There are several answers to this question:
Connection pool
There are third-party drivers that have a connection pool. rethinkdbdash , for example, is a great Node.js driver with a connection pool.
Maximum number of connections
I'm not sure that there is a hard limit on the number of connections on the RethinkDB side, but users usually encounter OS connection restrictions before they really work with the maximum number of connections on the RethinkDB side (I'm not sure, I think there is one). Basically, RethinkDB easily handles thousands of connections without any problems.
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