If this were a real life situation tried 99 times, are you telling me that if I stick I’ll win on average 33 time and if I change I’ll win 66 times? I’ll bet on average it’ll be 50 50.
Try it. Just get like two 10p coins and one 20p, and see what happens. Do it 10 or 20 times. I did it 10 times, and got the 20p 6 times, and the 10p 4 times, changing every time. Not very conclusive of course, its one time off 5/5, would be better to repeat it.
Also doing it for yourself makes it so obvious. You realise if you decide to change before you begin, you just have to pick up a 10p to win the 20p. You have a 2/3 chance of picking up a 10p. If you choose not to change before you play, you have to pick up the 20p, of which you have a 1/3 chance of winning it.