They appeared in 18th century's Roulette. Let's ignore the bank for a second. You can bet on red or black numbers and the chance to be right is 50% for both. If you are right you gain 1€ for every 1€ you invested. If you lose, you lose everything.
Now, if you play once this is a pretty dangerous game, especially if you invest a lot of money. But you don't have to. In fact, you can use a betting strategy that will make it extremely likely that you will win money in the end. It is called Martingales.
It's not even hard:
1) Bet 1€ on any color. If you lose you ..
2) .. bet 2€ on any color. If you lose you ..
3) .. bet 4€ on any color. If you lose you ..
4) .. bet 8€ on any color. If you lose you ..
5) .. bet 16€ on any color ...
As long as you go on with this system you will always gain 1€ eventually.
For example, let's assume you lose four times in a row, but win the fifth game. You lose 1€+2€+4€+8€=15€. And you win 16€ in the fifth game; 1€ profit. More mathematically, 1+2+4+8...+N^2=(N+1)^2-1
Now, there's nothing that keeps you from starting the same with 1000€ instead of 1€. In that case you always win 1000€ eventually. Of course, casino owners know this. That's why they have a limit.
Let's assume you play with a limit of 100€. To reach the limit you need to lose seven times in a row: The probability of losing seven times in a row is 1/128. That means that on average your strategy is successful 127 times out of 128. And each of these 127 times you win exactly 1€ for a total profit of 127€. But once in 128 games you lose seven times in a row and can't continue, due to the limit. You lose 1+2+4+8+16+32+64=127€. So, on average you make 0€. In fact, it is mathematically proven that there is no strategy that changes the expected value. All you can do is change the structure of the risk; repackage the risk.
Now let's move to financial markets. Let's assume that you have no idea where the stock prices are going to go. So you start playing Martingale. You invest 10,000 €. If you lose, you double, if you win, you start again. Other people in the industry see that although the market is extremely volatile (they win/lose 50% of the time), you win all the time. Consequently they give you their money. This raises your limit. You make more money. A lot of money. Your peers recommend you, because you can turn a risky market into a safe market, it seems. The volatility of your hedge fond (or whatever legal construct you use to pay yourself a very high risk-free salary) is almost non-existent.
Unfortunately, some day, you lose some 20 times in a row. Now that was unlikely .. unfortunately you don't have enough money to double again, and thus, you lose it all. Every single cent.
Next time someone argues that an investment is safe because volatility is low, you hopefully know better.