Probability and Stats

Question

You are offered a chance to play a game. The rules are simple. There are 100 cards, face down. Fifty-five of the cards say "win" and 45 of the cards say "lose." You begin with a bankroll of $10,000. You must bet one-half of your money on each card turned over, and you either win or lose that amount based on what the card says. At the end of the game, all the cards have been turned over. How much money do you have at the end of the game?

 

Answer 1

55% chance of winning, 45% of losing 11 win cards for 9 lose cards

100 cards

bet 1/2 each time start with 10K

end with how much?? on average, expected winnings?

1st card win 5K

2nd card lose 7.5K

3rd card win half 7.5K = 3.75K now have 11.25K

4th card lose half = 5.625K down to 5.625K

you've won about 5/8 K over what you started with

do that 25 times and you win 25x5/8K = 125/8K = 15 5/8K

add the initial 5K and you end with 21. 5/8K = $21,625 minimum expectation

first 20 cards have 11 wins and 9 losses, 2 more wins than losses so you'll likely end with more than 21 5/8K

maybe 30K+