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868 paces is about one-third as long as The Kentucky Derby.
In other words, it's 0.3287880 times the length of The Kentucky Derby, and the length of The Kentucky Derby is 3.04147 times that amount.
(Churchill Downs, Louisville, Kentucky) (total race length)
The total race length of the Kentucky Derby run at Churchill Downs is 2,640 paces. First run in 1864, the Kentucky Derby is one of the oldest continuously-running sporting events in America, almost two years older than the Westminster Kennel Club Dog Show
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