Is it permissible to play games on Shabbat?
The Gemara in Masechet Eruvin (103) records a prohibition against playing on Shabbat with nuts and apples, which people in those days would use for games like marbles. Initially, the Gemara suggests that this is forbidden because of the noise produced when the nuts strike each other. Ultimately, however, the Gemara concludes that playing these games is forbidden because of the concern that the nuts or apples might smooth the earth on the ground as they roll (such as by filling holes in the ground with earth), which constitutes a Shabbat violation. The Shulchan Aruch (338:5; listen to audio for precise citation) codifies this prohibition and mentions the reason that the nuts and apples might smooth the earth.
Since the concern here involves the issue of smoothing the earth on the ground, this prohibition applies only to games played on unpaved ground. It would not apply to games played on tables, tiled floors or pavement.
Nevertheless, the Kaf Ha'chayim (Rabbi Chayim Palachi, rabbi of Izmir, Turkey, 19th century), in this chapter, writes that it is improper for adults to play any sort of games on Shabbat. (We are not speaking here of gambling, which is forbidden even during the week.) Shabbat is to be used for loftier pursuits, such as prayer and Torah study, and therefore spending one's time on Shabbat playing games is inappropriate. Children may be allowed to play games on Shabbat, but adults should refrain from doing so. It should be noted that the Chida (Rav Chayim Yosef David Azulai, 1724-1806) observed that certain Rabbis would play chess on Shabbat, and he speculated that they perhaps suffered from a kind of depression and felt the need to engage in some form of entertainment to overcome their melancholy. But generally speaking, one should refrain from playing games on Shabbat.
Summary: Halacha forbids playing games like marbles on unpaved surfaces on Shabbat, as there is concern that the marbles might smooth the earth on the ground, which constitutes a violation of Shabbat. On other surfaces this is, strictly speaking, permissible, but in any event playing games of any kind on Shabbat is inappropriate and at odds with the spirit of Shabbat.
