Hi everyone!
And again, this is Kate.

At the end of the previous article, I intrigued you with an interesting video that illustrated the fascinating problem of the probability theory. And today I would like to tell you about this phenomenon in details and also show you how to apply this theory in life and even win a little money on the roulette wheel!

Monty Hall Problem

The problem is formulated as a description of the game, based on the American TV show «Let's Make a Deal» and is named in honor of the host of this show.

I will repeat a description of this problem from my previous article where you can also observe fascinating video from "21" movie.

Imagine that you participate in a TV show and you have to choose one door out of three – there is a car behind one door and goats behind two others. You pick the 1st(where you think the car is standing) door but the host, who knows what's behind each door, opens another door, let it be the 3rd, and there is a goat. Then he offers you to change your initial choose saying that probably car is behind another door. Would you change your choice? (write answer in comments).

You wouldn't change your choice due to emotions or just a paranoia, am I right?

And now I’ll tell you why you should change you choice!
Almost every player think that after the moment when there only two closed-doors left and behind one of them there is your car, the chances to get it are 50-50. It is simple that when the host opens one door and offers to change your choice, he starts a new game. Whether you change your solution or not, your chances will still be equal to 50%, right?

NO! Certainly no. It turns out that in fact, changing your decision, you double the chances to win. Why?

The exact answer is based on conditional probability, that I'll not detail describe here. The simplest explanation for this answer is the following.

In order to win the car without changing your choice, the player must guess the right door, behind which there is a car, from the first time. The probability of this is equal to 1/3. If the player initially chooses the door, behind which there is a goat (a probability of this event is 2/3, as there are two goats and only one car), then he can definitely win a car, after changing his choice, as there is one car and one goat, and a door with a goat has already been opened by the host.

Thus, without changing the choice you still have got your original 1/3 probability of winning, but when you change your choice, you twice increase your chance to win the car.

Can you win the lottery or roulette with the help of probability theory?

Each of us at least once in his life has bought a lottery or played gambling games, but not all of us used a pre-planned strategy. The fact is that every event has a certain mathematical expectation, according to the probability theory, and, if you evaluate the situation correctly, it is possible to have a positive outcome and win some money. For example, when you play any roulette game, you have an opportunity to play with the 50% chance of winning, betting on an even number or on red.

In order to get profit, make a simple plan of the game. For example, we are able to calculate the probability of having even number 10 times in a row is 0.5 multiplied by itself 10 times

P = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.0009765625

Multiply by 100% and we get ~ 0.097%, or about 1 chance in 1000. You won’t be able to play all these games even during all your life, so the probability of getting 10 even numbers in a row is almost equal to "0". Let’s use this tactic in a game.

But that's not all, even just 1 of 1000 - that's a lot of us, so we will reduce this number to 1 of 10 000. You may ask how this can be done?

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The answer is simple - time. We wait until there are 2 even numbers in a row. This will be one of four times. Now set the minimum bid on an even number, for example, 5$, and win 5 $ for every loss of an even number, when the probability of this is 50%.

If it is odd, 2 times increase your next bid, setting up 10$. In this case, the probability of losing is equal 6%. But do not panic, if you lose even this time! Make your bid two times higher. Each time, the mathematical expectation of winning increases and you will remain in profit. It is important to know that this strategy is only suitable for small amounts of money.

Over time you will see that this method is simple in practice and very effective! This approach won’t gain you millions, but you’ll have enough money to live.

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The probability of life according to fire statistics

	Number of Fires	Deaths in Fires
2009	1.348.000	3010
2010	1.331.000	3120
2011	1.389.000	3005
2012	1.375.000	2885

You can find the official US fire statistics here

In a stable system, the probability of occurrence of the event is saved from year to year (you can see it above, as numbers do not vary a lot). From the point of view of a man, this was a random event. And in terms of the system, it was predictable.

An intelligent person must try to think based on the laws of probability. But often people make decisions emotionally.

For example, people are afraid to fly by planes. Meanwhile, the most dangerous thing in flying by plane - is the road to the airport by car (statistics shows that cars are much more dangerous than planes).

According to research: in the United States in the first 3 months after the attacks of 11 September 2001 one thousand people died ... indirectly. They were frightened to fly by planes and began to move around the country by car. And since it is more dangerous, the number of deaths has increased.

I hope that now you understand how important it is to know the basics of probability theory as you can use it everywhere even playing a roulette wheel what can even bring you some money!

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With Love,
Kate