Paradoxes of formal logic and logical errors. Cognitive errors, distortions, misconceptions that prevent you from making money by trading and betting
Good day to all poker fans! Today we will talk to you about such a thing as " false conclusion Monte Carlo." This is also called the "gambler's error". Anyway, let's get started!
How well do you understand the essence of chance? Are all the events that happen to us in our life random? Everyday life? Everyone will answer their own question this question. And I am sure that each of the answers will be correct. Because in this situation to be categorical... Such a turn, so to speak, seems incorrect to me.
But, still, I would like to go a little deeper into this topic and ask you a few questions. Let's take as an example a very simple, so to speak, situation. 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 again black! And... You know what? Black came up nine times in a row. And then you come into psychological game, Yes? Nine times in a row the roulette gave the players black, and now for the tenth time it will probably come out red! Or not? What do you think about it?
So here it is. How would you act in such a situation? Obviously, there can be three main scenarios. Choose). You will bet on red because black has come up nine times before. Black can’t fall out ten times in a row!? Or you will bet on black, because now, apparently, there is a series of black drops... No, well, black cannot just fall. A series is a series. Or do you prefer the third option? The essence of which comes down to passing 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 roulette, the chance of getting black and red is still fifty-fifty. And it doesn’t matter what color came out before that. And how many times in a row did this color appear? It doesn't matter. Every new draw- this 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 to a greater extent depends on skill, not luck, will consider odds of 1 in 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 Monte Carlo fallacy or "gambler's fallacy". 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 may happen that heads come up nine times in a row. And before the tenth throw, you can ask people their opinion regarding the results of throw number ten.
It may well be that many people, having learned that heads have landed nine times in a row, will bet on tails after the tenth toss. After all, it’s already a miracle that the eagle fell nine times! The tenth will definitely be tails! No matter how it is... The point is that the chances of getting both heads and tails remain equal - fifty to fifty.
True, there is one nuance here that makes sense to pay attention to. And most people, by the way, see it without even thinking. We must differentiate some concepts. The appearance of heads or tails in a particular case. And the same side of the coin falling out, say, ten times in a row. Do you feel what we're talking about?
By the way, what about the situation when one of the players gets into a cool Spin-and-Go multiplier? What do other players think about after this? That's right, they get upset, starting to convince themselves that after this event there is a possibility that they will end up in the same situation. big prize decreased significantly. However, the point is that the chances of getting the same big prize remain the same as they were before big win. This is one example of poor thinking as a poker player. And this example is not the only one.
Now I invite you to delve a little into your memory. I will ask you questions, and you will try to answer them honestly. So let's get started. Situation one. Your opponent in the previous hand showed pocket aces, say. Probably, in the next hand you had the thought that since in the previous hand he had a pair of pocket aces, then in this hand this will definitely not happen again... The example is very conventional, but I think you understand the essence more than . Have you ever caught yourself this kind reasoning?
Situation two. Should you call your pocket pair for set value if you've already been dealt a set twice before? Surely you can’t step into the same river a third time? Or is everything wrong? So, do you understand what we are talking about?
Listen, let's remember the incident that took place at the WSOP 2007. What I mean is that even experienced players may fall into this trap... So, let's move on to that case. There was a hand when a seasoned and quite experienced poker player, Hevad Khan, decided to go all-in with a pocket pair of queens. In response, receiving a call from Remy Boukaya. Who, 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 ultimately “run over” his opponent’s aces. And only then Hevad told his losing opponent something like this: “When I pushed preflop, I couldn’t believe that you had a pair of pocket aces, because in the previous hand you had pocket kings. And such hands don’t come in very often... ".
So, I have already begun to say that even the most experienced players sometimes succumb to this nuance and are led by erroneous thinking. And what can we say about players who do not have decent gaming experience? The moral of this story is...). Each new distribution is new life! Each new distribution is in no way connected with the previous one. And it doesn’t depend in any way on the distribution that happened before. Therefore, you have no way of predicting the cards of your opponents 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 business against your rivals? If so many poker players are prone to incorrect thinking. I apologize for my erroneous thinking. It will be more correct this way. How to do this? I think that you yourself already understand what is required of you. But for greater clarity, let's give simplest example. Let's say you get a premium hand several times in a row. And, you know, your opponent may not believe you. After all, in his opinion, powerful hands cannot enter so often. Your task is to play your hand without any slowplay. Play it confidently and aggressively. Your opponent will probably take the bait and fall for the hook you kindly provided him with.
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 bluff. True, there are also many nuances there. I think that you yourself understand this no worse than I do.
Therefore, to summarize, 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 the "gambler's mistake." You should always remember that each new distribution is in no way related to the previous distribution. And if your opponent had a pair of pocket aces before, this does not mean that he definitely does not have them now, in the new hand. I know very well that you cannot step into 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 concepts of impossibility, so to speak. Everything is possible! Anything is possible in poker! Therefore, try to correctly identify your opponents, recognizing them as those who will make the gambler's mistake. And use it to your advantage!
Soon we will be talking about changing your lifestyle and improving your results in poker. This will be the final part of our conversation. Therefore, now I would like to make a short introduction and say a few words about rest and so-called workaholism.
Each of us understands that you can achieve something significant in life only when you really want it. However, it is quite obvious 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 for this. Sometimes you have to work tirelessly. Sometimes it happens for sixteen hours a day (or even more), tirelessly. You set yourself specific goals, you know what you want and are moving forward towards your dream. Hard work is, of course, a very commendable quality. This is 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 his intended goals. I am not kidding. Sometimes this really happens. How are you doing with the topic of relaxation? If so, of course, you can put it that way. Do you know how to relax, have fun and at the same time restore the strength necessary for further productive work? Do you have any favorite activities or hobbies that can “distract” you from work for a while, that “have stuck like a nail” in your brain? After all, a lot can depend on the quality of your vacation. Having no idea that rest is still necessary, you risk accumulating, over time, chronic fatigue, which will negatively affect your ability to work and affect your performance. But it is vital for us poker players to be “fresh” and think clearly.
A very common “erroneous” opinion is that one can do without entertainment and hobbies, and, often, without rest (meaning that time for rest is reduced to an unreasonable minimum). Life philosophy The expression of such “pseudo-enthusiasts” is: “Let’s rest in the next world.” And, although we all know about the saying: “there is time for work, an hour for fun,” not everyone is able to understand it correctly. Some people take it literally. I do not encourage you to become lazy and idle. In no case! I'm just trying to convey to you very simple thought– the right balance is important in everything. That same notorious golden mean. Find it between your work and your rest. Consider that you have taken a huge step in the right direction. After all, this is actually so.
Recent graduates preparing for their first interview at a potential job, students before an important exam, athletes before an important competition - they are all trying to study, train and prepare for the upcoming event as much as possible, so much so that sometimes twenty may not be enough. four hours in a day. Well, you know what I mean... Not everyone is an athlete. 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. This approach will not be useful for business; after a certain “rise” and reaching a certain peak, a decline will inevitably occur. And this decline will be very powerful. Both physically and emotionally. This will definitely be reflected in a person’s performance. Moreover, as you yourself understand, this will not have the best effect.
With this, dear poker fans, we will conclude our conversation. Remember one thing simple rule. The fewer mistakes we make ourselves, and the more more errors If we force our rivals to commit, the better our financial situation will be. All I can do is say goodbye to you and wish you all the best. Good luck, patience, development and success! See you again, dear friends!
The material is prepared at information support http://playvulkanstavka.com/igrovye-avtomaty-vulcan/
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of mature odds, is the mistaken belief that if something happens more often than usual over a period of time, it will happen less often in the future, or if something... something that happens less frequently than usual over a 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 “rule of justice.” In situations where confirmation of a given false conclusion is observed (i.e., a random result is accepted as a consequence of the correctness of the judgment), a person’s faith already turns to to the human mind, as a result of which false concepts turn into proven theories. 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 fallacy" originates from the most famous example of this phenomenon, which occurred at 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. It is, in fact, an extremely rare occurrence, although no more or less common than any of the other 67,108,863 possible sequences 26 of red or black. Players lost millions of francs betting against black, incorrectly reasoning that the streak was caused by an "imbalance" in the random behavior of the wheel, and that it should have been accompanied by a long streak of red.
The reverse fallacy also occurs. According to the reverse Monte Carlo fallacy, players can make the assumption that "fate" is on their side and will continue to hand out black, as was the case on August 18, 1913 for the 27th and even the 101st time. Again, the fallacy is the belief that the "Universe" somehow carries within itself the memory of past results, which tend to produce favorable or unfavorable subsequent results. However, this is not necessarily a fallacy; sometimes this fallacy is true, since for example, as stupid as it may sound, 2+2 will always equal four. The gambler's fallacy also works in the theory of predicting the gender of a child. Many people believe that the chance of giving birth to a boy for a given girl, with one healthy fetus, is always lower, because “for ten girls, according to statistics, there are nine boys,” although this chance is 50 percent.
P.S. My name is Alexander. This is my personal, independent project. I am very glad if you liked the article. Want to help the site? Just look at the advertisement below for what you were recently looking for.
Gambler's fallacy
O.I., or Monte Carlo fallacy, reflects a common misunderstanding of the randomness of events. Suppose a coin is tossed many times in a row. If there are 10 heads in a row, and if that coin is the “right” coin, it would seem intuitively obvious to most people that there is a delay in landing tails. However, this conclusion is false.
This error has received the name “negative recency effect” in the specialized literature and consists of a tendency to predict the imminent cessation of something that often occurs in Lately events. It is based on the belief in local representativeness (i.e., the belief that a sequence of randomly occurring events will have the characteristics of a random process even when it turns out to be short). Thus, according to this misconception, a generator of random events, such as 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 occurs, there is an expectation that the random sequence will correct itself in the near future, and a deviation in one direction will thereby be necessarily balanced by a deviation in the other. However, randomly generated sequences, especially if they are relatively short, turn out to be completely unrepresentative of the random process that produces them.
Gambler's fallacy is more than just a reflection of simple statistical ignorance, since it can be observed in privacy even people experienced 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 calculation-based estimates of probabilities in favor of intuition. Although logic may convince us that random process does not control our outcomes, our intuitive reaction can be very strong and at times overwhelm logic. Reed, who explored the comparative power of logical and intuitive thinking, argues that the latter is often more compelling than the former, probably because such conclusions come to mind suddenly, therefore, are not amenable to logical analysis and are often accompanied by strong feeling of being right. In contrast to the fundamental impossibility of tracing the process by which such intuitive “solutions” are found, the process of logical reasoning is open to analysis and criticism. That's why people rule logical thinking, and from intuitive thinking they simply get results, which fill the latter with a strong sense of rightness.
O. and. most common in situations where outcomes are generated purely by chance. If some skill factor is involved in the development of events, a positive recency effect is more often observed. An observer is likely to view a series of successes (eg a billiards player) as evidence of his skill, and will base his predictions of subsequent outcomes in a positive rather than a negative direction. Even throwing dice can lead to a positive novelty effect to the extent that the individual is convinced that the outcome of the event is somehow influenced by the “skill” of the thrower.
See also Barnum Effect, Player Behavior, Statistical Inference
176 Gya. 1K paradox in basic probabilities
e) Literature
Vapas 5., Tagb1 A. "5nr 1a yesogproyshchop ye epepegpyy ye rogp1y ep ragpe gerres11nepgepg sopigpep1e", Rnny. Mvy., 6, 244 - 277, 11924)
51gorpegi K. "Tie Vapas - Tag21 ragajokh", Tlv Lgpsysvp May. Mopiny, 66, 161 - 160, 11979).
3. The paradox of the Monte Carlo method
a) History of paradox
The Monte Carlo method is a numerical method based on random sampling. When solving computational problems, you can often find a suitable probabilistic model that includes the unknown number you are looking for. Then, to solve the problem, the outcomes of random experiments included in the probabilistic model are observed many times so that the desired number can be estimated with a given accuracy (based on the observed values). Although the idea of this method is quite old, its real application began only with the advent of computers, when E. Neumann, S. Ulam and E. Fermi used the Monte Carlo method to approximately solve 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 casinos, for example, in Monte Carlo. However, in practice, the random numbers needed for the method are generated by the computer itself. Consequently, the cute name 1was first used in 1949 by N. Metropolis and S. Ulam) is misleading 1method is unlikely to help you win in Monte Carlo). The idea of the Monte Carlo method first appeared in 1777 in the work of Buffon 1cm. 1. 11), which outlined a method for estimating the number n by throwing a needle at random. Suppose that parallel lines are drawn on the table at a unit distance from each other, and a needle of length E (1) is thrown onto the table at random, while the angle between the lines and the needle and the distance from the middle of the needle to the nearest straight line are independent random variables, uniformly distributed accordingly to 10.2p) and 1 - 1/2, 1/2). Then the needle will intersect some line with probability 2b/n. If the experiment is carried out many times, the relative frequency of intersections will be very close to theoretical probability 2b/n, and in this way the value of n can be calculated. This method of finding an approximate value has a purely theoretical value, since to get two exact decimal places you need to make several thousand throws. 1Using another method, you can determine the mil-
8. The paradox of the Monte Carlo method
lion digits of n, see the article by G. Mila.) Buffon's needle problem shows that the Monte Carlo method is not suitable for very accurate calculations. Even obtaining results accurate to two or three digits requires thousands or millions of experiments. Therefore, the Monte Carlo method is only applicable 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 hypothesized needle and whether it intersects with the hypothesized straight lines. Since a computer can produce several million numbers per minute, simulating millions of experiments will not take too long; without a computer, this would take a lifetime.
The theory of generating random numbers on computers has become an important area in mathematics. Instead of real random numbers (which arise during random physical processes, for example, during radioactive decay) are becoming popular pseudorandom numbers, constructed using deterministic computational algorithms.
In connection with non-pseudo-random numbers there arises next question. In what sense can they be considered random if they are obtained using deterministic 1non-random) algorithms? Since von Mises's paper in 1919, several eminent mathematicians have explored this problem. 1The philosophical aspects of the problem were studied 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 could be considered random. The main idea is as follows. The more difficult it is to describe the sequence 1t. that is, the longer the “shortest” program that constructs this sequence), the more random it can be considered. The length of the “shortest” program is naturally 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 shortest Turing machine program that generates the sequence. Complexity is a measure of irregularity. Sequences of length L1 are called random if their complexity is close to maximum. 1It can be shown that most sequences are like this.) Martin Löf proved that these sequences can be considered random, since they satisfy all statistical tests
This is how the boy decided that the flashlight was the cause, and salvation was the effect, when in fact the flashlight would only light his way to retreat.
Monte Carlo False Conclusion
Players are undoubtedly aware of the Monte Carlo fallacy. Some, however, will be surprised to learn that this is a false conclusion - they consider it a “Monte Carlo strategy.” Well, that's exactly what the dealers are counting on.
We all know that the roulette wheel has half black and half red sections, which means we have a 50% chance that when you turn the wheel, you will land on red. 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 marks on it. contraptions, then red will appear approximately 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 come out, right? No it is not true. On the seventh time, the probability that red will appear will be the same 50%, as well as every next time. This is true no matter how many times black appears in a row. So here's some very reasonable advice based on the Monte Carlo error.
If you have to fly on an airplane, for the sake of own safety take a bomb with you: after all, the likelihood that two guys with bombs will meet on the same flight is extremely small.
Vicious circle in proof
A vicious circle in proof is a situation in which the statement itself is used to prove a certain statement. Often this logical error itself becomes a real joke: the narrator doesn’t even have to invent colorful details.
Autumn. The Indians on the reservation ask the new chief whether the coming winter will be cold. The leader, however, was modern man and knew nothing about how his ancestors knew whether the winter would be warm or cold. Just in case, he ordered all Indians to stockpile firewood and prepare for the cold winter. A few days later, the idea occurred to him, albeit belatedly, to call the National Weather Service and inquire about the winter forecast. Meteorologists reported that the winter is indeed expected to be very cold. Then he ordered his people to be even more active in collecting firewood.
After a couple of weeks, he decided to check the forecast with meteorologists.
– Are you still predicting for us? cold winter? – he asked.
- Yes, sure! - they answered him. – Winter looks like it will be extremely frosty!
After this, the leader ordered the Indians to carry every piece of wood that they could pick up into the reserves.
Again, a couple of weeks later, he called the National Weather Service to find out more precisely what experts thought about the coming winter.
– We expect this winter to be one of the coldest on record! - they answered him.
- Really? – the leader was amazed. - How do you know?
- Yes, the Indians are stocking up on firewood like crazy! - meteorologists answered.
So, as evidence of the need to collect as much firewood as possible, the Indian chief eventually cited his own instructions to store as much firewood as possible. The vicious circle in the proof forced the Indians to cut great amount wooden rounds. Fortunately, by that time they already had circular saws.
Statements supported by references to higher power, loved by all bosses without exception. However, argumentation based on authority in itself is not a logical error: expert opinion is no worse than other types of evidence and has every right to life. It is a mistake, however, to cling to the opinion of authority as a straw to confirm that you are right, despite compelling evidence to the contrary.
Ted, meeting his friend Al, exclaimed:
- El! I heard you died!
- It is unlikely! – Al burst out laughing. – As you can see, I’m quite alive!
“That’s impossible,” Ted said in response. “I trust the person who told me about your death much more than you.”
When appealing to expert opinion, you always need to understand who exactly you consider to be the authority.
A customer in a pet store asks to show him parrots. The seller leads him to two beautiful birds.
“One of these parrots costs $5,000, and the other costs $10,000,” he says.
- Wow! - the buyer gasps. – What can the one who costs 5 thousand do?
– He performs all the arias from all Mozart’s operas!
- And second?
– He reproduces Wagner’s “Ring of the Nibelungs” in its entirety. Oh yes, I have another parrot, it costs 30,000.
- Wow! And what can he do?
“Personally, I haven’t heard anything from him yet.” But these two call him "maestro"!
In our own expert opinion, some authorities are much more trustworthy than others. The problem, however, is that your interlocutor may have different authorities than you.
The four rabbis regularly engaged in theological debates, during which three usually united against the fourth. One day, an elderly rabbi, as always, left alone and unable to withstand an argument with three rivals, decided to turn to higher powers.
- God! - he cried. – My heart tells me that I am right and they are wrong! Please give me a sign so they can see that I'm right!
It was a beautiful summer day. However, after the rabbi finished his prayer, a black cloud appeared in the sky, directly above the heads of the four “colleagues”. Thunder rumbled and the cloud disappeared without a trace.
- Here it is, God's sign! I knew it! Now do you understand that I'm right? - exclaimed the old rabbi.
However, three of his comrades disagreed with him, saying that such clouds were not uncommon on hot days. And then the rabbi prayed again:
- Lord, I need more clear sign, which would show that I am right and they are wrong! Lord, give me a more impressive sign!
This time, four black clouds appeared in the sky at once. They instantly merged together, and lightning struck the top of the nearest hill.
– I told you that I was right! - the rabbi cried.
But his friends again stated that everything that happened could be explained completely natural causes. The rabbi was ready to ask God to give him a huge, undeniable sign, but as soon as he had time to say: “Lord!..”, the sky turned black, the earth shook and a powerful thunderous voice rumbled:
– HE’S PRRRRRAAAAAAW!
The old rabbi, arms akimbo, turned triumphantly to his comrades:
- Well, now you see?!
“Well,” one of the rabbis shrugged. – Now we are three against two!
Zeno's paradox
A paradox is a reasoning that seems quite sound and is based on supposedly adequate evidence, but ultimately leads to contradictory or outright false conclusions. If you tweak this sentence a little, it becomes a ready-made definition of a joke - at least, most of the jokes in this book would fall under it. There is something absurd in the way true statements become false, and absurdity always makes us laugh. If you try to hold two opposing ideas in your head, you will become dizzy. But what is more important is that with the help of the paradox you can make the company laugh at any party.
