Brain games mostly improve the game itself. What research shows on near and far transfer, the trap in reaction-time scores and what actually helps.
Play a memory game daily and your score will certainly rise. The question is what caused the rise. Mostly it is familiarity with the rules, tactics suited to that specific layout, and faster hands. Calling that an improvement in memory itself is hard to justify. When the score plateaus, it is usually a sign you have learned most of that game's tricks.
Trained ability carrying over to another task is called transfer. What studies repeatedly show is that transfer occurs to some degree with very similar tasks and barely at all with different ones. Practising digit recall improves digit recall, but evidence that this reaches study or work performance is weak.
The millisecond figure from a reaction test does not measure human response alone. Device and browser delay sit between when the screen actually changes and when input arrives. That is why the same person scores differently on different hardware. Comparing against your own records is meaningful; comparing absolute numbers with others is not. To compare records at all, measuring on the same device and browser at a similar time of day is the minimum.
The evidence for cognitive function is stronger for the body and daily life than for on-screen training. Regular aerobic exercise, sufficient sleep and social contact are the factors that keep appearing. If time on brain games displaces those, it may be a net loss. You can also combine the two, such as thinking through a puzzle on a walk.
Playing because it is fun, or to reset your focus during a short break, is reason enough. The problem is spending significant money or time on the expectation of getting smarter. Being clear about why you play also means fewer disappointed expectations.
Products that promote brain training lean heavily on scientific language. When you see such claims, asking what exactly improved and how it was measured filters out most of them. A rising in-game score may simply mean, as above, that you got used to the game. Even when a study is cited, conclusions are hard to accept at face value if the sample was small, there was no comparison group, or the company itself ran the research.
If the aim is fun and a break, brain games make a fine hobby, and variety keeps them enjoyable longer than scores do. Repeating one game quickly hardens into technique and gets dull, while rotating number puzzles, word games and spatial puzzles makes you think in a new way each time. Solving the same puzzle with family or friends and comparing methods also reveals the pleasure of seeing how differently people reach the same answer.
If you are reaching for brain games because your memory seems worse lately, there are things to check before any game. Lack of sleep, stress, low mood and medications can all temporarily weaken memory and concentration. If forgetfulness has become frequent enough to interfere with daily life, or people around you noticed a change first, it is better to consult a medical professional than to try to fix it with games. Whatever the cause, checking early widens the range of options.