How
to Calculate Lottery Odds
Calculate
the odds of winning the lottery with the lottery calculator below,
it will return your answer with a full and detailed explanation.
Don't
forget you can dramatically increase your lottery odds
by using the unique e-lottery
syndicate system
Enter
the numbers into the form below:
This Lottery Odds Calculator submits your numbers
to the webmath
lottery odds calculator script and returns the results in a new
window.
Sample Results:
A Sample Response based on 6 numbers drawn, low
number 1 and high number 49:
You want to calculate your odds at winning the
lottery given:
* You
must choose a sequence of 6 numbers correctly to win.
* The lowest number you can choose is 1
* The highest number you can choose is 49
* A given number can only be chosen once per try (per lottery
ticket, etc.)
When
you select your 1st number, you have 49 numbers to choose from,
and...
...a
1 in 49 chance of picking the right one.
(Mathematically,
1 in 49 is represented by the numerical fraction 1/49 or 0.020408.)
When
you select your 2nd number, you have 48 numbers to choose from,
and...
...a
1 in 48 chance of picking the right one.
(Mathematically,
1 in 48 is represented by the numerical fraction 1/48 or 0.020833.)
When
you select your 3rd number, you have 47 numbers to choose from,
and...
...a
1 in 47 chance of picking the right one.
(Mathematically,
1 in 47 is represented by the numerical fraction 1/47 or 0.021277.)
When
you select your 4th number, you have 46 numbers to choose from,
and...
...a
1 in 46 chance of picking the right one.
(Mathematically,
1 in 46 is represented by the numerical fraction 1/46 or 0.021739.)
When
you select your 5th number, you have 45 numbers to choose from,
and...
...a
1 in 45 chance of picking the right one.
(Mathematically,
1 in 45 is represented by the numerical fraction 1/45 or 0.022222.)
When
you select your 6th number, you have 44 numbers to choose from,
and...
...a
1 in 44 chance of picking the right one.
(Mathematically,
1 in 44 is represented by the numerical fraction 1/44 or 0.022727.)
In order
to win, you have to pick the first number right AND the second
number right AND the third number right, etc. In the language
of statistics, AND usually means to multiply.
So, to
figure out your odds of winning, multiply together all of the
fractional odds of picking a given number correctly, as stated
by the red fractions above.
1/49
× 1/48 × 1/47 × 1/46 × 1/45 × 1/44
= 1/10068347520
So, at
this point, your odds of winning are 1 in 10068347520. But, since
you can choose your winning numbers in any order, your chances
of winning are somewhat better than this. Your chance betters
by the number of different ways that a sequence of 6 numbers can
be written down, which for 6 numbers is 6! (6 factorial) or 720.
Divide 10068347520 by 720 to account for this, to get 13983816.
In other
words, there are 720 different ways that the 6 numbers you choose
can be filled out on your lottery ticket--if you choose your 6
numbers correctly, any of these ways will make a winning ticket.
That's
it! You have a
1 in
13,983,816
chance
of winning the lottery you described.
(How
do I pronounce this number?)
Here
are some other odds for the sake of comparison:
* You
have about a 1 in 2,000,000 chance of being struck by lightning.
* A pregnant woman has a 1 in 705,000 chance of giving birth to
quadruplets.
* Someone eating an oyster has a 1 in 12,000 chance of finding
a pearl inside of it.
Now,
lottery odds can be pretty incomprehensible. How can we possibly
have any "feeling" for the number 13,983,816? To help
you with this, here's a little experiment you can try to "get
a handle on" what a 1 in 13,983,816 chance really means.
1. Get
a piece of rope or string, that's 39 feet long.
2. In
a wide open area, arrange the rope or string in a circle, end
to end, the best you can.
3. Get
a single grain of sand or dirt (use tweezers!) and place it anywhere
you wish inside the circle.
4. Get
a second grain of sand. Close your eyes, and "disorient"
yourself as to where the grain of sand is that you placed inside
of the circle (have someone spin you around or something!).
5. While
you're inside the circle, drop the second grain of sand from 1
foot up.
6. Your
chances of hitting the first grain of sand with the second is
roughly equal to the odds of "1 in 13,983,816."
7. If
the rope's length mentioned in #1 is a little unreasonable, for
every foot above the circle that you drop the second grain of
sand, you can reduce the length of the string by the same amount.
For example, if you dropped the second grain of sand from a ladder
10 feet up, you'd need a length of string that is 10 times shorter
than the one in #1, or a 39/10 = 3.85236 foot long piece of string.
Good
luck! And sorry to say that the only way to increase your chances
of winning is to buy more tickets! Choosing birthdays, your age,
addresses, years, phone numbers, etc. does not help at all!
