There is a deck of 100 initially blank cards. The dealer is allowed to write............Would you accept this challenge?

Question

There is a deck of 100 initially blank cards. The dealer is allowed to write ANY positive integer, one per card, leaving none blank. You are then asked to turn over as many cards as you wish. If the last card you turn over is the highest in the deck, you win; otherwise, you lose.

Winning grants you $50, and losing costs you only the $10 you paid to play.

Would you accept this challenge?

Answer 1

Yes

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Divide the deck in half and turn over all lower 50 cards, setting aside the highest number.
Then turn over the other 50 cards, one by one, until you reach a number that is higher than the card you set aside: this is your chosen “high card.”
There is a 50% chance that the highest card is contained in the top 50 cards, and a 50% chance that the second-highest card is contained in the lower 50. Combining the probabilities, you have a 25% chance to win every time.
This means that you’ll lose three out of four games, but for every four games played, you pay $40 while you win one game and $50. Your net profit every four games is $10.