I'm not a mathematician; I do have some reasonable math knowledge, but have always had struggles with probability. So while I am looking for the calculation to my problem, I would also desire some explanation. I've edited this question from an earlier version that seemed to be getting off track on my price movement illustration (as all the comments by lulu show), rather than focusing on what I'm really trying to understand and solve with respect to probability. I hope what I have now is clear and more focused mathematically.
Assume the following: An integer value between 20 and 200 is generated each day for 10 days. There is a level of randomness to this, but two things affect the randomness:
- No day will be exactly equal to the day before, some variation will occur.
- Over any 10 days, at least by day 10, 100 will be what the average of the set calculates to; this means that if a large number of greater than 100 values are generated early in the period, there are increasing odds of the latter days being less than 100 (perhaps significantly less, and vice versa). Of course, there could be just small pushes to each side of 100 level, as each day corrects the day before, in which case the probability remains fairly "normal" and "equal" on which direction from 100 the next day's number would be.
At some point, since the assumption is that it will return to an 100 average at least by day 10, given how far it has moved away from average and how many days are left in the set, there is the possibility of yielding an increasing probability that a day (or series of days) will end up opposite the earlier move to counter balance it to reach the 100 goal by the end of the set 10 days.
I'm seeking a formula to calculate the probability that the next day in the sequence begins and/or completes a corrective move back to the 100 average, given the varying history of what might have transpired before and what is capable of happening in the time remaining. So the first day would be completely random, but the 2nd and following days would begin to shift probabilities of a correction (or expansion/contraction if day 1 = 100 value or any set of days prior already averaged to 100) based on the finite time remaining, amount needing to be corrected to get to 100, and allowable values in the range to get to that correction.