Rummikub ? It encourages some logical thought and analysis. It seems to have at least one mathematical paper on it

http://comjnl.oxfordjournals.org/content/49/6/665.abstract

and it's popular and fun.

Rummikub ? It encourages some logical thought and analysis. It seems to have at least one mathematical paper on it¹

https://doi.org/10.1093/comjnl/bxl033

and it's popular and fun.

¹D. Den Hertog, P. B. Hulshof, Solving Rummikub Problems by Integer Linear Programming, The Computer Journal, Volume 49, Issue 6, November 2006, Pages 665–669, https://doi.org/10.1093/comjnl/bxl033