VS.

# Odds vs. Odd

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• Odds

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways (see below), and sometimes the term is used incorrectly to mean simply the probability of an event. Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of the likelihood of some possible event.

If you bet on rolling one of the six sides of a fair die, with a probability of one out of six, the odds are five to one against you (5 to 1), and you would win five times as much as your wager. If you bet six times and win once, you win five times your wager while also losing your wager five times, thus the odds offered here by the bookmaker reflect the probabilities of the die.

In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 5 to 1 mean the first party (normally a bookmaker) stakes six times the amount staked by the second party. In simplest terms, 5 to 1 odds means if you bet a dollar (the "1" in the expression), and you win you get paid five dollars (the "5" in the expression), or 5 times 1. If you bet two dollars you would be paid ten dollars, or 5 times 2. If you bet three dollars and win, you would be paid fifteen dollars, or 5 times 3. If you bet one hundred dollars and win you would be paid five hundred dollars, or 5 times 100. If you lose any of those bets you would lose the dollar, or two dollars, or three dollars, or one hundred dollars.

The odds for a possible event E are directly related to the (known or estimated) statistical probability of that event E. To express odds as a probability, or the other way around, requires a calculation. The natural way to interpret odds for (without calculating anything) is as the ratio of events to non-events in the long run. A simple example is that the (statistical) odds for rolling a three with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 three event for every 5 times the die does not show three (i.e., a 1, 2, 4, 5 or 6). For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 threes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) odds against, the order of the pair is reversed. Hence the odds against rolling a three with a fair die are 5 to 1. The probability of rolling a three with a fair die is the single number 1/6, roughly 0.17. In general, if the odds for event E are

X

{\displaystyle X}

(in favour) to

Y

{\displaystyle Y}

(against), the probability of E occurring is equal to

X

/

(

X

+

Y

)

{\displaystyle X/(X+Y)}

. Conversely, if the probability of E can be expressed as a fraction

M

/

N

{\displaystyle M/N}

, the corresponding odds are

M

{\displaystyle M}

to

N

M

{\displaystyle N-M}

.

The gambling and statistical uses of odds are closely interlinked. If a bet is a fair one, then the odds offered to the gamblers will perfectly reflect relative probabilities. A fair bet that a fair die will roll a three will pay the gambler \$5 for a \$1 wager (and return the bettor his or her wager) in the case of a three and nothing in any other case. The terms of the bet are fair, because on average, five rolls result in something other than a three, at a cost of \$5, for every roll that results in a three and a net payout of \$5. The profit and the expense exactly offset one another and so there is no advantage to gambling over the long run. If the odds being offered to the gamblers do not correspond to probability in this way then one of the parties to the bet has an advantage over the other. Casinos, for example, offer odds that place themselves at an advantage, which is how they guarantee themselves a profit and survive as businesses. The fairness of a particular gamble is more clear in a game involving relatively pure chance, such as the ping-pong ball method used in state lotteries in the United States. It is much harder to judge the fairness of the odds offered in a wager on a sporting event such as a football match.

Wikipedia
• Odds (noun)

The ratio of the probabilities of an event happening to that of it not happening.

"I'd say the odds are strongly in favor of the sun rising tomorrow morning."

• Odds (noun)

The ratio of winnings to stake in betting situations.

• Odds (noun)

plural of odd

Differing from what is usual, ordinary or expected.

"unusual|strange|Thesaurus:strange"

"common|familiar|mediocre|Thesaurus:common"

"She slept in, which was very odd."

Without a corresponding mate in a pair or set; unmatched; mismatched.

"single|mismatched"

"Optimistically, he had a corner of a drawer for odd socks."

"My cat Fluffy has odd eyes: one blue and one brown."

Left over, remaining after the rest have been paired or grouped.

"I'm the odd one out."

Left over or remaining (as a small amount) after counting, payment, etc.

Scattered; occasional, infrequent; not forming part of a set or pattern.

"I don't speak Latin well, so in hearing a dissertation in Latin, I would only be able to make out the odd word of it."

"but for the odd exception"

Not regular or planned.

"He's only worked odd jobs."

Used or employed for odd jobs.

Numerically indivisible by two.

"even"

"The product of odd numbers is also odd."

Numbered with an odd number.

"How do I print only the odd pages?"

About, approximately; somewhat more than (an approximated round number).

"There were thirty-odd people in the room."

Out of the way, secluded.

On the left.

"He served from the odd court."

Singular in excellence; matchless; peerless; outstanding. since the 1400s

• Odd (noun)

An odd number.

"So let's see. There are two evens here and three odds."

• Odd (noun)

Something left over, not forming part of a set.

"I've got three complete sets of these trading cards for sale, plus a few dozen odds."

Wiktionary
• Odds

Difference in favor of one and against another; excess of one of two things or numbers over the other; inequality; advantage; superiority; hence, excess of chances; probability. The odds are often expressed by a ratio; as, the odds are three to one that he will win, i. e. he will win three times out of four

• Odds

Quarrel; dispute; debate; strife; - chiefly in the phrase at odds.

Not paired with another, or remaining over after a pairing; without a mate; unmatched; single; as, an odd shoe; an odd glove.

Not divisible by 2 without a remainder; not capable of being evenly paired, one unit with another; as, 1, 3, 7, 9, 11, etc., are odd numbers.

Left over after a definite round number has been taken or mentioned; indefinitely, but not greatly, exceeding a specified number; extra.

Remaining over; unconnected; detached; fragmentary; hence, occasional; inconsiderable; as, odd jobs; odd minutes; odd trifles.

Different from what is usual or common; unusual; singular; peculiar; unique; strange.

Webster Dictionary
• Odds (noun)

the probability of a specified outcome

• Odds (noun)

the ratio by which one better's wager is greater than that of another;

"he offered odds of two to one"

not divisible by two

not easily explained;

"it is odd that his name is never mentioned"

an indefinite quantity more than that specified;

"invited 30-odd guests"

beyond or deviating from the usual or expected;

"a curious hybrid accent"

"her speech has a funny twang"

"they have some funny ideas about war"

"the peculiar aromatic odor of cloves"

"what a rum fellow"

"singular behavior"

of the remaining member of a pair, of socks e.g.

not used up;

"leftover meatloaf"

"she had a little money left over so she went to a movie"

"some odd dollars left"

"saved the remaining sandwiches for supper"

"unexpended provisions"

Princeton's WordNet