Let's imagine two people are playing a gambling game with six dice. They both throw the dice. Mr. British gets 3,2,4,6,1,2. Mr. Fendi gets... 6,6,6,6,6,6! Does that make Mr. Fendi luckier!? Well, that depends...
The word "luck" is usually used to describe a favorable outcome. Chance, on the other hand, is simply how likely the outcome is.
Often something with a low chance is often considered lucky / unlucky when it happens, but many things with a very low chance of happening are not considered lucky or unlucky because the outcome has little or no effect on us.
Luck is really just our reaction to an outcome and has little to do with chance. Winning a coin toss for 1,000,000 dollars would be considered by most to be very lucky, whereas winning the coin toss to start a game of ping pong probably wouldn't. However, both outcomes are equally likely.
So let's look at the dice. What is the chance of getting six 6s? It's 1/(6^6), or roughly 1 in 50,000. That seems very low! How about getting 3,2,4,6,1,2? The chance is exactly the same. In fact, throwing six dice gives a potential of about 50,000 outcomes, with each outcome having the same chance of happening.
In other words, luck is subjective, and chance is objective.
So are Mr. British and Mr. Fendi equally lucky in the above case? The chance of both results is equal, but the result might not be. Perhaps six 6s wins you a huge cash prize, in which case Mr. Fendi is indeed luckier. But if the game penalizes the result of six 6s with a huge fine, Mr. British is the lucky one.
This might all seem very obvious, but the human mind has a huge propensity to notice patterns, and assume that chance is affected by those patterns. When people play roulette, they are often very surprised if the same color comes up many times in succession. Many casinos display previous results in order to give the impression of patterns.
The idea that the ball remembers where it landed last time and is somehow using that information to influence where it lands next is ludicrous. At the same time, it seems that getting the same number twice in a row is unlikely. Casinos are clever at exploiting this idea to entice their customers to lose more money!
Luckily, I've never fallen for such tricks. Or is that just chance?