Hi maxdancona, thank you for your reply!
Yes, you are right, from 100 to 150, I could always sell it like this each time. But I do not know this is the best strategy.
Usually, I could see from 100, there is a top, like 300(potential highest value), but it could be 160, or 500, even 1000. The hard part is, I know there is a dropping(like when it reached 150 in this case), but I do not know how low it could reach, and when the price is down enough, it would prove me wrong, that there would not be a higher price, in this case, if it goes lower than 80, then the 150 will be the top value I could get, and if I still hold this stock, the price could go much lower than 80.
And I forget to say one thing, I could not afford to lose all of my money even once. Because when I have 100 dollars, I buy 1 stock, when I have 10000 dollars, I buy 100 stocks. Of course I could do something to avoid to lose everything I have, like only put 60% of money into stocks each time, then if I keep on winning, it still gives me very good money.
So, about the probability that it will go higher than 150, as you know in poker games, it is different each time, and not like poker we could have exactly probability each time, the problem is, I do not exactly know, I think I could use another example to state the probability:
When we go skiing, we would consider rent or buy a ski board, the price of a board is 200 dollars, and rent it would be 10 dollars a time. we do not know how many times we would give up skiing(probability is unknown), but I heard that in Math, it is still possible to calculate that buy this board when you rent half price is the best strategy. (I could not find this strategy solution right now, sorry about this, I just know I read it somewhere many years ago, but I could not remember the solution process. By the way, this solution helps me a lot in life of buying or renting something)
I hope I explained what you need, thanks again!