"It was certainly tough to lose. I'll never forget that Bangladesh ends with an 'h' for the rest of my life!" Schneider, 42, tells PEOPLE.
On Wednesday, the final category was "Countries of the World" and the clue read: "The only nation in the world whose name in English ends in an H, it's also one of the 10 most populous."
While Schneider did not provide an answer, Rhone Talsma, a librarian from Chicago, responded correctly with "What is Bangladesh?" At the end of the night, Talsma finished in first place with a score of $29,600 and Schneider finished in second place with $19,600.
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"When I started, my biggest goal was just to win four games. Not only did I end up winning 10 times as many, but I've heard from so many people, especially trans people and their loved ones, about how much it's meant to them to see me succeed, and that's something I will always, always be proud of," the quiz show champion says.
Casey Durkin/Jeopardy Productions, Inc.
Schneider is the first transgender contestant to qualify for the Tournament of Champions, and she's the highest-earning woman in the competition's history, with a total of $1,382,800 from 40 wins.
Schneider is also now the fourth-highest earner in regular season play, after Ken Jennings, James Holzhauer and Matt Amodio.
"Growing up, I always watched, and so did my parents — my dad had tried out for it and nearly got on — so it was always a part of my life," she says. "I've got a good brain for it, so I just sort of felt like, 'It'll probably happen someday.' "
Schneider adds, "This Jeopardy! run is most likely what I will be remembered for, and if so, I'd be quite content to have that as my legacy."
That legacy has also been praised by GLAAD's Director of Transgender Representation, Nick Adams. Following Schneider's loss on Wednesday, Adams issued a statement about her history-making run.
"Amy Schneider has given Jeopardy!'s nine million-plus nightly viewers a historic 40-game run full of masterful gameplay, while her media interviews and Twitter recaps of each game have given fans a glimpse into her life as a smart, charming transgender woman with a girlfriend and a rescue cat named Meep," Adams said. "Her visibility has been a bright spot, allowing millions of people to root for her success and start conversations about being transgender at a time when proposed bills in states like Arizona, Iowa, Indiana, Oklahoma, South Dakota, and Amy's home state Ohio, are targeting transgender Americans for discrimination. Amy's achievement will be celebrated for years to come by Jeopardy! fans and LGBTQ people everywhere."
Now that Schneider has a bit more free time, she's looking forward to spending some of her $1,382,800 winnings with partner Genevieve Lewis.
"We're going to take a trip to Ireland and we're thinking about where else we might go with it," she says. "And buying some fancy designer clothes I think is definitely, definitely on the list."
Schneider will return for the show's Tournament of Champions this fall.