When you go into a casino look at what people’re saying about betting on the internet or listen to your friends talking about the way they bet you will always hear them say something like this: I was unlucky. People always say that luck is the reason they lost and they say luck is the reason they won. They think of luck as something that just happens sometimes. On the hand probability is like a math problem that is not fun. People do not like to think about probability because it’s, like a rule that is not exciting. Luck and probability are two things that people talk about when they bet and luck is what people usually talk about when they win or lose.
The idea that things can go our way is nice to think about.. It does not always show us the whole picture. People think that luck is something that happens to them. On the hand probability is just a concept. However when we are talking about money or taking risks or what will happen in the run probability is really what is making things happen. Luck is just what we say to make ourselves feel better after something has happened.
This article gets rid of all the made up stories. It does not want to ruin the fun of luck. It wants to replace guesses with clear facts. When you understand how chance really works luck does not seem special anymore. It starts to seem like something we can figure out in a very specific way. The article shows us how probability actually works and that is what makes luck seem predictable. Luck and chance are not as mysterious as they seem. The article helps us see that luck and chance can be understood.
Defining luck and probability
To really understand these ideas you need to be clear about what you mean. A lot of the time when people argue about luck and probability they are actually disagreeing about what these words mean because they never took the time to define them properly. This is what the arguments about luck versus probability are usually, about.
What is luck, really?
Luck is something that we cannot measure. It does not have any rules or patterns that always work. When we talk about luck in our lives we usually say something was lucky after it has already happened. For example if a coin lands on heads ten times in a row the person who flipped it will say they are lucky.. If someone else flips the same coin and loses some money they will say they are unlucky. The thing is the coin is not doing anything differently in these two situations. Luck is a word we use to describe what happened with the coin. The coin itself is a coin it does not change how it works people are just saying they were lucky or unlucky, with the coin.
People think luck is real because we are made to feel things. When something good happens to us we say it is because of luck. Because we are good at something. When something bad happens we say it is luck or it is not fair. The way we feel about these things is very strong. We only feel this way after it has happened. Luck does not tell us what will happen next. It helps us understand how we feel about what has happened. We use luck to explain our feelings, about things that have already happened to us like luck.
When people gamble this thing gets worse. If they win it makes them feel good because it gives them dopamine. If they lose it makes them feel bad because it gives them stress. The brain tries to make sense of what’s happening with the wins and losses. People say things are because of “luck” when really it is something random that is happening and they do not like it or they cannot explain it. The brain is always looking for a reason and “luck” is a way to explain the things that happen when people gamble, like wins and losses and the “luck” becomes a way to make sense of it all.
Probability 101: the math behind chance
When we think about probability we are looking at what might happen in the future. Probability tells us how likely something is to occur before it actually happens. It does not take into account how we feel about something or the stories we tell ourselves or even what has been happening lately. The thing that probability really cares about is the structure of the situation the probability itself. Probability is about the structure and that is all the probability is interested, in.
So what is probability about? It is about something basic. Probability tells us that when we have possible results how often will one particular result happen over a long period of time. Probability is like a guide that helps us understand how often we can expect something to happen. We use probability to figure out the likelihood of one outcome, like probability happening again and again over time.
When we talk about things being random people usually forget one thing. Random is not the same as being mixed up. Things that are random actually have a pattern. This pattern follows rules, like the Law of Large Numbers. The Law of Large Numbers helps us understand why random things can seem crazy for a short time but when you look at them over a long time they start to make sense and even out. Random things have rules and the Law of Large Numbers is one of them.
If you flip a coin ten times you might get eight heads.. If you flip a coin ten thousand times the number of heads will be very close to fifty percent. The coin does not change what it does to make things even. The coin just does what it always does when you flip it times. The coin will still be fifty percent heads when you flip it a lot of times.
People often think that luck plays a role in their lives than math does. This is really interesting because math is around us and it is very important.
Math is like a set of rules that helps us understand how things work.. People still believe in luck.
For example when you flip a coin it is math that decides whether it lands on heads or tails. However people will still say that they got lucky if they guess correctly.
People believe in luck because it is easy to understand and it is more fun to think that something good can happen to us without any reason.
- Luck is like a power that can make good things happen
- Math is like a science that helps us understand how things work
People like to think that luck is on their side even though math is what really makes things happen.
People believe in luck, over math because it is more exciting to think that anything can happen.
People think probability is really good at figuring things out so why do people still believe in luck? The reason for this is, inside the brain. Probability is something that people can count on. People still trust luck instead of probability.
Cognitive biases fueling superstitions
Our minds are really good at finding patterns. We do this even when there are no patterns to find. This helps us when we are outside in nature and need to stay safe.. It can be bad, for us when things are random and we start to see patterns that are not really there. Our minds do this because it helps us survive in the wild.
One big problem is confirmation bias. When a superstition seems to work we remember that time.. We forget all the times it did not do anything.
Another issue is that we think we have control, over things that we really do not. We believe that what we do can change things that’re actually independent.
For example pressing a slot button hard or picking a lucky number makes us feel like we are doing something that matters even though it does not actually change the result. Confirmation bias and the illusion of control are really important to think about when we look at superstitions.
Daniel Kahneman, a psychologist really got into these tendencies in his book Thinking, Fast and Slow. He found out that the fast part of the brain, which’s intuitive usually makes decisions when we are not sure about something. The slower part of the brain, which’s analytical often does not say anything unless it is forced to. Daniel Kahneman showed that this is how the brain works when it comes to decision-making and uncertainty and that the fast part of the brain the part is usually, in charge.
When we talk about probability it needs us to think slowly and carefully. On the hand luck is something that works well with fast thinking it just seems to fit in. Probability is about thinking things through taking our time to figure out what might happen. But luck is different it is, like something that happens quickly. It goes well with making fast decisions like when we do not have a lot of time to think. Probability and luck are two things that work in ways and they need different types of thinking probability requires slow thinking and luck fits neatly into fast thinking.
People think that sometimes things just go well for them and they are on a lucky streak.. Is that really true? Stories of streaks are not really accurate. They are a myth. The idea of a streak is something that people like to believe in.. If you look at the facts you will see that it is not true. Lucky streaks are a way of explaining things that happen by chance. The truth is that things do not always go well for people who’re, on a lucky streak. Sometimes they get lucky. Sometimes they do not. It is all a matter of chance. Stories of streaks are debunked because they are not based on facts. They are based on what people want to believe.
People really like it when things happen over and again. Like when a roulette wheel lands on five times in a row the room gets really excited. Some people start betting on red because they think it is, on a roll. Others start betting on black because they think red cannot keep winning like that. The roulette wheel and the people betting on it are pretty interesting to watch when this happens with the roulette wheel.
People seem to forget one thing about roulette: each spin is completely separate, from the others. The wheel does not remember what happened before. When you play roulette the chances of winning or losing do not change because of what happened in the last few spins. Roulette spins are independent which means the wheel has no memory of history. The odds of winning at roulette do not shift because of what happened. Roulette spins are independent.
This thing happens all the time in sports betting and in stock markets. A trader does well for a while and thinks it is because they are good at guessing or just got lucky but they do not think about the fact that sometimes things just happen by chance. When the trader starts doing they change what they say. The stock market is not fair, to them. Their luck has run out. The stock market and sports betting are examples of this. The trader and the stock market are connected in this way.
What really happened is actually pretty simple. Things just happened to go a way for a little while and that made it seem like something important was going on. But the thing is, the chances of things happening that way were always the same. The randomness that happened in the term made it seem like there was a pattern but really the probability of things happening never changed. The short-term randomness is what created a run of outcomes that felt meaningful. That is all it was, just short-term randomness.
Luck vs. probability in real scenarios
Math that is really hard to understand becomes easier when we can see how it works in life. Things, like betting and gambling are examples of this. They help make abstract math clearer because we can relate to them. Abstract math is easier to grasp when we look at it in the context of gambling.
Gambling examples: slots, roulette, lottery
Slot machines are basically about chance. That is right in a way. You do not have any control, over what happens when you spin the wheel.. When people say it is all luck that does not tell the whole story. The thing is, slot machines have a set system that determines the odds and people know how it works. Slot machines have a system that is not going to change. That is what really matters when you play slot machines.
Each slot machine has an amount of money that it is supposed to pay back, to people who play it. This is decided when the slot machine is made. If you play a slot machine a million times it will give back an amount of money that people have put into it. Sometimes when you play for a time you might get very lucky or very unlucky.. If you play for a long time the slot machine will always do what it is supposed to do. The slot machine will always pay back the amount of money in the long run.
Roulette is a game that works in a simple way. The European roulette wheel has thirty seven numbers on it. When you bet on the color red you get a payout that’s almost the same as the money you put in but there is a green zero on the wheel that makes sure the house always has an advantage. You can try any betting pattern you want. It does not change the math, behind the game. The odds of winning or losing stay the same for every spin of the roulette wheel. Roulette odds are always stable no matter how times the roulette wheel spins.
Lotteries are an example of this idea. The chance of winning a big prize is very small. So small that buying tickets all the time does not really increase your chance of winning. People still buy tickets because they like to think they might get lucky. The idea of getting lucky is more fun to think about than the fact that it’s very unlikely to happen. Lotteries make people think about the story of luck, not the fact that the oddsre, against them.
Everyday decisions like lotteries or bets
When you are not in a casino you still make choices that involve chance. For example office pools and fantasy leagues are things that people do that are based on probability. When you buy insurance you are making a decision that has to do with probability whether you think about it that way or not. Probability is a part of these choices, like office pools and fantasy leagues and insurance decisions.
The birthday problem is really famous. A lot of people think you need a group of people before two people have the same birthday.. The truth is, when you have just 23 people, the chance that two people share a birthday is more, than fifty percent. This is surprising because when we think about it we do not realize how fast the number of combinations of birthdays grows for the birthday problem. The birthday problem is an example of this.
The Monty Hall problem is a classic. People who are on the show think it does not make a difference if they switch doors.. The Monty Hall problem clearly shows that switching doors is a good idea. The reason people do not want to switch doors is because they think the Monty Hall problem is fair either way. They think the Monty Hall problem is the same no matter what they choose.. That is not true. The Monty Hall problem is actually not the same. Switching doors, in the Monty Hall problem really does make a difference.
When you think about it luck seems like a reason, for what happens in both situations.. Then you start to think about the chances of things happening and that is when you realize luck is not the reason. Probability is what really makes you understand that there is something going on with the situations. Luck is what you think of at first but probability is what makes you change your mind about the situations.
People often have trouble with math concepts. Math concepts are really tough for a lot of people. The math concepts that people struggle with are usually the ones that’re a little more complicated.
Some people have a time understanding the basics of math concepts.
The thing, about math concepts is that they can be very confusing. Math concepts are something that a lot of people find difficult to grasp.
People have a lot of ideas, about luck. This is because they do not understand a few things. When we understand these things luck is not so mysterious. Luck is something that people think about a lot and when we think about luck we can see that it is not that hard to figure out. Understanding these things about luck makes luck easier to understand.
The Law of Large Numbers is what makes casinos so successful. Sometimes a person who plays games at a casino can win a lot of money. When you look at what happens to all the people who play it usually works out to what you would expect. There is no plan to make this happen. The Law of Large Numbers is what makes casinos thrive because Time is what does the work. The Law of Large Numbers is really important here.
The Central Limit Theorem tells us that Central Limit Theorem outcomes tend to cluster into shapes.
Central Limit Theorem is really important because it shows that weird Central Limit Theorem distributions start to look normal when we add them all up.
That is why Central Limit Theorem is so important to risk managers. They need to think about the Central Limit Theorem distribution, not just a few unusual stories.
Regression to the mean is something that happens a lot. When people do something well like a golfer who has the best game of their life they usually do not do as well the next time. The golfer will probably play a game the next day. It seems like they lost their luck or something.. The truth is, regression to the mean is a thing where really good or really bad things do not happen all the time because they are not normal. Regression to the mean is what makes things go back to normal. So when the golfer plays a game after a really good one it is just regression to the mean happening. The golfer is just going back to how they play. Regression to the mean is a thing that happens with regression, to the mean.
The expected value is what ties everything together. This is because it takes the probability and the payoff and turns them into a number. This number tells you what the average outcome will be each time you try something. When you play games that have an expected value you will lose money over time. This is true even if you feel really lucky at the time. The expected value of these games will still drain your money.
The illusion of randomness
People often say they want things to happen by chance. What they really want is for things to be fairly random. Real chance events do not look perfect. They have groups of things happening together spaces where nothing happens and unexpected things happening. People think true randomness should look neat. It does not. It has patterns like streaks and gaps. It is full of surprises. True randomness is, like that. It has lots of surprises. It can look really strange.
People get suspicious when a coin lands on heads five times in a row. It just seems like something is not right. The same thing happens when we listen to music and the same artist comes on over and over again. We think something is wrong, with the playlist. Companies are aware of this problem. They make changes to the way things are chosen so that it feels more random. The thing is, real randomness is not what people expect. People cannot handle the fact that sometimes the same thing can happen times in a row even if it is a truly random coin or a shuffled playlist. Companies want to make things feel more random than they actually are because that is what people want.
People think that luck is real because things do not always happen the way we think they will. When random things happen and they are not what we expected we try to figure out why. The idea of luck helps us make sense of things that seem to happen for no reason. Luck is what we use to explain these things.
Understanding variance is really helpful. It shows us how much the outcomes are spread out from the average. Games with variance are very dramatic. On the hand games with low variance are pretty steady. One is not luckier than the other. Variance just means that the outcomes are given out in ways over time. Games with variance and games with low variance are just different, in how they give out outcomes.
So the question is can probability ever favor the player.
I think about this a lot when I play games of chance.
Probability is like a rule that says what is likely to happen.
The player is the person taking a risk and hoping to win.
In cases probability does not favor the player because the game is set up so that the other person wins more often.
The player can sometimes win because probability is not a sure thing.
It is, like a guide that says what will probably happen.
So yes probability can favor the player sometimes.
The player just has to be lucky and make choices.
Probability favors the player when the player makes smart decisions and things go the way.
The player has to understand probability to make the choices.
Then probability can favor the player and the player can win.
This is the part that’s really interesting. Probability is not something that automatically helps the house or the system. It actually helps the people who take the time to understand probability and also respect it. The people who understand probability and respect it are the ones who will see the benefits of probability.
In games like blackjack players can make the game more fair by making choices. Sometimes like when people count cards right the odds can actually be a little bit in their favor. This is not because they are lucky. It is because they are using the information they have about blackjack to make decisions, about blackjack.
When you invest your money spreading it around is an idea. This helps because it makes the ups and downs smaller. You still get the average result but you do not have as many big surprises. Doing well in the run is not just about picking the right thing by chance. Investing is really, about dealing with all the things that can happen and making smart choices about each one.
Insurance is an example of this idea. People do not know what will happen to them. They might get sick. Have an accident. Insurance companies put all the people together. Use the idea of probability to make things more predictable. Insurance companies, like this because it helps to balance out the risks. Insurance works because of this principle.
Pascal’s wager and the misuse of probability
People often use probability in the way when they are making philosophical arguments. The thing that comes to mind is Pascals Wager, which people say is a bet when it comes to what you believe. But other people do not agree with this they say it makes probability too simple. It does not think about other things that could happen. Probability is something that gets misused in these kinds of arguments like Pascals Wager because it does not consider all the possibilities.
The main thing to remember is not about theology. It is about how easy it’s to twist probability to fit a story. When the numbers are not clear or the assumptions are not shown people start to think that luck is involved, even when it is dressed up with math. The thing, about probability is that it can be bent to support a story. Probability is easy to twist when the numbers are vague or the assumptions are hidden.
When we are talking about probability we need to have an idea of what we are assuming. If we do not have these assumptions then math is not really helping us understand things it is just being used to tell a story. Probability and math are supposed to give us answers but without clear assumptions probability is really not doing its job.
Luck still matters to people on a level. It is because luck has an impact, on our lives. We feel happy when good things happen to us. We think it is because of luck.
Sometimes people believe that luck helps them. They think that luck is the reason they’re successful.
Luck still matters emotionally because it affects how we feel about ourselves. When we have luck we feel sad and unhappy.
We also feel angry when bad things happen to us. We think it is because of bad luck.
- Luck can make people feel happy and sad at the time
- It can also make people feel angry and unhappy
Luck is a part of our emotional lives. We think about luck when good or bad things happen to us.
Luck still matters emotionally to people because it is a part of how we feel.
We care about luck because it affects our state. Luck still matters emotionally.
Stripping luck of its power does not mean that we should act like our emotions are not real. People are not machines that can figure out the chances of something happening. We go through things one by one. We feel the effects of luck one at a time. Luck is still a part of our lives. It can affect how we feel. We are people, not computers that can calculate the odds of everything. We experience luck and its outcomes one at a time. That is what makes life so unpredictable. Luck is a part of our lives and we should not try to ignore it or pretend it does not exist.
Luck matters because it helps people deal with things that’re not certain. When something does not go well saying “I was unlucky” makes the disappointment a little easier to handle. On the hand when something good happens saying “I got lucky” helps people stay humble. These stories about luck do jobs for people socially and psychologically. They are, about luck. How luck affects people. Luck is a part of these stories and luck is what makes them work.
The problem comes up when people start making decisions based on stories instead of using actual decision-making tools. This is what happens when people think luck is a plan, rather than just something that happens sometimes. Mistakes are sure to follow when people rely on luck to make things work because luck is not something you can count on. Emotional stories about luck can be really misleading. That is why mistakes happen when luck becomes a strategy rather, than just a feeling.
Embracing probability without killing the fun
Learning about probability is really not, about becoming a person or acting like a machine. It can actually make the things that happen in our lives more interesting and richer. Probability is something that can make experiences richer.
When you know the odds winning is a surprise. It does not feel like it was meant to be. Losing does not hurt much. The Sports Team makes decisions because they are calm. The Fans have expectations, about the Sports Team and that is what happens with the odds of the Sports Team.
People who gamble and know about probability are usually better at managing their money. Investors who think about what they can expect to get from something can rest easy when things are not going well. Even people who just play games for fun have fun when they stop thinking that random things should be fair to them. Probability is important for gamblers to understand. Investors should think about expected value to make good decisions. When casual players do not expect fairness, from things they enjoy games more because they know what to expect from probability and randomness.
The big change is really small. You do not ask yourself “Am I lucky” anymore. Instead you ask yourself “What are the chances of something happening and do I feel okay with the football odds of the situation what are the odds and am I comfortable, with the odds?”
Final takeaway: embrace the math
Luck is something we talk about after it happens. The real thing that is going on is probability. That is what is really behind the story of luck. Probability is what makes luck happen it is, like the foundation of the story of luck.
When you flip a coin spin the roulette wheel pick lottery numbers or make a choice there are rules that apply. These rules do not care what you believe in or what you hope for. They do not mean you will get the result you want away.. Over time the rules of the coin toss the rules of the roulette spin the rules of the lottery draw and the rules of risky decisions will always be, in charge.
When you finally understand this the world looks different. Winning does not feel magical anymore. Losing does not feel like a curse. The sports team choices become clearer. You stop chasing luck and start managing the risk of the sports team.
And ironically, that mindset often feels luckier than luck ever did.
