~Before you
can get the odds related to an event, you have to get the
probability of the event. For example, say the probability of an event
comes out to 3/5. First decide if this is greater than
1/2, that's .5 as a decimal. If it is, then the odds are in favor, if not, the odds are against.
~For this example, 3/5 =.6 so the odds are in favor (event is likely to occur). Now, to state them. Look at the bottom number of the probability, that is 5. Consider this the
number of times this experiment is done. The event should theoretically occur 3 times (top number) and will not occur 2 times.
So, the odds are 3 to 2 infavor. (3:2 infavor)
~Let's do another example: Say the probability of an event comes out to 17/39. If you divide 17 by 39 it will be less than .5,
so the event is unlikely to occur, so the odds will
be against the event occurring. Now, consider doing the experiment
39 times (bottom number). This event will theoretically occur 17 times
and will not occur 22 times. So, the odds are against this event 22 to
17. (22:17 against)
~Note: the two numbers of the odds always add to the bottom
number of the probability and the bigger number is always first.
You should always indicated whether or not the odds are infavor or
against the event occurring, however, in many cases it would be obvious
and not stated (i.e.,winning a lottery or getting a jackpot on a slot
machine).
~Note: In the real world, odds are stated in different forms.
Sport books at casinos will give numbers on events like +160 (bet $100
to win $160) or -130 (bet $130 to win $100). Also, for horse racing,
you'll see a smaller number first, like 2-7. A strong favorite will
have this type of listing. This means that you must bet $7 to win $2. A
long shot would have odds like 20-1 or 40-1.
See Sports Betting
~Note: Payoff odds are different from the real odds. For
example, at a casino, if you bet on a number on a roulette wheel and
win, the casino will pay you $35 for every $1 you bet. (payoff is
35:1). The real odds are 37:1, since the probability of winning on any
number is 1/38. So, to compute the payoff odds for any activity, simply
state your net profit to the amount bet.
~Note: Odds can also be used to determine the fairness of a
game. If the odds are exactly met, no one wins in the long run. No one
has an advantage. The game is considered fair. However, Casinos would
quickly go out of business. For example, at a carnival, the operator of
a booth will pay you $4 if you roll a 7 with an honest pair of dice.
You must pay $1 to play. Is this fair? Let's see. P(7)=6/36=1/6 (from
the dice triangle). So, the odds are against rolling a 7 and they are 5
to 1. No! Not Fair! That booth operator should pay you $5, not $4.
However, this is reasonable, since he or she is in a business to make
money. I will often buy a lottery ticket if the jackpot is huge and $1
is a good bet. (i.e., if the odds are 175 million to 1 against and the
jackpot is greater than 175 million).