1 in 100 won’t be enough games for the amateur to exceed 150.
A chess master could have a heart attack in the midst of a game. It doesn’t help demonstrate a useful point about competitive comparisons. As @Left_Hand_of_Dorkness says below, it would be breaking the spirit of the question.
We’re assuming that the games are under normal conditions, right, i.e., not back-to-back? Because otherwise, under certain conditions, an amateur might be able to wait for exhaustion to hit the pro and then win, which breaks the spirit of the question.
Which, to be honest, is what we do here. 
To clarify, I am talking about people who may have played a game their whole life, but have never played professionally or been in a major big money tournament. The 1 week training is so that the amateur would understand the format and mechanics of the high level professional competition.
I was inspired to ask this question after watching videos of a very good chess player getting beat in a matter of minutes by Magnus Carlsen, videos of very talented high school players going against a Major League pitcher, and stories about these high stakes poker tournaments and wondering if someone’s Uncle Joe has ever stumbled into one and won it all.
Also, a few days ago while playing around on the basketball court, I was on fire from the three point line. It turns out I could have beat a few NBA all stars in at least one round of a three point contest.
I think we need to define “average person with a weeks worth of training?” Are we talking about someone who has literally never seen a bowling ball before or someone who has bowled occasionally at parties and such. Because I think with a weeks worth of training, they would definitely get a few 150+ over a hundred games.
In the spirit of breaking the spirit, then, I submit marathon-running. As an amateur, I spend a week building up my stamina. On the first marathon I run for a quarter-mile (to convince the pro that I’m serious) then fall back and rest for two hours; at the end of that two hours I hop in a car, forfeiting that first match. Immediately afterwards I start the second marathon. I have some chance of winning, if the professional ran their hardest for the first one and doesn’t have the strength to run a second one right away.
Well, then, this puts my amateur darts player suggestion back on the table. Even the pros have a few bad misses in televised games, which opens up the 1-in-a-hundred win potential for a skilled amateur.
Probably worse – the 400m sprinter might trip or get cramp.
Meanwhile for the chess game, the only way I can see it happen is if the pro has to play 100 games consecutively and misses a trivial battery mate, or back rank mate, due to simple fatigue. You’d still need to run this experiment hundreds of times (each time with a hundred games) to get even odds of even this happening though.
The chance of the amatuer simply winning a game by playing better moves for long enough to win a game would be many trillions to one.
That’s true, it’s a different situation entirely. As a reasonable talented amateur I can hit a streak of sub 15-dart finishes and a pro can have a streak of 15+ dart finishes.
A poll a while back found that one in eight men (in the UK, I think) thought they could win a point in a match against Serena Williams.
That might make sense if those who said yes were, in fact, the top 12.5% of tennis players in that group, but I’d bet that they’re not. There is almost certainly a significant Dunning-Kruger curve on that graph.
In high school I was an OK tennis player. If I, in my prime, played a match against Serena now, I’m pretty sure the only time I would touch the ball is when I was serving or when Serena chose to hit me with it.
I can attest to this.
I my University days I became an avid bridge player and began joining duplicate tournaments aroud town. My partner and I were relative noobs and were matched against two older very skilled players. After all the hands were played out, people were shocked that we had just beaten the Canadian champs.
If I remember correctly, it all boiled down to a really wild hand where we agreed on a spades contract but then began looking for slam but were missing 2 Aces. I bailed at 5S, my partner jumped to 6S and was subsequently doubled to which he redoubled. Turns out he was long in spades too and had a void against one of the missing Aces… which came as the opening lead! After pulling trump and setting up a cross-ruff, I claimed.
I like your choice of sport.
One out of hundred games? I would have a chance at mia or at liar’s dice. Risk would be feasible too, but one hundred games would be tediously long. No other professional sport that I could think of.
We must be thinking of different games.
I see no reason why an average person with the weeks worth of training
and a bit - ok, a lot - of luck shouldn’t win 1 game.
Of course it depends on who’s doing the training.
The only times luck is involved in snooker is when playing a shot to open a pulk or any similar situation where a fluke can happen, but that’s rare. There’s no way a hobby player could win a frame against a top 32 pro.
ETA: I googled to no avail, but I think the word “pulk” which we use in German is not the English word for the concept I mean, so maybe sorry. What I mean is a group of red balls close together that must be opened to have a chance to pot in the next shot. Most snooker terms we use in German are untranslated from English, but “pulk” seems to be only a German term, so please help me out with the right term.
I think top ranked tennis players, male or female, would destroy an average joe.
I remember one of the first seasons of The Apprentice that had a guest appearance by Anna Kournikova. She bet any of the men that they couldn’t score a single point against her. She won that bet.
I’ve participated in one ball pinball tournaments where I can easily imagine a top player scoring below an amateur in about one in twenty games.
Too late to edit: I just found that “pulk” is an English word, but it only means a dog-sled. But I’m unable to google the word I’m fishing for.
“pack” is the standard snooker word, and yes, that is one of the few areas of the game that relies somewhat on luck.
Thanks, NB!