Data analysis for "aviator" online casino game This casino game called aviator gives random returns each round. For example
1st round : x2.1
2nd round : x1.43
3rd round : x56
4th round : x1
etc. The game continues 24/7 and you essentially bet what the payoff you think will be for the next round.
Win Scenario : I bet 1 dollar ( always 1 dollar for simplicity) that the next rounds return will be let's say 1.6. The actual payoff is 2.1 so I am safe (I undershoot) and I win 0,60$.
Loss Scenario : I bet 1 dollar that the return will be x2.5 but the actual return turns out to be x1.23 that means I overshoot and I lose my bet (1 dollar).
They claim to randomly generate numbers but just by taking a look they are not all over the place but usually rather small from 1 to 5 and at times 20 30 even to 1000. I provide a screenshot of some consecutive rounds returns I gathered to make it clear:

Supposing I have a couple thousand of consecutive rounds, what are some data analysis techniques I can use in order to create a basic strategy, starting from basic statistical concepts to advanced strategies? I know that the question is not specific but I would be grateful for some initial guidance on the subject.
 A: Suppose you always guess a constant $x$ with $x>1$, and the outturn is a random variable $Y$. Since I do not know what happens with ties, let's suppose $Y$ is a continuous random variable so the probability of a tie is $0$.
For your expectation to be profitable, you need $(x-1) P(Y>x) -P(Y \le  x) >0$
which is equivalent to $P(Y \le  x) \lt 1-\frac1x$
You can test whether this ever happens by looking at the empirical cumulative distribution function and seeing whether any of it lies below or the right of the curve.  Here is an example of the $30$ data points in your question (three graphs of the same data and curve, but with different ranges for $x$ so you can see more of the detail)

and you may be able to see that on those particular $30$ draws, something like $x=1.3$ or $x=20$ or $x=1000$ would have been profitable guesses (black below or to the right of red), but most of the curve has black above or to the left of red and so unprofitable.
These specific winning values are likely to have been the result of the particular values seen, and the online casino presumably sets the actual probability distribution for $Y$ so it can expect to make a profit for each value of $x$ that might be guessed, but not such an excessive profit that nobody wants to gamble.
