Expected Value Made Simple

From the Chicago Tribune Business section last week, via BettingExpert.com, this is a good article on value - with a little investment advice thrown in.

For gamblers and investors alike, expected value is the name of the game

August 07, 2012|By Elliot Raphaelson, Tribune Media Services | The Savings Game

What does casino owner Sheldon Adelson have in common with Bill Gross, co-chief investment officer of the giant money management firm Pimco? Many of you will probably say not much. I believe there is something, and it is important. They both understand the concept of expected value.

Expected value is the sum of each monetary outcome multiplied by its probability. Here is an example: A casino pays $30 at the craps table for a $1 wager if two sixes are rolled. The expected value is 1/36 -- the probability of the only roll that pays off -- times $30, or $0.83. This means the casino has a 17 percent edge on this bet.

As a successful casino owner, Adelson clearly understands the profitability of his games, especially slot machines. He will make sure "the house" has the edge on every bet.

There are very few ways for a gambler to make a profit in casinos because most games have negative expected value. For example, most slot machines in the United States return approximately 90 cents on average for a $1 bet. This gives the casino has a 10 percent edge on average for each bet. If you bet $1 in a slot machine 100 times in an hour, your expected loss (the casino's expected gain) is $10. Over a few days, if you "invest" for 10 hours your expected loss would be $100.

Any single bet can force a casino to pay out, but on a long-term basis, it will make a lot of money off almost all gamblers. I say almost all because some blackjack players have succeeded in making a substantial profit by "counting cards." After college and before his Wall Street career, Gross reportedly was one of them.

Card counting is a complicated art, but here's the basic idea: A card counter assigns a value to each card played. If at some point there is a predominance of high cards (aces, tens and picture cards) remaining in the deck to be played, the card counter has an advantage, and increases the size of his bet.

I don't recommend becoming a counter in blackjack. It is very difficult, and casinos will bar you if you become good at it. You would have a slight long-term edge, but you would have to be willing to invest a substantial amount of money in order to win.

Most other games in Vegas, or any other casino, do not provide you with a positive expected value. Do some research before you bet in a casino and determine the negative expected value of any game you play. (A good place to do research online is Wizardofodds.com.) Games that it is possible to play with positive expected value are poker, horse racing and sports betting, but to succeed you would have to have expertise or inside information that most individuals don't have. (If you want to learn more, I recommend Mike Caro's books.)

When I visit my grocery store, I notice a lot of people "investing" serious money in lottery tickets, even though the expected loss of purchasing lottery tickets is about 50 percent (except when there is a large carryover). This means that if you spend $1,000 annually on lottery tickets, you can expect an average loss of $500 per year. That money would be better spent or invested in other ways.

Bill Gross has gone from counting cards to managing highly successful bond funds. One of them, Pimco's Total Return Fund, has done well by conservative investors (count me among them). Return on the fund's Class D shares year-to-date as of August 6 was 7.5 percent. The five-year return measured from December 31, 2011 was 7.7 percent, and the 10-year return was 6.4 percent.

Gross wrote in his August investment outlook column that he does not believe that common stock investments will do as well in the future as they have in the past. He may be wrong about that, of course. He has made some mistakes in the past, but not many.

Although investments in common stocks and bonds are not foolproof, on a long-term basis, they should provide a positive expected return, especially in contrast to lotteries and casino games.

Long-term investors should have some money invested in the stock market, such as S&P 500 index funds or other broad-based index stock funds. I also believe that older investors, either close to retirement or already retired, should have a substantial portion of their investments in no-load intermediate-term bond index funds and other intermediate-term high-quality bond funds, such as those offered by Vanguard, Fidelity and T. Rowe Price.

You will not become rich with these investments, but you will do much better than you would with lottery tickets or slot machines. Adelson has enough money.