Solving optimal stopping problems with statistical algorithms

Las Vegas and Everyday Life

Just as there are correct and incorrect ways of winning at certain games in Las Vegas – and although I am amazed at how few people actually take them into consideration to at least statistically give the casino as little chance as possible to win – it is important in everyday life to keep the upper hand in randomly driven processes and always consider the most likely possible outcome of such a situation.

However, what is demonstrably the optimal strategy, if you do the math, is sometimes of little practical value for stop problems. In a casino that pays back triple your bet after tossing a coin with a winning percentage of 50 percent, the theoretically correct approach would be to keep on playing and never quit. But, as you can imagine, the players would go home bankrupt every time if they followed this strategy.

Infos

  1. Secretary problem: https://en.wikipedia.org/wiki/Secretary_problem
  2. Optimal stopping: https://en.wikipedia.org/wiki/Optimal_stopping
  3. Christian, Brian, and Tom Griffiths. Algorithms to Live By: The Computer Science of Human Decisions. Henry Holt and Co. April 2016: http://algorithmstoliveby.com
  4. Vitality curve: https://en.wikipedia.org/wiki/Vitality_curve
  5. Listings for this article: ftp://ftp.linux-magazine.com/pub/listings/magazine/190

The Author

Mike Schilli works as a software engineer in the San Francisco Bay Area. He can be contacted at mailto:mschilli@perlmeister.com. Mike's homepage can be found at http://perlmeister.com.

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