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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:

some consecutive returns

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.

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    $\begingroup$ I'm not familiar with the game, but I suspect there's something wrong or missing in your explanation. You're saying that if you undershoot you win the difference, and if you overshoot you only lose $1. If this was the case, the best strategy would be to always guess the minimum possible return, wouldn't it? $\endgroup$
    – Adrià Luz
    Commented Sep 29, 2021 at 12:08
  • $\begingroup$ @AdriàLuz I see a $1.01$ near the bottom of the list. Perhaps you lose on ties, so if that happens $1\%$ of the time or more often then guessing $1.01$ would be a losing strategy $\endgroup$
    – Henry
    Commented Sep 29, 2021 at 12:52
  • $\begingroup$ @Henry I'm definitely missing something (as I said I don't know anything about the game apart from what the OP shared). Just with the info shared, assuming that (1) you also lose on ties, that (2) the lowest allowed guess is 1.01, and that (3) 1.01 happens 1% of the time, guessing 1.01 every round would result in winning something 99% of the time (and this something could potentially be very large e.g. if the actual return was x1000). Based on these assumptions and my very limited knowledge I don't see why guessing 1.01 would be a losing strategy. But again, I'm sure I'm missing something! $\endgroup$
    – Adrià Luz
    Commented Sep 29, 2021 at 12:58
  • $\begingroup$ Note I'm also assuming (as per the details shared by the OP) that when you lose you only lose your bet for that round ($1). $\endgroup$
    – Adrià Luz
    Commented Sep 29, 2021 at 12:59
  • $\begingroup$ @AdriàLuz I did not know anything about it either (I invented the tie idea, so may be wrong. But if $99\%$ of the time you would win $0.01$ while $1\%$ of the time you would lose $1$, then your expected change is $+0.01\times 0.99 - 1 \times 0.01 = -0.0001$, i.e. losing. This promotional link says "The lowest playing coefficient in Aviator is 1. It does not fall out very often, on average every 50 rounds." $\endgroup$
    – Henry
    Commented Sep 29, 2021 at 13:04

1 Answer 1

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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)

enter image description here

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.

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