Theorem on the presence of memory in random sequences - page 30
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Suppose there is a bookmaker who accepts bets on the difference between the results of the tosses of the dice.
Let's denote by: t - the number of the last toss-up, respectively: t-1 - the number of
the number of the penultimate toss and t+1 the number of the next toss.
In this case:
Xt-1 is the result of the penultimate toss, the value of which is known to the player.
Xt - the result of the last toss, the value of which is known to the player.
Xt+1 is the result of the next toss, the value of which is unknown to the player.
Game conditions:The player can make a bet on the next move or refuse it.
Two kinds of bets are accepted:
1. The result of the next toss will be bigger than the result of the last toss
On the fact that the result of the next flip will be bigger than the result of the last flip. In this case the player gets the winnings: Xt+1 - Xt money units
units
2. It is a good chance that the result of the next toss-up is smaller than the result of the
is less than the result of the last toss. In this case, the player receives the winnings: Xt - Xt+1 units of money
units
The trailer contains a fresh revision of the theorem. In the beginning there is a problem when a dice is tossed twice, and then the player must play for rise or fall, i.e. to get the difference between the last result of the dice toss and the future result. To make it clearer, attached to the problem there is a table with all 216 possible outcomes of triple rolls of the dice, by which you can easily calculate the positive expected value for the player.
Well, and after the problem, there is a detailed analysis with the proof of the very inequality you are asking about?
The tables there are already smaller - only six lines each. So, it won't be hard to figure it out, if you have proper knowledge of mathematics of course.
In the table below all the options when the player does not bet, i.e. under the condition Xt-1 ≤
Xt are crossed out, and the options when the player bets, i.e. under the condition Xt-1 ≤ Xt, are not
are not crossed out and bolded:
A typo?
Where to find such a sucker bookmaker?))
A typo?
That's the one. Thanks for the tip, I'll fix it on the website.
The correct way would be:
"In the table below, all options when the player does not bet, i.e. under the condition Xt-1 ≤ Xt, are crossed out, and options when the player bets, i.e. under the condition Xt-1 > Xt, are not crossed out and are shown in bold:"
Yes indeed any kitchen takes bets on the difference between the current Xt price value and the subsequent Xt+1 value. Only discussion or even pointing to any kitchens is not allowed on this forum.
Where to find such a sucker bookie?)) Xt=6 and I'm willing to bet all my money on the second kind of betting. Xt=1 then on the first. Knowingly positive mo when playing against the bookie. What to calculate further?
By the way, yes.
If I bet on Xt+1 > Xt only when Xt <= 3, I get 162 lines (including the previous toss-up) and an expectation of 1.5.
There is clearly a relationship between Xt and (Xt+1 - Xt).
It's obvious!
Accordingly, I can easily, knowing only the last throw, put the system in the plus. I don't even need to know Xt-1.
There seems to be a substitution of notions here. They seem to be talking about the independence of adjacent realizations (they are indeed independent), and the system is based on the difference between adjacent realizations, depending on the realization at step -1.
The point here is that the die cannot roll more than 6 and less than 1. That is, under these conditions with the die, the game is with a positive mo against the bookie. There are no such restrictions on binary.
The cube is just an example to whet your interest to read on.
Binarok has a bookmaker's commission of 30% - 40%, i.e. you will get into minus.
I can advise betting on sports, on totals, the commission is acceptable: in the range of 10% - 15%.
But for non-binary betting the theorem advisor is in the trailer, but only for MT5.
By the way, yes.
If I bet on Xt+1 > Xt only when Xt <= 3, I get 162 lines (including the previous toss-up) and an expectation of 1.5.
There's clearly a correlation between Xt and (Xt+1 - Xt).
...
It is explicit!
Therefore, I can easily, knowing only the last throw, make the system on the plus side. I don't even need to know Xt-1.
The cube is just an example to whet your interest to read on.
Binarok has a bookmaker's commission of 30% - 40%, i.e. you'll end up with a minus.
I can advise betting on sports, on totals, the commission is acceptable: in the range of 10% - 15%.
But for non-binary betting the theorem advisor is in the trailer, but only for MT5.
Yuri, just a word of advice to take your mind off the calculations. Your theorems used to be quite non-trivial and required strain of mind to disprove or confirm them. It's just elementary arithmetic laid down in the condition. Give it a rest, you have a lot of potential.
Unless, of course, it's not a PR move. But even in this case you are capable of more)
Yuri, just a word of advice to take your mind off the calculations. Your theorems used to be quite non-trivial and required strain of mind to disprove or confirm them. It's just elementary arithmetic laid down in the condition. Give it a rest, you have great potential.
Unless, of course, it's a PR move. But in that case, too, you are capable of more).
One minute you're being scolded, the next you're being praised. Then they stress you, then they advise you to take a rest.
Who knows what's going on in this forum?