I. Preliminary Considerations

It is apparent that skill, and not mere guessing, is involved in the games. The underlying skills relate to the ability to understand, process and analyze information about the performance of performers in real-world competitions. Such analysis must include the skill of comparing and ranking players, and the use recent past performance as a possible supportive variable.

However, the clear existence of skill does not necessarily mean that chance is not involved in the likelihood of winning a game, and that chance is immaterial. Thus, it is necessary to measure the role of skill vs. chance in the game.

To quantitatively measure the dominance of skill vs. chance among typical competitive users of the game, we must first define what "typical competitive game users" are. These are human users that play a sufficiently large number of competitive matches to allow their performance to be expressed and measured reliably. These users are defined as the target set and their performance serves as the benchmark for both measuring and analyzing the role of skill vs. chance and its dominance. As noted below, the target set size must be sufficiently large to allow admissible statistical analysis. Statistical inferential approach is used because the data (described below) constitute SAMPLES from the entire body of users, and inference is needed on whether sample findings can be extended to the entire population of the users of the company's games above a reasonable doubt.

Once we have defined our set of typical users, we can prove the predominance of skill over chance, if we find that:

(1) Within this set of "typical users," there exists a non-negligible subset of individuals that exhibit an outstanding number of repeated wins ("high performers")

II. Data Description

The data I have received from the company was in a form of seven files related to the respective following seven games. Each file contains information about games played by unique users:

Power 2 (P2) with 1,316,054 users

Power 3 (P3) with 1,223,036 users

Power 4 (P4) with 1,211,062 users

Flex 3 (F3) with 1,057,267 users

Flex 4 (F4) with 845,640 users

Flex 5 (FS) with 1,196,652 users

Flex 6 (F6) with 1,043,636 users

While within each file all users are unique, it is possible that a user will be reported in more than one of the seven files.

All seven files comprise data on games played during the period January 1st, 2019 through Mid-June 2023. It only includes players who are at least 4 months old in the company's platform. The information on users' games in all files was:

Total_games - Number of games played that resulted in "win" or "loss."

Total_wins - Number of games won.

Total_losses - Number of games lost.

Time in the system (in months).

Win ratio (WR = the number of games won per number of games played) was computed by me for all platforms, and was added to the 7 data files.

By means of sample-theoretic methods and algorithms, I was able to define sets of typical users corresponding to each of the seven platforms . These are users of all platforms playing at least 20 games and no more than the upper 97.5th percentile of games played in their original respective sets.