Nice find! You didn’t say what denomination you are playing, which is important, so I’m going to assume dollars. For five-coin maximum bet, the number of doubles required for a win of w (where w<1200) is 1+int(log(1200)-log(w))/log(2). The following table shows for each initial hand the pre-double win, pre-double probability, number of doubles required, post-double win, and probability achieving the post-double win, including the $250 bonus. The lower right cell shows a return of 115.5%. You will get a jackpot every 297 hands on average, with an average jackpot of $1,717.46.
8-5 Triple Bonus Return Table with $250 Bonus for Wins of $1,200 or More
Pre-Double WinPaysPre-Double ProbabilityDoubles RequiredPost-Double WinPost-Double ProbabilityReturn Royal flush$40000.0000260$42500.0000260.02193 Straight flush$5000.0001182$22500.000030.013322 4 aces$12000.0002350$14500.0002350.068227 4 2-4$6000.0005421$14500.0002710.078557 4 5-K$2500.0016293$22500.0002040.091637 Full house$400.0105465$15300.000330.100842 Flush$250.0110556$18500.0001730.063913 Straight$200.0127386$15300.0001990.060902 3 of a kind$150.0755427$21700.000590.256136 Two pair$50.1230658$15300.0004810.147101 Jacks or better$50.2115758$15300.0008260.252898 Total0.447071000.0033641.155465