# Understanding the Role of Probability

Millions of merry gamblers frequent casinos all over the world every day without a clear understanding of one important concept – probability. Mastering one of the more complex branches of mathematics isn’t necessary for successful gambling. But an elementary understanding of probability is certainly helpful in making sound gambling choices.
Probability is the study of the laws of chance, the identification of how often certain events can be expected to occur. For example, to express the probability
that a coin will turn up heads, you can give the result in numerous ways, such as a
– Ratio – 1 in 2 times
– Fraction – Y2 or half the time
– Percentage – 50 percent
– Decimal- .50, which is the same as 50 percent
– Odds – 1 to 1

Odds expresses the number of times something won’t happen next to the number of times it will happen. So, 1-to-1odds means the event is an even money event; it has an equal chance of occurring or not occurring. This section looks a bit closer at probability’s role in casino gambling. Identifying independent events
Another important term to understand here is independent outcomes. Being independent has nothing to do with successfully ditching your loser boyfriend in the keno lounge. In gambling, independent refers to events (such as roulette spins or dice throws) that aren’t affected by any previous results. Craps and roulette are great examples. The dice and roulette table ball don’t have a tiny brain inside, so each new throw or spin is independent of all previous turns. In other words, the dice or ball doesn’t know what numbers are running hot or cold, so the probability of outcome for each and every spin is exactly the same.
Slot machines are also independent. Recent jackpots do not change the likelihood of the same combination coming up again. If your chances of lining up three cherries are 5,000 to 1and you just hit the jackpot, the three cherries have exactly the same chances of appearing on the very next spin.

Recognising dependent events
So you may be asking yourself, what constitutes a nonindependent or dependent event? Dependent events are occurrences that are more or less likely based on the previous occurrences. Imagine a bag of five black balls and five red balls. Before you pull a ball out, you know you have a 50 percent chance of pulling out a black ball and the same odds of pulling out a red ball. Then you reach in and pull out one red ball and toss it aside. Now the odds have changed – you no longer have a 50 percent chance of pulling either ball. Your chances of pulling out a black ball are now greater (56 percent).
So in some situations, the past does affect the future. Another classic example is the game of blackjack. Because cards are removed after they’re played, the remaining composition of the deck changes. For example, your chances for getting a blackjack drop dramatically when a disproportionate number of aces are used up.
Almost all casino games consist of cards, dice, spinning wheels, or reels. These games almost always yield independent events. Blackjack is the rare exception, which is the main reason for its popularity.