What is it? - page 13
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
A lot of people got caught trying to catch him by the balls.
They've caught it by the tail, too. Maybe you should catch it by the ears....
The paradox of envelopes ruins natural symmetry
You are offered two envelopes with money (you can't weigh, touch or peer through them, of course). You only know that one of them contains exactly twice as much money as the other, but you do not know which one and what it is. You are allowed to open any envelope you choose and look at the money in it. Then you have to choose whether to keep this envelope or exchange it for a second envelope (without looking). The question is - what should you do to win (i.e. get a bigger amount of money)?
After all, the probability of finding more money in envelope A is initially the same as the probability that more impressive money is in envelope B. And opening one of the envelopes (A) tells you nothing about whether you see the largest or smallest sum of the two offered. But calculating the average expected "value" of the second envelope tells a different story.
Let's say you see $10. That means the other envelope has either $5 or $20 in it, with a probability of 50 x 50. By probability theory, the weighted average amount in envelope B is: 0.5 x $5 + 0.5 x $20 = $12.5. Of course, when you open the alternate envelope you won't see this amount, but either $20 or $5, simply by the terms of the game. But 12.5 is (by calculation) what it would seem to be the average winnings per stake for a large enough number of rounds if you always switched envelopes.
And this result is independent of the original amount of money. After all, different pairs can be used in different rounds (10 and 20, 120 and 60, 20 and 40, 120 and 240 and so on). That is, in general terms, if envelope A contains C, then statistically the expected amount in envelope B would be 0.5 x C/2 + 0.5 x 2C = 5/4 C.
Thus, theory says, it is always profitable to change your initial choice (12.5 is greater than 10), although you will lose in some rounds. But against such a conclusion rebels intuition, which simply cries out for a fundamental equality of envelopes. After all, by swapping them you can start all your reasoning again (without opening the second one) and swap again.
The paradox of envelopes ruins natural symmetry of chance
Would you be so kind as to clarify the point of this bayan?
Obviously an attempt to attract attention of those who are friendly with mathematics (in the global sense) and theorists to find an opportunity to use seemingly random process, but as we see in this example not random at all to be used on FX
Those who are good at maths and TV understand the delirium of this "paradox".
Homebrewers can enlighten themselves by reading about it on Wikipedia.
PapaYozh, housewives and housewives:)))
Just, please, no references to Housewives ;)
I'm confused, I meant housewives.
Парадокс конвертов губит природную симметрию случая
Вам предлагаются два конверта с деньгами (взвешивать, ощупывать и просвечивать их, понятно, нельзя). Вы знаете только, что в одном из них содержится сумма ровно вдвое большая, чем во втором, но в каком и какие именно суммы — совершенно неизвестно. Вам позволено открыть любой конверт на выбор и взглянуть на деньги в нём. После чего вы должны выбрать — взять себе этот конверт или обменять его на второй (уже не глядя). Вопрос — как вам поступить, чтобы выиграть (то есть получить большую сумму денег)?
Ведь вероятность нахождения большей суммы в конверте A изначально такая же, как вероятность, что более внушительные деньги лежат в конверте B. И открытие одного из конвертов (A) ничего не говорит вам о том — видите вы наибольшую или наименьшую сумму из двух предложенных. Однако вычисление средней ожидаемой "стоимости" второго конверта говорит об ином.
Допустим, вы увидели $10. Стало быть, в другом конверте лежат либо $5, либо $20 с вероятностью 50 х 50. По теории вероятности средневзвешенная сумма в конверте B равна: 0,5 х $5 + 0,5 х $20 = $12,5. Разумеется, открыв альтернативный конверт, вы увидите не эту сумму, а либо 20, либо 5 долларов, просто по условиям игры. Но 12,5 — такова (по вычислениям), как кажется, будет средняя сумма выигрыша на кон при проведении достаточно большого числа раундов, если вы всегда будете менять конверты.
И этот результат не зависит от первоначальной суммы денег. Ведь в разных раундах могут использоваться разные пары (10 и 20, 120 и 60, 20 и 40, 120 и 240 и так далее). То есть в общем виде, если в конверте А лежит сумма С, то статистически ожидаемая сумма в конверте B составит 0,5 х С/2 + 0,5 х 2С = 5/4 С.
Таким образом, теория говорит, всегда выгодно менять первоначальный свой выбор (12,5 больше 10), хотя в отдельных раундах вы будете проигрывать. Но против такого вывода восстаёт интуиция, которая просто кричит о принципиальном равенстве конвертов. Ведь поменяв их вы можете начать все рассуждения сначала (не открывая второй) и поменять снова.
Read it here. I hope it all falls into place.
Парадокс конвертов губит природную симметрию случая
There was such a thing in the movie Twenty-One.Thanks for the extended reply. But....
I'm not saying you can't be in the black over a given finite period. Of course you can. But you probably want to keep it that way. That's what people want.
And I'm just arguing that we should have gone broke several times over a given period. (~600 average TV bets in deficit, with a starting capital of ~100 bets).
So why didn't that happen? The big question looms - what patterns were exploited?
In roulette, a person deals with a series of independent events. He consciously builds them into a process and tries to find a pattern in the process. But this process does not exist, it is only in the mind. Roulette completely forgets its history with each new spin
I) In roulette events are not dependent -- Understand and accept.
II) If the number of trials is n, the number of events A will tend to n*P(A) -- I understand and accept.
All of this together -- UNDERSTANDING!
Let me explain. You create a new object, an event system (e.g., roulette). There is no zero. Red/Black is 50/50. Made 1000 trials. Red = 600, Black = 400.
Question: On the one hand - the next event is independent and equally likely. The next series of n events is the same.
On the other hand, the balance is out of balance, the difference will tends to 0 (and it will reach it, sooner or later). So it is not 50/50?
So some other, global probability or ratio of probabilities of this system of events has changed?
.............
How could it not have shifted itself? )))