Just over a week after announcing that he has been diagnosed with stage 4 pancreatic cancer, Jeopardy! host Alex Trebek is calling himself a "lucky guy."

In a new video posted to the show's social media channels, Trebek says he has been heartened by the outpouring of support he has received from fans and former show contestants as a result of his announcement.

"I just want to take a few moments so say thanks to the — believe it or not — hundreds of thousands of people who have sent in tweets, texts, e-mails, cards, and letters wishing me well following my recent health announcement," Trebek said in the video. "I've heard from former contestants — even Watson, the IBM computer, sent me a 'get well' card.

"Now, obviously I won't be able to respond to all of you individually, but I did want you to know that I do read everything I receive," Trebek continued. "And I am thankful for the kind words, the prayers, and the advice you have offered, and I'm extremely touched by the warmth you have expressed in your comments to me. I'm a lucky guy."

The legendary game show host first revealed his diagnosis March 6. Trebek admitted that the prognosis for his disease is not "very encouraging" but said he vowed to fight for his life.

"I have to host Jeopardy! for three more years!" Trebek said to add some humor to the news. "So help me. Keep the faith and we'll win. We'll get it done. Thank you."

Trebek has hosted Jeopardy! since 1984, when it was revived by Merv Griffin.

Jeopardy! airs weeknights at 7/6c on ABC.