Question regarding repetition of a string

[Montgomery]

Greetings all. I have a question regarding the correct probability of a repeating string. Assuming you observe 6 even bet outcomes, and note the sequence from the latest to oldest in the format of color, parity, level, color parity, level, for example REHBOL what is the true probability of the wheel being able to re-spin the same exact string back to back?

Given the permutation for 6 unique characters is 720 or 1/720 probability for any string to occur. That is 0.00138. Therefore, what is the probability of any string happening twice in a row?

Also if we bet on the reverse of this string using a 6 level progression, is our probability of losing, the same as the string happening twice in a row or is it still the percentage of  single even odds bet?

Looking forward to your input.

[Arthur Lambert]

You are looking at a sequence of betting results that has the character string "REHBOL". To find out the probability of the same string occurring twice in a row, you should consider the following aspects:
The probability of getting the string "REHBOL" the first time: As you have correctly pointed out, there is 1 possible way out of 720 ways to get this string, so the probability of this is 1/720.
Probability of getting the string "REHBOL" repeatedly: Since the string has already appeared in the previous sequence, there is only 1 possible way to get it again.
In general, the probability of the string "REHBOL" appearing twice in a row is equal to the product of the probabilities of both events:
(1/720) * (1) = 1/720
Thus, the probability that this line will appear twice in a row is 1/720 or approximately 0.00138.

[huskerdu]

The propability of a 6-string to appear again is 1 to 64.
It doesn't matter if it is a string of R-B or H-L, or  O-E or mix of them. The probability is the same. 1/64.
So if you have a string REHBOL the propability to appear again is 1/64.
If you want to play with a progression betting the reverse string (in order not to appear again the previous string) you will bet a six step 1-2-4-8-16-32 which means a total of 63 units. Theoritically you will win 63 times 1 unit and you will lose one time 63 units.
I've been there....

[huskerdu]

I forgot to note that the above is without considering the "zero" factor.  Which means that theoritically in 1 to 37 spins you will also have one more lose because of the zero.

[Arthur Lambert]

To determine the probability that the wheel will spin the same line again after 6 equal betting results, you need to take into account the number of possible combinations of outcomes and the number of favorable combinations (combinations where the line repeats).

[TriCycle]

Everything is equal and likely, until you un-equalize it and play the way nothing matters anymore. Stop looking at the probability of the game and look at the probability of how you want to play it.

[rochitnis]

I have been playing even bets for long and are very risky as you have to stake a lot with martingale.
But if you have a bigger bankroll and lot of time and low start on side bets u can regularly make a living