Players are no doubt aware of false conclusion Monte Carlo. Some, however, will be surprised to learn that this is a false conclusion - they then consider it a "Monte Carlo strategy." Well, that's exactly what the croupiers are counting on.
We all know that a roulette wheel has half black and half red sections, which means we have a 50% chance that red will come up when the wheel is turned. If we spin the wheel many times in a row - say a thousand - and at the same time it will be in good order and there will be no tricky devices on it, then red will fall out about 500 times. Accordingly, if we spin the wheel six times and all six times black comes up, we will have reason to think that by betting on red, we will increase our chances of winning. After all, red should fall out, right? No it is not true. On the seventh time, the probability that red will fall out will still be the same 50%, as well as every next time. This is true no matter how many times black is rolled in a row. So here's a very sensible piece of advice based on Monte Carlo's fallacy.
If you're going to be on a plane, for your own safety, take a bomb with you, because the chances of two guys with bombs meeting on the same flight at the same time are extremely small.
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gambler "s fallacy) O. and., or the false conclusion of Monte Carlo, reflects a common misunderstanding of the randomness of events. Suppose a coin is tossed many times in a row. If 10 "eagles" fall in a row and if this coin is "correct" , for most people it would seem intuitively obvious that the loss of "tails" is late. However, this conclusion is false. This error has been called the "negative recency effect" in the specialized literature and consists in the tendency to predict the imminent cessation of a frequently occurring Lately events. It is based on the belief in local representativeness (i.e., on the belief that a sequence of randomly occurring events will have the characteristics of a random process even when it is short). Thus, in accordance with this erroneous notion, the generator random events, for example, tossing a coin, should lead to outcomes in which - even after a short time - there will not be a significant predominance of one or another of the possible outcomes. If a series of identical outcomes falls out, there is an expectation that the random sequence will correct itself in the near future, and the deviation in one direction will thereby be subject to mandatory balancing by a deviation in the other. However, randomly generated sequences, especially if they turn out to be relatively short, turn out to be completely unrepresentative of the random process that produces them. Player error is more than just a reflection of ordinary statistical ignorance, as it can be observed in privacy even experienced people in statistics. It reflects two aspects of people. cognitive function: a) a strong and unconscious motivation of people to find order in everything that they observe around them, even if the sequence of outcomes they observe arises as a result of a random process, b) universal human. the tendency to ignore calculated estimates of probabilities in favor of intuition. Although logic may convince us that random process does not control its outcomes, our intuitive reaction can be very strong and at times overwhelm logic. Reid, who has studied the comparative power of logical and intuitive thinking, argues that the latter often turns out to be more coercive than the former, probably because such conclusions come to mind suddenly, therefore, do not lend themselves to logical analysis and are often accompanied by strong feeling his rightness. In contrast to the fundamental impossibility of tracking the process, through which such intuitive "solutions" are found, the process logical reasoning open to analysis and criticism. That's why people rule logical thinking, and from intuitive thinking they simply get results that fill the latter with a strong sense of a sense of rightness. O. i. most common in a situation where outcomes are generated purely by chance. If some factor of mastery is involved in the development of events, a positive effect of novelty (positive recognition effect) is more often observed. An observer is more likely to view a series of successes (eg, a billiards player) as evidence of his skill, and will build his predictions of subsequent outcomes in a positive rather than a negative direction. Even throwing the dice can produce a positive novelty effect to the extent that the individual believes that the "art" of the thrower is somehow influencing the outcome of the event. See also Barnum effect, Behavior of players, Statistical inference J. Elcock
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Gambler's fallacy, also known as the Monte Carlo fallacy or mature odds fallacy, is the mistaken belief that if something happens more than usual over a period of time, it will happen less often in the future, or if something If something happens less frequently than it usually does for some period of time, it will happen more often in the future. As proof of this conclusion, people, and especially gamblers, often cite the so-called "balance of nature" or the "rule of justice." In situations where confirmation of this false conclusion is observed (i.e., a random result is accepted as a consequence of the correctness of judgment), the belief of a person is already appealing to the human mind, as a result of which false concepts turn into a proven theory. This error can occur in many life situations, although it is directly associated with gambling where such errors are very common among players.
The use of the term "Monte Carlo False Conclusion" originates from the most famous example of this phenomenon, which occurred in the Monte Carlo casino in 1913. Most famous example A gambler's error occurred in a game of roulette at the Monte Carlo casino on August 18, 1913, when the ball landed on "black" 26 times in a row. This is, in fact, an extremely rare occurrence, though not more or less common than any other of the other 67,108,863 possible sequences of 26 red or black. Players have lost millions of francs betting against black, wrongly reasoning that the band was caused by an "imbalance" in the wheel's chaotic behavior, and that it should have been accompanied by a long red band.
The reverse fallacy also exists. According to Monte Carlo's reverse false conclusion, players can assume that "fate" is on their side and will continue to give out black, as in the case of August 18, 1913 for the 27th and even 101st time. Again, the delusion is the belief that the "universe" somehow carries a memory of past outcomes that tend to favor or unfavorably yield subsequent outcomes. However, this is not necessarily a delusion, sometimes this delusion is true, since for example, no matter how stupid it may sound, 2 + 2 will always equal four. Gambler's error also works in the theory of predicting the sex of a child. Many believe that the chance of giving birth to a boy in this particular girl, in the presence of one healthy fetus, is always lower, because "according to statistics, ten girls have nine guys," although this chance is 50 percent.
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Good day to all poker lovers! Today we will talk with you about such a thing as "false Monte Carlo conclusion". This is also called "player error". So, let's get started!
How well do you understand the essence of randomness? Are all the events that happen to us in our Everyday life? Each one will answer for himself. this question. And, I am sure that each of the answers will be correct. For in this situation, to be categorical... Such a turn, so to speak, looks incorrect to me.
But, nevertheless, I would like to go a little deeper into this topic, and ask you a few questions. Let's take a very simple, so to speak, situation as an example. Moreover, it will be close to us on the topic. So. Casino. Roulette. You stand aside and watch what color "falls out" on it. Black. Black. Black again. And black again! And... You know what? Black came up nine times in a row. And here you enter psychological game, Yes? Nine times in a row, the roulette gave players black, and now for the tenth time, red will surely come out! Or not? What do you think about it?
So. How would you act in such a situation. Obviously, there can be three main scenarios for the development of events. choose). You bet on red because black has come up nine times before. Can't black come up ten times in a row!? Or you bet on black, because now, apparently, a series of black falling out ... No, well, black cannot fall just like that. A series is a series. Or do you prefer the third option? The essence of which is to get past the roulette wheel.
What would you do? In my understanding, if you are a poker player to the core, as they say, then you will prefer option number three to all the others. Why? Yes, because during the tenth "draw" on the roulette wheel, the chance of black and red falling out is still fifty-fifty. And it does not matter at all what color fell out before that. And how many times in a row this color fell out. It doesn't matter. Every new draw is a game with clean slate. Either yes or no. Either black or red. Fifty fifty. And poker players who are accustomed to the fact that in "their" game, so to speak, success depends more on skill than luck, will consider odds 1 to 2 not the best financial investment. I repeat the question: "What would you do in this situation?".
So, now we can talk about the so-called false Monte Carlo inference or "player's error". These concepts imply an incorrect understanding by the poker player of the essence of the randomness of the events that take place.
We just talked to you about roulette, and about the colors on which the ball stops. We can say the same about a coin being tossed. The essence is the same. When tossing a coin, it can happen that heads come up nine times in a row. And before the tenth roll, you can ask people for their opinion on the results of roll number ten.
It may well be that many people, having learned that heads have fallen nine times in a row, will bet on the loss of tails after the tenth toss. After all, it is already a miracle that the eagle fell nine times! The tenth will definitely be tails! No matter how it is ... The bottom line is that the chances of falling out as an eagle and tails remain equal - fifty-fifty.
True, and here there is one nuance to which it makes sense to pay attention. And most people, by the way, see it without even thinking. We must distinguish between some concepts. Loss of an eagle or tails in a single case. And the falling out of the same side of the coin, say, ten times in a row. Do you feel what it's about?
By the way, what about the situation when one of the players hits a steep Spin-and-Go multiplier? What do other players think about after that? That's right, they get upset, starting to inspire themselves that after this event, the likelihood that they will fall into the same big prize decreased significantly. However, the bottom line is that the chances of landing the same big prize remain the same as they were before. big win. This is one example of the wrong mindset of a poker player. And this example is not the only one.
And now I invite you to dig a little in your memory. I will ask you questions, and you will try to answer them honestly. So let's get started. Situation one. Your opponent showed pocket aces in the previous hand, let's say. Probably, in the next hand, you thought that since in the previous hand he had a pair of pocket aces, this will definitely not happen in this hand... The example is very conditional, but the essence, I think, is more than clear to you . Have you caught yourself in this kind of reasoning?
Situation two. Should you call your pocket pair for set value if you've already hit a set twice before? Surely after all, the third time in the same river is no longer possible to enter? Or is it all wrong? Now, do you understand what we are talking about?
Listen, let's remember the case that took place at the WSOP 2007. This is me to the fact that even experienced players can fall into this trap... So, let's move on to that case. There was a hand when an experienced and quite experienced poker player Hevad Khan decided to go all-in with a pocket pair of queens. In response, having received a call from Remy Boukaya. Who, as it turned out, had pocket aces. But the whole point here is that in the previous hand, Remy had a pair of pocket kings.
Surprisingly, Khan managed to catch two of his outs and ended up running over his opponent's aces. And then Hewad said something like this to his losing opponent: “When I pushed preflop, I couldn’t believe that you had a pair of pocket aces, because in the previous draw you had pocket kings. And such hands do not come so often ... ".
So, I have already started talking about the fact that even the most experienced players, at times, give in to this nuance, and follow the lead of erroneous thinking. And what can we say about players who do not have a decent gaming experience? The moral of the story is... Each new distribution is new life! Each new distribution has nothing to do with the previous one. And it does not depend on the distribution that was before it. Therefore, you have no way of predicting your opponents' cards at the poker table based solely on information about the cards your opponent had in the previous hand. Dot.
By the way, have you ever thought about using this whole thing against your rivals? If so many poker players are prone to wrong thinking. I'm sorry, wrong thinking. So it will be more correct. How to do it? I think that you yourself already understand what is required of you. But for the sake of clarity, let's take the simplest example. Let's say you get a premium hand several times in a row. And, you know, your opponent might not believe you. After all, in his opinion powerful hands can't come in that often. Your task is to play your hand without any slowplay. Play it confidently and aggressively. It is likely that your opponent will take the bait and fall on the hook that you kindly provided him.
Or, for example, let's say a few words about some offline players. You know, there are guys who talk about how often this or that card comes to the board. Know that these are your potential victims that you can "punish" with a bluff. True, there are also many nuances. I think you yourself understand this as well as I do.
Therefore, summing up, I once again want to draw your attention to the fundamental provisions regarding randomness. Try not to give in to temptation, and don't make a "player's mistake". You should always remember that each new hand is in no way connected with the previous hand. And if your opponent had a pair of pocket aces before, this does not mean at all that he definitely does not have them now, in the new hand. I know perfectly well that you cannot enter the same river twice. But, you know, in the context of poker, I would argue with this statement.
Try not to succumb to this euphoria and notions of impossibility, so to speak. Everything is possible! Everything is possible in poker! Therefore, try to correctly identify your opponents, recognizing in them those who will make a player's mistake. And use it to your advantage!
We'll be talking to you shortly about changing your lifestyle and improving your poker results. This will be the final part of our conversation. Therefore, now I would like to make a small introduction and say a few words about rest and the so-called workaholism.
Each of us understands that it is possible to achieve something significant in life only when you really want it. However, it is clear that desire alone will not be enough here. In any case, for most situations this will be a fair statement. We have to make every effort to achieve this. Sometimes you have to work tirelessly. Sometimes, it happens for sixteen hours a day (or even more), tirelessly. You set certain goals for yourself, you know what you want and move forward towards your dream. Diligence, of course, is a very commendable quality. It's the opposite of laziness.
As for such a thing as workaholism ... I will say this ... Often, it harms the person himself in the context of moving towards the intended goals. I am not kidding. Sometimes this really happens. And how are you doing with the topic of rest? If so, of course, it can be expressed. Do you know how to relax, have fun and at the same time restore the forces necessary for further productive work? Do you have favorite activities, hobbies that can “distract” you from work for a while, “settled with a nail” in the brain? After all, a lot can depend on the quality of your vacation. Having no idea that rest is still necessary, you run the risk of accumulating, over time, chronic fatigue, which will negatively affect your ability to work and affect performance. And it's vital for us poker players to be "fresh" and think clearly.
A very common is the "erroneous" opinion that you can do without entertainment and hobbies, and often without rest (meaning that the time for rest is reduced to an unreasonable minimum). life philosophy such "pseudo enthusiasts" is the expression: "Let's rest in the "other world"". And, although we all know about the saying: “business is time, fun is an hour,” not everyone is able to understand it correctly. Some people take it literally. I do not urge you to become lazy and loafers. In no case! I'm just trying to convey to you a very simple idea - the right balance is important in everything. The same notorious golden mean. Find it between your work and your leisure. Consider that you have taken a very important step in the right direction. Indeed, this is indeed the case.
Recent graduates preparing for their first interview at a potential job, students before an important exam, athletes before important competitions - they are all trying to learn, train and prepare for upcoming event, as much as possible, so much so that, at times, twenty-four hours in a day may not be enough. Well, you know what I mean... Not all athletes. But almost all of them were students. Although they may understand that they need at least sleep and food, they continue to act irrationally and, in fact, stupidly, forgetting even about such simple, but extremely necessary things. Such an approach will not be useful for business, after a certain “rise” and reaching some kind of peak, a recession will inevitably come. And this recession will be very powerful. Both physically and emotionally. This will definitely reflect on the performance of a person. And, as you yourself understand, this will not be reflected in the best way.
On this, dear poker fans, we will complete our conversation. Remember one thing simple rule. The fewer mistakes we make ourselves, and the more more bugs force our rivals to commit, the better will be our financial position. I can only say goodbye to you and wish you all the best. Good luck, patience, development and success! Until we meet again, dear friends!
176 Gya. 1K paradox in the basics of probabilities
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3. Paradox of the Monte Carlo method
a) The history of the paradox
The Monte Carlo method is a numerical method based on a random sample. When solving computational problems, it is often possible to find a suitable probabilistic model that includes the desired unknown number. Then, to solve the problem, outcomes are observed many times random experiments, included in the probabilistic model, so that with a given accuracy of 1 based on the observed values) the desired number can be estimated. Although the idea of this method is quite old, its real application only began with the advent of computers, when E Neumann, S. Ulam and E. Fermi used the Monte Carlo method to approximate the solution of difficult computational problems associated with nuclear reactions. The name of the method is explained by the fact that it uses the sequences random numbers, which could be the regularly announced results of games held in a casino, for example, in Monte Carlo. However, in practice, the random numbers required for the method are generated by the computer itself. Consequently, the cute name 1 was first used in 1949 by N. Metropolis and S. Ulam) is misleading 1 method is unlikely to help win in Monte Carlo). The idea of the Monte Carlo method first appeared in 1777 in the work of Buffon 1cm. 1. 11), where the method of estimating the number n by throwing a needle at random was outlined. Suppose that parallel lines are drawn on the table at a unit distance from each other, and a needle of length E (1) is randomly thrown onto the table, while the angle between the lines and the needle and the distance from the middle of the needle to the nearest line are independent random variables uniformly distributed, respectively, on 10.2p) and 1 - 1/2, 1/2). Then the needle will intersect some straight line with probability 2b/n. If the experiment is carried out many times, then the relative frequency of intersections will be very close to theoretical probability 2b/n, and in this way one can calculate the value of n. This method of finding an approximate value is of purely theoretical importance, since several thousand throws are needed to obtain two exact decimal places. 1Using another method, you can determine the mi-
8. Paradox of the Monte Carlo Method
Lion signs of the number n, see the article by G. Mila.) Buffon's needle problem shows that the Monte Carlo method is not suitable for very precise calculations. Even getting results accurate to two or three decimal places requires thousands or millions of experiments. Therefore, the Monte Carlo method is applicable only when the experiments are simulated by a computer. Instead of throwing a needle, two independent random numbers are given that determine the position of the 1 supposed) needle and whether it intersected with 1 supposed) straight lines. Because the computer is capable of producing several million numbers per minute, it won't take too long to simulate millions of experiments; without a computer, it would take a lifetime.
The theory of constructing random numbers on computers has become an important direction in mathematics. Instead of real random numbers 1 that arise in the course of random physical processes, for example, during radioactive decay), pseudo-random numbers constructed using deterministic computational algorithms are becoming popular.
In connection with non-random numbers, the following question arises. In what sense can they be considered random if they are obtained using deterministic (non-random) algorithms? Since the paper by von Mises in 1919, some eminent mathematicians have investigated this problem. 1Philosophical aspects of the problem were dealt with by P. Kirschenmann, P. McShane and others.)
b) Paradox
In 1965 - 1966 Kolmogorov and Martin-Löf presented the concept of randomness in a new light. They determined when a sequence of 0s and 1s can be considered random. The main idea is the following. The more difficult it is to describe the sequence 1m. i.e. the longer the "shortest" program that constructs this sequence), the more random it can be considered. The length of the "shortest" program, of course, is different for different computers. For this reason, a standard machine, called a Turing machine, is chosen. A measure of the complexity of a sequence is the length of the most short program on the Turing machine that generates this sequence. Complexity is a measure of irregularity. Sequences with length L1 are called random if their complexity is close to the maximum. 1It can be shown that most sequences are exactly like this.) MartinLöf proved that these sequences can be considered random, since they satisfy all statistical
