# The difference between gambling and investing

Eddie Sammon Investments

Monte Carlo Casino, there’s a reason why citizens of Monaco are banned.

What is the difference between gambling and investing?

When investing your expected return is positive, when gambling it is negative. That’s the simply answer, now for a more in-depth explanation and to show that there is a mathematical difference between gambling and investing.

Why is expected return negative in gambling?

I will explain with two examples, a casino and a sports betting company. In a casino, there is a house advantage built into every game, so if you play them for long enough then the house, the casino, should win. One of the best examples is the roulette table which has a green pocket (or two!), which means if you decide to bet on red or black, your chances of winning are less than 50%.  In poker and other card games, the total payout will be less than the sum of all the contributing players. We can calculate the casino advantage, the house edge, which I will now do for the more complicated example of sports betting.

Some people think they can get around house advantage by betting on sports, but this is not really true because a house margin is also factored into the sports betting odds, known as vigorish. To show you, I’ll take an example from real tennis odds that I found today:

Odds for player 1 to win: 1/2 = 66.67% implied probability. Yes, 1/2 equals 50% but you have to factor in that you will get your original stake back if you win so the probability formula in this case is 2/(1+2) = 66.67%

Profit for the gambler if player 1 wins on a €1oo bet = €50

Odds for player 2 to win: 13/8 = an implied probability of 38.1%.

Profit for the gambler if player 2 wins on a €100 bet = €162.50

However, if the fair odds of player 1 winning are 1/2, then the fair odds for player 2 winning should be 2/1 = 33.33% implied probability. If these were the odds then the profit for the gambler if player 2 wins on a €100 bet would have been €200.

Adding the two original applied probabilities together equals 104.77%, which means they should be offering better odds by 4.77%. The gamblers expected return is negative and the betting company’s expected return is positive.

What is the expected return when investing?

There are many different methods to estimate the expected return of an investment, but the most important concept to think about here is risk premium.

What is risk premium in investing?

To keep it simple, if we assume that a bank account is paying 3% interest, then we can assume that the risk-free rate is 3%. In reality, government bonds are usually used to calculate the risk-free rate, but in this example we will use bank accounts.

In order to invest into risky assets, such as company shares, investors need to expect to gain more than the risk-free rate, otherwise why would they even bother to take a risk and invest into companies? If analysts expect a company share price to grow by 4% plus pay a dividend of 3%, then we can see that the total expected return from the share is 7%, a risk premium of 4% over the risk-free rate. If we invest €100 here, we are expected to make €7 over the course of the year.

How does this relate to your gambling example?

If we go back to my sports betting example, if we gamble then our expected return is negative due to the 4.77% house advantage. However, if we buy shares in the sports betting company then our expected return should be positive (as long as their overheads do not exceed their gross profit margins).

Does this mean that we should invest into betting companies and casinos?

No, every company forecasted to make a profit should have a positive expected return, there is nothing special about gambling companies. However it does mean that you probably shouldn’t gamble.

Does this mean I should open a trading account and start investing into random companies?

No, because the goal of an investor should be to invest into the most suitable portfolio for you, not a random one. Also, share prices can be extremely unpredictable in the short-term, moving in any direction, almost as if they were on a random walk. Finally, some financial products can be extremely risky and you can lose more than your initial investment.

How can Aisa International help me?

By offering regulated investment advice and diversified investment portfolios which aim to maximise your expected return for any given level of risk.