Clue to Puzzle #14: 52 Cards Win a Dollar
This puzzle is really very hard. It's a puzzle though that you can make decent progress with long before getting a full answer. I cover this at length in the main answer page but for this hints page I'm going to breeze over that and go straight to giving clues to the final solution. Quant experts read on.
If you're going to solve this the following might be considered prerequisite.
- We can't lose. We can always play to zero.
- I'll quit when I get 'x' dollars pays the best return for x=4
- Consider the case where I am one dollar up with one card left to draw. I should always quit here.
- I'll quit when i get x dollars ahead, where x is static, is not an adequate rule.
At this point I'm dangerously close to giving too much away so feel free to stop. We essentially now have a cash position for each point in the game and the probabilities of moving to a better or worse position. We need to convert that into an expected return and compare the expected return from gambling to our current cash position.
The final clue, and feel free not to read on.... ....The expected return should be calculate as a probability weighting of the expected returns from the possible outcomes of the gamble. It's helpful to start at the end and work backwards.
© Nigel Coldwell 2004 - – The questions on this site may be reproduced without further permission, I do not claim copyright over them. The answers are mine and may not be reproduced without my expressed prior consent. Please inquire using the link at the top of the page. Secure version of this page.