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Playing with the gee gees (or geegees) is a euphemism for gambling on horse races.
But the gee gee is the horse that breaks out in the lead from the gate. It’s the position at the finish line that matters to gamblers, and it’s pretty rare that a horse leading at the start is in the top three (or in some races,top four) positions. So betting on a gee gee might be exciting, but disappointing and expensive.
But where did gee gee come from?
Telling a horse to gee-up is requesting more speed, but that’s a soft g, like ghee, Telling a horse gee with a hard g means to turn right (haw means to turn left), but I don’t ever recall seeing a horse race oval that raced clockwise. As you sit in the stands outside the oval, the horses race left to right. (When I was growing up, we called the fruit of a horse chestnut a hawhaw. but I’m given to understand that real hawfruit comes from thornapple trees.)
The term apparently comes from the UKGB&NI, and a politician on Chester in earlier times was Mr Gee, but from reading Dick Francis, I’ve gotten the impression that the Chester track is just another track, not a leader in prestige that would inspire copycats (copyhorses?)