Life's increments & excrements.
After eliminating symmetries, there are only 138 unique games. Assuming once again that X makes the first move every time:
Potato is the term which applies either to the starchy tuberous crop from the perennial plant Solanum tuberosum of the Solanaceae, or nightshade, family, or to the plant itself. Potato is the world's most widely grown tuber crop, and the fourth largest food crop in terms of fresh produce — after rice, wheat, and maize ('corn').