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I am looking for something we could play online and which is free. We had a lot of fun when we were just starting to play chess, and after a while it became a bit boring as there wasn't enough room for creativity anymore. We're trying out some chess variants and checkers now, so something like that?

We've already looked at Go, Renju, Reversi, Hexxagon and Connect Four. The game may include some element of chance, if required.

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Here are three fairly simple two player strategy games on Yucata.de that I've enjoyed playing with friends on-line:

Drako http://www.yucata.de/en/GameInfo/Drako (overview and play on site)

Three dwarves battling a dragon in an asymmetrical, well balanced game that uses both card play and movement on a board. Card drawing adds element of chance.

Kahuna http://www.yucata.de/en/GameInfo/Kahuna (overview and play on site)

Two wizards trying to control a connected chain of islands on a board using cards. Cards add element of chance.

Hive https://en.boardgamearena.com/#!gamepanel?game=hive

Tile playing game with insects protecting queen that feels strategically similar to a chess end game, but lighter. Not much chance involved.

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