Have you ever bowled? Based on the stipulations in the OP, the ‘average person’ (based on observing myself, friends, family, and others on the lanes on any given day) would be extraordinarily lucky to hit the front pin 12 times in a row, never mind the luck required for that to translate into 12 strikes. Propelling a 14lb ball in a straight line over 60 feet is not easy.
Put another way, pro bowlers have averages well into the 200s, your average Joe considers 100 a very good score. There is no chance they could win 1 in 100 games against a pro.
The only plausible candidate I can think of is eight-ball pool, where the pro might pot the eight ball on their break but also foul, losing the game, 1 in 50 times, or the amateur might pot the eight ball on their break, winning, 1 in 50 times. But the latter is much less likely than the former, and the pro could avoid the former by not breaking so hard. So even that is a stretch.
As the first reply notes, tennis might qualify if we define “winning” as “winning 1 point out of 100” - I saw a bit of fuss on Facebook recently about a poll that supposedly said 12% of men think they could win a point against Serena Williams. A lot of people were saying that showed men vastly overestimated their ability, actually I thought it was pretty reasonable IF defined as “winning one point in a set” (which would be a lot fewer than 100 points) - there is always a chance of just getting your racquet to a serve and fluking a winner, or similar. On the same basis, I might (as a casual tennis player) win 1 point in 100 versus Djokovic. But winning a set (or even a game)? Zero chance, barring injury, as mentioned.
Really I think this question tells us something about pro sport/games - they are basically the definition of something where it’s functionally impossible for a casual player to beat a pro, that’s a big part of what makes them entertaining and popular. There is no (serious) world championship for Tic-Tac-Toe because the skill level required to play it perfectly is pretty trivial. Not so for chess, backgammon, poker, Go etc. Similarly for sports with a physical element - you can win money by playing darts (where the margin between success and failure is very, very small), not so much for throwing a bean bag in a garbage can (yes I am aware of professional Cornhole, but that has a bit more to it. In fact, it’s just possible it qualifies as an answer to the OP, but I don’t follow it closely enough to say either way. If it does, it is because it has a relatively small pool of pro players and a pretty low physical and mental bar to success, no offence intended).