With flute
Turns		Odds		Time
1			0.70		6.5
2			0.21		10.0
3			0.06		13.5
4			0.02		17
5+			0.01		~22.0

Average: 8.02s

Without flute
Turns		Odds		Time
1			0.143		2.2
2			0.143		5.2
3			0.143		8.2
4			0.143		11.2
5			0.143		14.2
6			0.143		17.2
7			0.143		20.2

Average: 11.20s