(source)
From Freddie Simmons, a guessing game:
Take a standard deck of cards, and pull out the numbered cards from one suit (the cards 2 through 10). Shuffle them, and then lay them face down in a row. Flip over the first card. Now guess whether the next card in the row is bigger or smaller. If youâre right, keep going.
If you play this game optimally, whatâs the probability that you can get to the end without making any mistakes?
Extra credit: What if there were more cards â 2 through 20, or 2 through 100? How do your chances of getting to the end change?
After running a simulation millions of times, the probability of âwinningâ with a deck of cards 2 through 10 is:
~17%.
Lowest Card:
Highest Card:
Simulations:
Running with deck of 2 - 10...