The problem posed here is actually a variation of a classic riddle known as the “Tax Collector” problem. The modern version was popularized by Dan Finkel - the author of this riddle - in the New York Times Numberplay blog in 2015. You can read the original puzzle and a discussion of its solution here.

The math educator Raj Shah also made a video posing the problem, available here.

An older version of the problem is discussed in some detail here. 

The 538 Riddler column riffed on this puzzle as well, with another interesting variation. Read it here.

Practice some variations on the riddle with these problems below:
-What’s the largest sum you could take if you weren’t concerned about getting the 2, 6, or 10? 

-Try playing the game with 24 cards instead of 23. How does the outcome change? Play with larger and smaller decks (i.e., 12 cards, or 40 cards). Do larger decks tend to favor you, or favor Fate? Is there any number of cards that would be unwinnable for you?