In this case we are considering the words “Win and Lose” not in the standard sense, but from the point of view of Mathematics. From the point of view of Mathematics, the end result is unimportant-the rightness or wrongness of the decision is evaluated at the moment of making the decision.
A key concept in understanding why you can’t win the lottery is such a concept as Mathematical Expectation.
The mathematical expectation is the average of the results in a series of experiments. In the case of the Lottery, the Mathematical Expectation means that if you repeatedly buy Lottery tickets, on average you will lose more money than you win.
In terms of Mathematics, there is almost no difference between the cases:
- when they give you $1 with 100% 1000 times
- when you are given $100 with a 1% probability of 1,000 times
In the first case, you are guaranteed to get $1,000. In the second case, you get about $1,000. There’s a 96% chance you’ll get exactly $1,000. There can be a slight variation – it could be $900, it could be $800, it could be $1,100, it could be $1,200. But the further away from $1,000, the less likely that number is, either up or down. The most likely scenario is that you will get exactly $1,000. And the more attempts you make – not 1000, but 2000, or 10,000, or 1 million (with a corresponding change in the probability of winning $100 by 0.5%, 0.01%, and 0.0001%) – the more likely you are to get $1000, and the more likely all around $1,100, $1,200, 900, 800 – decreases.
In both cases the mathematical expectation of each move is +1$.
We looked at the case where you are only given money. What happens when not only you are given money, but you also give money? For example, what if you give with 100% probability $2 every time you are given $100 with 1% probability? That is, you essentially buy a lottery ticket for $2 to have a 1% chance of winning $100.
It is exactly the same. In this case, the mathematical expectation of each attempt is -1 $. That is, on average, for 100 moves, we will win $100 once, but we will spend $200. And the total “profit” for 100 moves will be -$100.
From the point of view of Mathematics, any move with a negative Mathematical expectation is bad, and any move with a positive expectation is good.
The Mathematical Expectation of the Lottery is always negative – if it were otherwise, the Lottery organizers would suffer a loss. Every time you buy a lottery ticket, you are very likely to make your life a little worse.
Mathematical expectation can be applied not only to the Lottery, but to the whole of life. Whenever you can calculate the probability and possible damage and acquisition, at least approximately, you can present it not as a probability, but as what will definitely happen – at a distance both options are ravochenny.
For example, you know that if you don’t get enough sleep for 1 day, your reaction time is reduced to the level of a person with 0.5 ppm in his blood. This increases the probability of an accident by a factor of 8. Of course, it is difficult to calculate the exact percentage of getting into an accident for a particular person – many factors influence it. But it is important to change your approach – instead of “Yes, the risk is not so high, so we can ignore it, we will somehow get by”, start thinking “You need to multiply the probability that I will get in an accident by the damage from the accident. And take the resulting number as what you’re guaranteed to get.
And if the resulting number is greater than the benefit of this trip – for example, you need to go to the hypermarket at the exit of the city, where everything is cheaper by 5%, and you will save $ 10, but the average cost of travel, taking into account the possibility of getting into an accident $ 50, then it would be much more reasonable to walk to the nearest supermarket, pay more for food, but in the end pay less. Or consider any other options – take public transportation, ask a friend for a ride, order delivery, go on a different day.
Of course, it is not always possible to accurately calculate the mathematical expectation. But you don’t have to – the mathematical expectation is always a range. For example, from 0 to 65% is positive, from 65% to 100% is negative. If you have about 30-50%, you don’t have to know exactly how much, you’re within the right range of what you need to do to be in the range to win.
Apply this method and over time you will learn to consider more factors, which will make your steps more and more correct.
Learn to look at life as a continuous number of attempts, each with its own probability, its own gain and its own loss. And the distance is your whole life. And if you do the right thing as often as you can, you are more and more likely to do as well as possible over that distance.
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