Gambling and Probability

Although most of our students will not grow up to be professional gamblers, the study of probability involved in gambling is worth looking at since it is one way to peak student interest.

I know a guy who used to live in Los Angeles before moving up to Alaska.  At that point, he'd pop over to Las Vegas to earn extra money gambling.  He said the reason he never became a professional was he needed to spend time with his kids. 

Its interesting what things a gambler has to keep in mind while gambling.  I'm not talking about the old folks who hit the casinos once a month, or those who hit a gambling establishment occasionally.  I'm talking about those people who make a regular income with the game of chance.

There are three things both the casinos and the gambler must consider about the game.  First, they are dealing with definite possibilities.  Second, the expected value or the amount of money one can expect to get from the game.  Finally, the volitility index or standard deviation when the game is played.

Lets look at these in more detail.  As stated there are definite probabilities within the game.  A gambler knows the probabilities depend on the number of outcomes or sample space.  When you roll a six sided die you have a one in six chance of landing on a specific number but when you are talking poker which uses multiple decks, the probabilities are quite small.  In poker, trying to draw a four in five card is only 0.00024 while drawing a flush is even smaller.  Knowing these odds, helps guide a professional's betting choices.

A second factor in gambling is the expected return per game.  In other words, if the game were based on flipping a coin where you get $1.00 every time the coin comes up heads or  you lose $1.00 every time you get a tail, you would expect to end up with nothing because the probability is 50/50.  Mathematically, it is EV = (.5(1.00) + .5(-1.00)) = 0. Because the odds are equal, this situation is considered fair because no one has the advantage. 

If on the other hand the dealer gave you $1.50 every time a head came up and you lost $1.00 every time a tail came up the odds would change to EV = (.5(1.50) + .5(-1.00)) = .25 or you'd be 25 cents richer per game on average.  This means that for every 100 games played, you'd expect to be $25 ahead.

Usually, gambling casinos have negative EV's so they have the advantage.  They want to have enough money to pay all their bills.  Even thought the EV is negative overall, professional gamblers still come to play because the actual amount they win is often different than the theoretical or EV. 

The volatility index or the standard deviation is what gamblers are concerned with.  This tells them whether they can win or loose a bit more than what is normally expected. They use the deviation for a specific number of rounds to help them decide when to continue or when to stop playing.

Furthermore, its not just mathematical odds, its also their ability to read the body language of the other players to determine if they should stay in the game or fold.  Its not a straight calculation because there is a human element.

Let me know what you think, I'd love to know.  Have a great day.