Identical slot machine games might be programmed with entirely different probabilities. For example, you might play a game where you have a 1 in 2000 probability of winning the top jackpot of 1000 coins, but the identical machine right next to it might only give you a 1 in 2200 probability of winning that same amount. EXAMPLE 3.5.5 At the entrance to a casino, there are two slot machines. Machine A is programmed so that in the long run it will produce a winner in 10% of the plays. Machine B is programmed so that in the long run it will produce a winner in 15% of the plays. If we play each machine once, what is the probability that we will win on both. Slot machine odds used to be easy to calculate. When you’re dealing with three reels, ten symbols on each reel, and a limited pay table, then it’s just a simple math problem. But the rise of electromechanical slot machines and (later) video slots added some complexity to the situation. How Probability Works. Probability has two meanings. The truth is that on some machines, playing more coins could lead to bigger payouts. For example, playing 1 coin could let you win 1,000 coins while playing 3 could let you win as much as 6,000 coins. When you win, the payout on the max-coin bet is usually much better. Check the payout tables for each machine.

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2. Probability Slot Machine Example Problem

This depressing, yet pragmatic lesson explains how life seems to deliver results and how countless people die while chasing a non-existent mirage. How doing everything right, might still not give the results we long.

We grew up in an environment, where when we did something good, mommy would come and reward us. But life is not that way.

Even if we do everything right. When we work hard and put in the hours. Even if we are smart and are reading a lot of books. Even if we are humble and adaptive. Yet, life still doesn't give us the outcome we want. But why?

Because we live in a world of uncertainty.

There is no black or white. Convictions that were believed to be true 100 hundred years ago, are ridiculed today. And in the same way our convictions today might proof wrong in the future. It seems like we will never know for sure, how life truly works. What does it have to do with the reason we don't get the good life?

Having strong convictions about which business partner to choose, which product to launch, which partner to marry, to stay at the job or to built a business is like chasing a mirage.

A mirage is an imaginary place which we will never find. And the desert is full with the bones of people who have chased the mirage.

And in a similar way our convictions of what is right and wrong might lead us to get lost in time, miss the good life and die miserably.

Thus dropping those convictions, we are left with uncertainty and we got to be willing to accept uncertainty, because the only way to know for sure, which choices are the correct ones, is to built an alternate universe and to observe the outcomes of our decisions, which apparently can't be done by you an me.

Is there a certain way to get the good life? Unfortunately not.

But still there is a chance, and we get the best chance through moving towards the slot-machine probability.

Imagine two slot-machines. Machine A gives you a 1/10 chance of winning, while Machine B gives you a 1/20 chance of winning.

Sometimes Machine A is not going to give any results even though the chance is 1/10, and successively players will lose at Machine A. While sometimes when we use Machine B we win, even though the chance is 1/20. And that is how life seems to work.

Sometimes we can do all the right things and it still won't work out. And sometimes we get a little bit lucky, we did the wrong thing and we won. And then we get confused, because people are pointing at Machine B and sooner or later we are sitting at the 1/20 Machine. But this mentality is incorrect, because it is still better, even when we are losing, to sit at the 1/10 strategy.

In life we also got to choose. In health, wealth, love and happiness. We have to choose between business partners, between products to launch, between women. And we feel paralyzed, because we are looking at the needle in the height stack, to understand which is right and which is wrong. And we will never find it, because we live in a world of uncertainty and we can't bring certainty to all the things we wish we could.

But one choice is going to be Probability A and one is going to be Probability B. Therefore we should go down the path that wins 1/10 and not the path that wins 1/20, even though the 1/20 wins some of the time.

With which woman should we continue a relationship? Sometimes we just choose one and wish that things will work out, but we have to go with the numbers, if we don't want to chase a mirage.

Because a mirage is a dangerous game. People are chasing the mirage and think, that maybe there is a sea of water, if I follow what I see. But quite contrary this train of thought has low odds. The better odds are staked to the people who use a plastic stredge to collect the morning dew until they are rescued. The better odds might be not as cool, but it is slow and steady to get enough water to survive.

This way of thinking is harder.

And further accepting uncertainty and probability presupposes a scary conclusion. That we can do the right thing all our life and still not get what we want. And this is hard to cope with, because we are wired to think in anthropomorphic understandings of cause and effect, of black and white. That our mommy will reward us, if we do our best.

But even though we do our best, the world might still not acknowledge our efforts.

The way life seems to work, is that we need to know stuff. Therefore a good strategy to increase our probability of success is increasing our skills.

Increasing skills is a good slot-machine. Doing that long enough and eventually somebody is probably find out what we did. But it won't happen over night and it might not happen ever.

That's why we love get-rich-quick-schemes, because here we have cause and effect. We put a quarter in the slot-machine, we pull it, every time we win. But in reality we won't. We have to give the world time to catch up with our accomplishments.

There is a famous poem by Rudyard Kipling called “If.”

If we can stick with the plan. If we can stay at the table, even though we know we are doing the most likely path, the most probable, even though it is not giving results. If we can stick with it and do that, ours is the earth.

When we reach this plateau, where we don't see results. The steady continuation is what separates the children of the adults.

Failure is logarithmic, success is exponential.

At slot-machines we lose money, that can be regained. But in the slot-machine of life we loose time. Marrying the wrong person, taking the wrong diet, partnering up with the wrong partner. We are going to waste years of our life, and not all the money in the world can bring time back.

Side notes

The reason there are 67 steps, is because it takes precision to go where we want to go. Even a small misstep in direction, one omitted lesson, can make us miss the good life. Comparing it to a space rocket even the most marginal misdirection, will cause the rocket to miss the target by hundreds of miles. Don't miss the good life.

Questions

1. What is your thing that you have been able to stay with past the 18 month plateau?

   Continuing Web Application Development, Growth Hacking and Digital Marketing.

2. What's an example of something you gave up to quickly on?

   Definitely college. I got hot on business and hadn't the patience to stick with the odds of getting my Diploma therefore I dropped out. I am still going to finish it, by enrolling again. I live in Germany, so why not, free education is good.

3. What is the clear path that you know you should take but have not taken and what is your resolution to get there?

Back to college. Stick with it. Do business on the side. Or fifty-fifty. Hopefully business doesn't go to well, because I am going to stick with college.

1. What is an improbable 'horse' that you have been betting on?

Get-rich-quick start up idea. The idea is not bad, not at all. But it is naive to think that I can be a millionaire, when the foundation is unstable. Slow steady foundation and everything else might come.

Casino and gambling can be a lot of fun, especially when players do not understand the mathematics behind it, but being aware of these matters would offer players more fundamental understanding of the way probabilities and odds work.

Odds and probabilities are some of the most important aspects of gambling mathematics. They could be related even to the pay-off of a certain game. For example, there is an even money situation when it is explained that a bet pays off at the same odds as the probability of winning the bet.

Probabilities

Probabilities are often described as the very backbone of gambling mathematics.

Informally, probability is understood as the chance or the likelihood that a certain event will happen. It is also considered to be an estimate of the corresponding average frequency that is applied for a certain event to occur in a series of independent trials that have been repeated.

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The relative frequency of an event is somewhere between the probability of the event never to occur or always to occur, which basically means that it is always between 0% and 100%. Knowing how to use the probability would provide casino players with the opportunity to predict the eventual occurrence of an event. Unfortunately, it would not give them the chance to predict the exact moment when the event is to occur.

In addition, probability in gambling mathematics can be used when determining the conditions for acquiring certain results or even some financial expectations of a game in particular in the long term. Probabilities could also be helpful when determining how favourable a certain game would be and is it worth playing. This aspect of the matter is usually expressed as odds, as well as a fraction or a decimal fraction. Still, casino players should be aware of the fact that odds and probabilities are different things.

The estimate of the likelihood of a player winning divided by the total amount of available chances is called probability. The latter is also an ordinary fraction that can be expressed as a proportion between 0 and 1, or as a percentage.

What casino players should understand first is the formal theory of probability and are recommended to start with the term that is known as the “sample space”. It may sound somehow strange, but as a matter of fact, this is purely a description of all outcomes possible, or other words – of everything that can possibly happen. It is quite normal for sample spaces to be very large when it comes to casino games. As a matter of fact, they simply reflect the idea that too many things could actually happen to count them all.

The sample space is something that may occur in a large number of experiments and can normally be understood easily when considering the nature of the experiment. Still, the sample space does not have to be described in a explicit way.

Players will need be aware of some details in order to calculate the probability of a certain event. First, they will need a full count of the number of individual elements in the sample space. In addition, they will need to know the number of the individual elements related to the event. Once a player knows these values, they will be able to define the probability of the event by using the equation:

P(event) = Size of event / Size of the sample space

As shown in the equation, the letter P is used as a substitute of the word “probability”. What is not so evident by the above-mentioned equation is how the player should count the size of a variety of collections. Unfortunately, the counting problems in the gambling industry can be too complex. Of course, probabilities can be quickly calculated when counting is easy.

Odds

The most general definition of odds is the probability of a certain event happening in comparison to the probability of the same event not happening.

Odds are considered as ratios of the player's chances of losing to the likelihood of winning. In other words, they are the average frequency of a player's eventual loss to the average frequency of a win. As already mentioned above, odds are often mistaken with probabilities, but they are not the same thing.

As a matter of fact, odds almost never mean the actual likelihood of generating a win when it comes to gambling. In most cases, the term is used as a reference to a subjective estimate of the odds, and not as an exact mathematical calculation.

For example, if a player owns 1 of a total of 4 tickets, their probability to win is 1 in 4. Their odds, on the other hand, are 3 to 1. In order for a player to convert odds to probability, they need to take the likelihood for them to win, then use it as the numerator and divide by the total number of chances, including the ones for both winning and losing.

For example, let us take that the odds are 4 to 1. Then, the probability would be found by using the following equation:

1 / (1+4) = 1/5

In other words, the probability in this case would equal to 1/5, or 20%. What players need to know is the fact that the so-called “evens” are odds of 1 to 1. They are always paid even money.

The term “odds” could also be used as a substitute of the true odds that are the actual chances of winning. There are also payout odds, which represent the ratio of payout for each unit bet.

Just like probabilities, odds can also be expressed as a ratio of two numbers. The first number comes to represent the expected frequency of the occurrence of a specific outcome, and this is actually exactly what probabilities are. The second number, however, represents only the number of the rest of the possible outcomes. In comparison to probabilities, which could be expressed as percentages, odds are always displayed as ratios.