and wandering around randomly again... - page 60
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Dmitry, good day, please explain in more detail.
There is nothing so special here. It's not the laws on the basis of which you can predict the future. But the theory of probability exists and it is extensive and explains a lot. With a coin in particular, it's clear from the start. Two sides and probability of their falling out is equal, i.e. 1/2, so probability of winning and losing is equal, so in infinity perspective player will win or lose and stand by his chips. However, we know that a coin has no memory, its probability of falling out is always the same regardless of the history, so there is always a probability of falling out a long row of heads or tails (the length of row is not limited, just the longer the row, the lower the probability of its occurrence). And since the funds are limited, there is a chance of losing everything and not being able to win back. I.e. the probability of losing is higher than the probability of winning (except for the theoretical case with unlimited funds). This is the simplest of probability theory. It is like arithmetic before algebra.
Although probability theory does not allow predicting the future, it allows not to be a fool, for example, if someone offers to play a game of dice, you win when you roll 3, you lose the rest, knowing the basics of probability theory, you will not play such a game. This is of course a simple case, it is immediately clear that the game conditions lose, but there are less obvious problems requiring a deeper understanding of probability theory, which would calculate their chances and make a decision about participation in the game - for example, the famous problem from the movie "21".
There's nothing so special here. It is not the laws on the basis of which one can predict the future. But the theory of probability exists and it is extensive and explains a lot. With a coin in particular, it's clear from the start. Two sides and probability of their falling out is equal, i.e. 1/2, so probability of winning and losing is equal, so in infinity perspective player will win or lose and stand by his chips. However, we know that a coin has no memory, its probability of falling out is always the same regardless of the history, so there is always a probability of falling out a long row of heads or tails (the length of row is not limited, just the longer the row, the lower the probability of its occurrence). And since the funds are limited, there is a chance of losing everything and not being able to win back. I.e. the probability of losing is higher than the probability of winning (except for the theoretical case with unlimited funds). This is the simplest of probability theory. It is like arithmetic before algebra.
Although probability theory does not allow predicting the future, it allows not to be a fool, for example, if someone offers to play a game of dice, you win when you roll 3 and lose the rest, knowing the basics of probability theory, you will not play such a game. This is of course a simple case, it is immediately clear that the game conditions are losing, but there are less obvious problems that require a deeper understanding of probability theory, which would calculate their chances and make a decision about participation in the game - for example, the famous problem from the movie "21".
Thanks for the answer.
There's nothing so special here. It is not the laws on the basis of which one can predict the future. But the theory of probability exists and it is extensive and explains a lot. With a coin in particular, it's clear from the start. Two sides and probability of their falling out is equal, i.e. 1/2, so probability of winning and losing is equal, so in infinity perspective player will win or lose and stand by his chips. However, we know that a coin has no memory, its probability of falling out is always the same regardless of the history, so there is always a probability of falling out a long row of heads or tails (the length of row is not limited, just the longer the row, the lower the probability of its occurrence). And since the funds are limited, there is a chance of losing everything and not being able to win back. I.e. the probability of losing is higher than the probability of winning (except for the theoretical case with unlimited funds). This is the simplest of probability theory. It is like arithmetic before algebra.
Although probability theory does not allow predicting the future, it allows not to be a fool, for example, if someone offers to play a game of dice, you win when you roll 3, you lose the rest, knowing the basics of probability theory, you will not play such a game. This is of course a simple case, it is immediately clear that the game conditions are losing, but there are less obvious problems that require a deeper understanding of probability theory, which would calculate their chances and make a decision about participation in the game - for example, the famous problem from the movie "21".
There you go. I also wrote about it here in the thread.About playing against the second player. It's not a game against SB. The series isn't transitive. It will be one series against the other that wins. Both series by themselves have no positive mo. In order to capitalise on this, you need to find an idiot who will offer you a penny game, i.e. call the series first, giving you the advantage of the right to choose your opposing series.
I'll try to explain one more time, probably the last one, because it's very boring...
For example, take your favourite martingale. We have a series of 20 coin tosses.
In any given coin flip, there is a 50% chance of heads and tails...
does that mean a series of 20 heads in a row is as likely (50%) as a single flip of a coin? NO. The probability is extremely small... and the larger the series the less likely it is...
which series of 20 is the most probable? the one where heads and tails are about the same, and most of the time they will be that series i.e. 11:9 or 7:13 or 12:8 etc. they will be in the middle of the dome distribution and have the highest probability density... and only occasionally there may be series which are very different from the uniform distribution, they will be on the edges of the density and have the lowest frequency of falling out...
So answer your own question: may series +1-2 where heads are twice less than tails and in an infinitely large cycle be equal to any other series where numbers of heads and tails are more or less balanced?
I answer... and point by point:
1) "...in each particular coin toss there is a 50% probability of heads falling out, i.e. equal probability with tails..."
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Similarly...
2) "...does this mean that a series of 20 eagles in a row is as likely (50%) as a single coin flip? NO. The probability is extremely small... and the larger the series the less likely it is..."
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I absolutely agree with you (up to this point our views coincide. But further on...).
3) "...which series of 20 rolls is most probable? - the one in which heads and tails will fall approximately equally...".
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Exactly as the question was posed, the answer is one: none... All series are EQUAL. The probability of getting both 20 eagles in a row and any given series with 10 eagles and 10 tails is 1/2^20
But if you meant to say, "Which set is most likely to have a series of 20 shots?" - Then the answer "To the set of series where heads and tails will be approximately the same" is unlikely to be objectionable.
But the main point is that your current post lacks the words "tends" and "to zero"...
The fact that a significant percentage of all possible series have approximately the same numbers of eagles and tails falling out does not speak to any special "aspiration" of the trajectory to any particular level. At infinity, an infinite number of trajectories will also forever "stack" along the x-axis and above and below it, never touching it. And it is even in spite of the fact that "...the numbers of eagles and tails falling out in them will be approximately equal...". And this is exactly whatdanminin andDmitry Fedoseev strongly oppose.
Thus, if nobody continues to insist on the trajectory's "aspiration" to zero and on the inevitable return to the zero line ofany trajectory, we may end the argument as "arisen due to different understanding of used phrases"... and, based on everything said in this "branch", we may happily come to a conclusion about the reality of profitable trading on SB.
3) "...which series of 20 rolls is most likely? The one in which heads and tails are approximately the same..."
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Exactly as the question was posed, the answer is one: none... All series are EQUAL. The probability of getting both 20 eagles in a row and any given series with 10 eagles and 10 tails is 1/2^20
But if you meant to say, "Which set is most likely to have a series of 20 shots?" - Then the answer "To the set of series in which heads and tails will be approximately the same" is unlikely to cause any objections...
Something I doubt about your refutation of those words. But it can be verified by experiment, using a random number generator. Count the number of even and odd numbers in each series and the picture will be clear. If I'm not too lazy at the weekend, I'll make a script and check it out.
In fact, in paragraph 3) I think you contradict yourself.
I reply... and point by point:
1) "...in every particular coin flip there is a 50% probability of a heads roll i.e. equal probability with tails..."
-------------------------------------------
Similarly...
2) "...does this mean that a series of 20 eagles in a row is as likely (50%) as a single coin flip? NO. The probability is extremely small... and the larger the series the less likely it is..."
--------------------------------------------
I absolutely agree with you (up to this point our views coincide. But further on...).
3) "...which series of 20 rolls is the most probable? - the one in which heads and tails will fall approximately equally...".
--------------------------------------------
Exactly as the question was posed, the answer is one: none... All series are EQUAL. The probability of getting both 20 eagles in a row and any given series with 10 eagles and 10 tails is 1/2^20
But if you meant to say, "Which set is most likely to have a series of 20 shots?" - Then the answer "To the set of series where heads and tails will be approximately the same" is unlikely to be opposed.
Bullshit...
Think about it logically: in a normal distribution there are different probability densities for different series... at the centre of the distribution bell there are the most probable scenarios...
"To the set of series in which heads and tails will be approximately the same" is unlikely to be objectionable to anyone.
what do you mean by many? it's not quite clear.... but if you mean the most number of series then-
how do you think this set is formed? it is formed because any particular single series also has a higher probability of equal distribution than the others...this is the reason why there are more such series...don't you see...if any particular single series were always equally probable to all others we simply wouldn't have a distribution curve...there wouldn't be a peak and there wouldn't be tails... as there would be no difference in the probability of any scenario, any series...
if I flip a coin, I know ahead of time that the least likely scenario of all is 20 tails or 20 eagles...just as it is unlikely that out of 20 flips I will only get tails once, but already more likely...and even more likely that in 20 flips I will get tails at least 2 times, etc....
...and, on the basis of all that has been said in this "thread", happily conclude that profitable trading on SB is real.
You are overlooking one small nuance - the spread. If there is no spread, then yes, in half of the games your deposit will indeed increase, but in half it will decrease. If there is a spread, then the probability of winning in a round robin decreases proportionally to the number of rolls.
For instance, suppose for clarity the deposit is 100 roubles, you lose or win 1 rouble per one coin flip and the number of coin flips in one game is say 10 000, no spread. the game outcome is obvious here - with approximately 68% probability the deviation from expected payoff is 1 sigma, with approximately 93% probability it is 2 sigma, 99% - 3 sigma, etc. Expected payoff is 5000, sigma is (root of N), i.e., 100; therefore, after 10,000 coin tosses, your deposit with 68% probability is [100-100:100+100], 93% probability is [-100:300], 99% probability is [-200:400] rubles. If there is a spread in the game, let's say 2 kopecks per roll, then for 10000 rolls you have to pay 200 rubles, and then the final result will be - with a probability 68% - [-200:0], 93% - [-300:100], 99% - [-400:200]. No money management methods, notorious martin, can help improve the result of playing beagle.
Summary: the chances of winning at beagle games with a spread and a large number of coin flips are very small.
However, all this is true with one proviso - if the coin is symmetrical. If the coin is "wrong" and the probability of eagle is higher, and we can diagnose that, it's easy to win.
The market is a priori, due to its "physics", the great number of participants and many influencing factors, a random walk, but it is also obvious that this random walk is not generated by a symmetrical coin. Rather, the following model may be appropriate to describe it - let there be several croupiers, each with their own coin. One is symmetrical, another has a slight asymmetry to one side, another to the other. Some have more asymmetry and others less. The croupiers change randomly in the course of the game. The result is also an SB, but a rather peculiar one. This market model is in my opinion the most adequate, by the way, it naturally helps to explain the notorious market "fat tails".
Forget it, all of you. It's either a cheeky troll or a mentally handicapped man.
It's the most rational thing to do...
let him think he's right.... imagine sitting on a yacht, turning on his monkey on a tablet.... took a swim, wiped himself off, looked at the monitor and there was a couple more lemons...
he has his own economic theory, similar to Pinocchio's views... you bury your money in a field of miracles and live happily ever after on random processes...
the process is random and the earnings are systematic, everything is possible in wonderland.)
Guys, quit your jobs and business - all to the field of miracles!!! We'll get rich at any MOTION and the rest of the world will work for us and serve us... we will not tell them how easy it is to make money... if you go to a shop and there are no salespeople or cashiers, plants are shut down and everyone is sitting at home on monkeys
we will get rich on any MOTION
Theprofessors and guests were amazed when Vasilisa the Wise went to dance with the temple, waved her left hand and a lake of profitable deals was made, waved her right hand and the Spanish lots floated on that lake; the professors and the guests marvelled .
And the eldest daughter-in-law went dancing, waved her left hand - they sprinkled with wild slips, waved her right hand - the stake of Marjova hit the investor straight in the eye! The investor got angry and chased them away in shame.