What technologies do you need to master to develop a purely web-based chess and card game?
html css js may use algorithms
flash, c#, mysql
The frontend is html div css js framework Ajax flash
There are many backends: PHP, jsp, C#, etc. Any dynamic language will do, mainly for interacting with the frontend. Even C at the bottom level may be used. There are too many things involved in the server, including performance optimization, broadband stability, and security.
Instead of learning so many technologies, it is better to recruit people in these fields.