Date published: 2019-09-16

Originally published: Here. Excerpt below.

Executive compensation packages have gotten more complicated over time. To take one recent prominent example, Tesla CEO Elon Musk was "paid" around $2.3 billion last year by one valuation method, while actually receiving $0 in guaranteed value.

Indeed, some CEO pay plans are so complicated that a powerful mathematical technique originally developed to understand the behavior of neutrons in an atom bomb explosion is the most effective way to estimate what they are actually worth.

Monte Carlo methods, named for the famous casino, are a class of mathematical techniques for evaluating the possible outcomes of a complicated process that includes some random element. The basic idea in a Monte Carlo problem is to use a computer to simulate the random process many times — often thousands or millions of repetitions — and compare the various outcomes of those simulations.

According to a retrospective article on the development of Monte Carlo methods in the journal Los Alamos Science, Stanislaw Ulam, one of the lead physicists working on the Manhattan Project to develop the first nuclear weapons, took inspiration from analyzing a solitaire card game.

While many card games lend themselves nicely to straightforward direct calculations — calculating the odds of drawing particular poker hands, for example, is a classic exercise in basic probability theory— Ulam realized that trying to directly calculate the probability of a particular solitaire game being winnable in a similar fashion would be difficult or impossible.

That's because drawing a poker hand is a straightforward one-step process of picking up five cards, while evaluating a solitaire game generally involves looking at what happens to an entire card deck over a large number of steps or turns.

Instead of trying to figure out some elaborate formula for understanding the solitaire game, Ulam realized he could instead just play out a large number of solitaire games and count how many games were winnable and ...

Indeed, some CEO pay plans are so complicated that a powerful mathematical technique originally developed to understand the behavior of neutrons in an atom bomb explosion is the most effective way to estimate what they are actually worth.

Monte Carlo methods, named for the famous casino, are a class of mathematical techniques for evaluating the possible outcomes of a complicated process that includes some random element. The basic idea in a Monte Carlo problem is to use a computer to simulate the random process many times — often thousands or millions of repetitions — and compare the various outcomes of those simulations.

According to a retrospective article on the development of Monte Carlo methods in the journal Los Alamos Science, Stanislaw Ulam, one of the lead physicists working on the Manhattan Project to develop the first nuclear weapons, took inspiration from analyzing a solitaire card game.

While many card games lend themselves nicely to straightforward direct calculations — calculating the odds of drawing particular poker hands, for example, is a classic exercise in basic probability theory— Ulam realized that trying to directly calculate the probability of a particular solitaire game being winnable in a similar fashion would be difficult or impossible.

That's because drawing a poker hand is a straightforward one-step process of picking up five cards, while evaluating a solitaire game generally involves looking at what happens to an entire card deck over a large number of steps or turns.

Instead of trying to figure out some elaborate formula for understanding the solitaire game, Ulam realized he could instead just play out a large number of solitaire games and count how many games were winnable and ...

A mathematical technique originally developed to help build the atomic bomb is now used to figure out how much CEO pay packages are worth — like with Elon Musk https://t.co/OFlsHdRXXy #Carlo #Monte #Ulam #tech pic.twitter.com/YTNXWWwOEx

— NUS Trivia | tech news (@NusTrivia) September 16, 2019