What the Odds Mean
Odds are a mathematical calculation of the likelihood of a given outcome. For example, when you toss a fair coin, there are two possible outcomes: the coin will land either heads up or tails up. The likelihood of it landing heads up is 1 in 2. If you wager that a coin will land heads up, you have a fifty-fifty chance of winning the bet.
Figuring out odds is a relatively simple proposition. All you need to know is the total number of possible outcomes. When you toss one coin, there are two possible outcomes. When you toss two coins, there are four possible outcomes: both will land heads up, both will land tails up, the first coin will land heads up and the second coin will land tails up, or the first coin will land tails up and the second coin will land heads up.
Calculating the Odds
The easiest way to calculate this when more than one item is involved is to figure out the possible outcomes for one item — the coin — and multiply the outcomes for each item. So, in our two-coin example, multiply the possible outcomes of one coin (2) by the total number of outcomes for the second coin (2) to get the total possible number of outcomes (4).
Consider rolling a pair of dice, for instance. Each die has six faces, so there are six possible outcomes when you roll one die. If you roll two dice, the number of possible outcomes grows to thirty-six (6 × 6 = 36). If you roll three dice, you suddenly have 216 possible outcomes (6 × 6 = 36 × 6 = 216).
Outcomes and Probability
Once you figure out the possible outcomes, you can determine the probability of any one outcome or series of outcomes occurring. For example, in craps, you can bet that the dice will come up “any craps,” which is a 2, a 3, or a 12. There is only one way to roll a 2 with a pair of dice, and there is only one way to roll a 12. But there are two ways to roll a 3: the first die comes up 1 and the second die comes up 2, or the first die comes up 2 and the second die comes up 1. Thus, there are four possible ways to roll a craps out of thirty-six possible combinations, and the probability of rolling a craps is expressed as a percentage: 4 (the number of possible craps combinations)/36 (the total possible combinations)= 1/9, or 11 percent.
In mathematics, probability is often expressed as a value between zero and one — 0.42, for example. But most of us think of probability as a percentage, with an outcome more likely as its probability approaches 100 percent. To convert mathematical probability values to percentages, move the decimal point two places to the right. Thus, 0.42 becomes 42 percent.
You can use this formula to figure out the probability of virtually any outcome in virtually any game, and to figure out changes in probability. In a single-deck blackjack game, for example, the probability of drawing a given card changes according to how many cards have already been dealt and what those cards are. Suppose there are three players, plus the dealer, at the blackjack table. There are fifty-two cards in the deck, including four aces and sixteen cards that have a value of ten — the 10, jack, queen, and king of hearts, diamonds, spades, and clubs. Assuming you're the first player to receive a card, the odds of you getting an ace as your first card are 4 in 52, or about 7.5 percent (4/52 = .076 = 7.6 percent).
The odds of you getting a 10-value card first are 16 in 52, or about 31 percent (16/52 = .307 = 30.7 percent). The odds change after the first round of cards is dealt. We've got three players plus the dealer in our example, so the first round consists of four cards. Let's say those four cards are a 10, a king, an ace, and another king. Now, let's figure the odds for the second round. The deck now consists of forty-eight cards, including three aces and thirteen 10 value cards. The odds of getting an ace as your second card are now 3 in 48, or 6.25 percent (3/48 = .0625 = 6.25 percent). The odds of getting a 10-value card as your second card are 13 in 48, or 27 percent (13/48 = .270 = 27 percent).