The rate at the arcade is supposed to be near impossible. The claw machine at your house is better odds. Also, the odds get better with gaming lvl, not luck
It gets exponentially easier as you level. Your screenshot shows you are only level 1 gaming. You need to play games in the Arcade to level up, you won't level on the claw machine. You can only win the claw machine 1 time (it gives you a stuffed animal, super rare, permanent boost)