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I hope this is not off-topic:

How do you write things like this: The machine was tested in 5 3-players games, 2 4-players games...

Or: five 3-players games, two 4-players games...

I want to say e.g. that it was tested 5 times in games of 3 players, and so on.

Style guides usually allow for you to alternate numerals and text when you are writing about two kinds of numbers in the same sentence. APA 6th edition, 4.33 ("Combining Numerals and Words to Express Numbers") gives this case:

Use a combination of numerals and words to express back-to-back numbers.

2 two-way interactions

ten 7-point scales

It recommends spelling out both in text only if readability would be impeded otherwise.

In this paradigm, you could write "five 3-player games" or "5 three-player games." The former is perhaps preferable, as it never leads to a formation where you start a sentence with a number.

The Chicago Manual of Style has a similar recommendation. In 9.7 on "Consistency and flexibility" in numeral rules:

In the same sentence or paragraph, however, items in one category may be given as numerals and items in another spelled out. ...

A mixture of buildings—one of 103 stories, five of more than 50, and a dozen of only 3 or 4—has been suggested for the area.

So Chicago, too, allows the author to make decisions about what category of number to make a numeral and which one to spell out.

According to The Chicago Manual of Style, it's "...five three-player games, two four-player games, ..."