has a higher expectancy, and therefore, a higher potential for profit.
And that brings us to the Kelly criterion, the brainchild of John Kelly, a genius mathematician who came up with a formula to determine the optimal level of investment or leverage in order to maximize returns while minimizing risk. It's like a magic formula for investment success. One of the first to use Kelly criterion in practice was Edward Thorp, a mathematician and hedge fund manager, who applied the formula to the game of blackjack and developed a winning system that allowed him to beat the house consistently. Thorp's success with the Kelly criterion attracted the attention of Wall Street and he went on to become one of the most successful hedge fund managers of all time.
The Kelly criterion is a formula that was developed by John Kelly in the 1950s to determine the optimal level of investment or leverage in order to maximize returns while minimizing risk. The Kelly criterion is based on the idea that investors should invest a percentage of their capital equal to the product of the probability of winning and the return on the investment, minus the product of the probability of losing and the loss on the investment.
Kelly Criterion Calculation
Expectancy is a measure of the potential profitability of a trade, and it is calculated by multiplying the probability of winning by the potential profit, and subtracting the probability of losing by the potential loss. The formula for expectancy is:
Expectancy = (Probability of Winning x Potential Profit) - (Probability of Losing x Potential Loss)
For example, let's say you are considering a trade where there is a 40% chance of winning and a 60% chance of losing. If the potential profit for the trade is $1000, and the potential loss is $500, the expectancy would be calculated as follows:
Expectancy = (40% x $1000) - (60% x $500) = $400 - $300 = $100
This means that, on average, the trade is expected to make $100 in profit.
It's important to note that Expectancy is not a guarantee of profit, but rather an estimation of the average outcome over a large number of trades. A positive expectancy means that the trade is expected to be profitable in the long run, while a negative expectancy means that the trade is expected to be unprofitable.
Probability is like a magic wand that can help us make informed decisions in gambling and trading. Understanding probability, risk, and reward and using tools like expectancy and the Kelly criterion can help you maximize your returns while minimizing your risk. And who knows, maybe one day, you'll be the one sitting at the poker table with a smirk on your face, holding the winning hand, knowing that you made your decision based on the mathematical odds of probability, and not just gut feeling. Or maybe you'll be the trader who consistently beats the market by using the Kelly criterion to determine the optimal level of investment, and expectancy to evaluate the potential profitability of a trade. Whatever the case may be, understanding probability and its related concepts is essential for anyone who wants to make informed decisions in gambling and trading. It's the key to maximizing your returns and minimizing your risk. So, embrace probability as your new best friend, and watch your success soar.
