"I dare say you will have no objection to join us in a rubber"
Leather whist marker
Public DomainLeather whist marker - Credit: Charles Goodall

 Originating in the game of bowls, the term rubber also came to be used in cricket and tennis, and in card games such as whist, bridge, and cribbage. In these contexts, it has three different meanings. Firstly, it may refer to a series of 3 or 5 matches or games; secondly, it may refer to the winning of two games in such a series; thirdly, it may refer to the third game in a series which constitutes the tie-breaker.

Here, the reference is to a rubber of whist which was an extremely popular card game in the 18th and 19th centuries.