published: September, 28th 2017
What do Los Alamos, Solitaire, and Your Portfolio have in Common?
By: Rick Wedell, Chief Investment Officer
The year is 1946, and Stan Ulam is recovering from encephalitis. To pass the time, he starts work on solving a math problem (he’s just that kind of guy). Specifically, he asks himself, “what are the odds of winning in solitaire with a 52-card deck, shuffled randomly?”
Now Stan is not your ordinary guy – he’s a mathematician who will, in 1951, help design the mechanism which serves as the basis for all thermonuclear weapons. But right now he’s solving card game math problems in his spare time.
Stan wrestles with this problem, laying out various equations of combinatorial and conditional probabilities, as he attempts to come up with an equation that will calculate the solution. And then a thought occurs to him – what if instead of spending time trying to solve the problem directly, he instead plays a couple of hundred games of solitaire and keeps track of how frequently he won or lost? His observed winning rate should be pretty close to his odds of winning, even if he cannot solve it out in equation form.
This idea is revolutionary, and while playing a couple of card games sounds simple, the rapidly expanding field of computers paves the way for these types of calculations on much more advanced problems. As Stan is a scientist at Los Alamos, the initial application of the technique is on nuclear weapons, particularly neutron diffusion. Since nearly everything that is worked on at Los Alamos is classified, the technique is given the code name “Monte Carlo” – apparently Stan’s uncle is a fan of the casinos located there.
Fast forward to today, and Monte Carlo analysis is used in a wide range of fields, from engineering to artificial intelligence, and it forms the basis of a lot of the work that we do in analyzing investment portfolios and strategies.
Oh, and in case you were wondering, the odds of being dealt a hand that you can theoretically win in solitaire are about 79%, however in practice good players generally only win ~43% of the time (as wrong moves early in the game make the deck unwinnable in the later stages).
Monte Carlo Analysis in Investments
So how does playing a game repeatedly impact your portfolio, or your retirement savings strategy? I was recently working with Julie, who has been setting aside money to fund her retirement. Her core question, echoed by countless others, has always been - “will this be enough money to maintain my lifestyle?”
That’s a hard question to answer. It not only depends on how much her investments earn, but also how much she saves, inflation rates, and how much she wishes to withdraw. It incorporates a large amount of the unknown – how frequently will bear markets happen during her retirement years, and how severe will those be?
Julie, who is a spry 52, has a few savings accounts that already total about $400,000. As a nurse at a local hospital, she is planning to continue working and save about $20,000 per year out of her income for the next 10-15 years. In retirement, she would like to withdraw about $40,000 per year out of the portfolio, adjusted for inflation. Will that work?
Although Julie probably doesn’t want to hear this, her retirement savings strategy is not unlike a game of solitaire, in that whether or not she is successful will depend in part on the hand that she is dealt – i.e. the path of the market over the course of her retirement. So why not use a computer to simulate Julie’s “hand” a couple of thousand times based on her savings rate, withdrawal rate, life expectancy, etc.?
For every trial of the game, we use a random number generator in each year of the trial to predict the performance of her portfolio for that year within certain probabilistic ranges, depending upon her asset allocation, the expected volatility of those asset classes, and their correlations with each other. If, at the end of the trial, her portfolio has more than $1, we’ll consider it a win! If she winds up winning more than 75% of the time, she has a fairly good idea that her investment and savings strategy will meet her goals. If not, she may want to make some changes to her savings, her investments, her withdrawals, or all of the above to attempt to improve her odds.
That, in a nutshell, is precisely what we do when we analyze your probability of success in saving towards a goal, be it for retirement, education, a new home, or anything else you ask for help with. It’s also how we evaluate things like portfolio diversification, asset class allocation, or optimal investment strategies.
In Julie’s case, we were able to offer different savings and withdrawal strategies that changed her odds of success, and worked with her to choose one that seemed most appropriate. As the years go by, we’ll continue to check in on how Julie’s game is actually going, and if we can get a little more or less aggressive based upon her hand, we’ll make those adjustments as needed.
In the meantime, when was the last time that you took a look at the odds of winning your game?
Content in this material is for general information only and not intended to provide specific advice or recommendations for any individual. No strategy assures success or protects against loss. Investing involves risk including loss of principal.
Rick Wedell is not affiliated with LPL Financial.
 Eckhardt, Roger (1987). "Stan Ulam, John von Neumann, and the Monte Carlo method" (PDF). Los Alamos Science, No 15.
 “The Application of Human Monte Carlo to the Chances of Winning Klondike Solitaire” http://www.jupiterscientific.org/sciinfo/KlondikeSolitaireReport.html
 Names and details of the situation have been changed – you get the idea.