How to calculate your odds of winning the lottery

Many people want to know how to calculate the odds of winning a lottery.  This simple example can help you determine your odds of winning any lottery.

We’ll use the 5/39 lottery that operates in several USA states (like CA as “Fantasy Five”) as an average lottery in our example. To win the lottery grand prize you have to select all five numbers exactly as drawn in the daily contest.

To understand how to calculate your chances of winning this lottery one simply has to calculate the pool of potential numbers that you as a contestant have available to select.  Then, you have to divide that pool of numbers by the total number opprtunities that you have to win.

That is, the pool/opportunities = odds of winning

  • When you select the first number, you have a one in 39 chance of selecting a correct number.
  • When you select the second number, you have one less in the pool of potential numbers available for your selection.
  • To choose the second number you have a one in (39 times 38)= 1,482 chance of getting them both correct.
  • When you select the third number, you have one less in the pool of potential numbers available for your selection.
  • To pick the third number you have a one in (39 x 38 x 37) = 54,834 chance of getting all three of them correctly.
  • When you select the fourth number, you have one less in the pool of potential numbers available for your selection.
  • To pick the fourth number you have a one in (39 x 38 x 37 x 36) = 1,974,024 chance of getting all four of them correct.
  • When you select, the fifth number you have one less in the pool of potential numbers available for your selection.
  • To pick the fifth number you have a one in (39 x 38 x 37 x 36 x 35) = 69,090,840 chance of getting all five of them correct.

Therefore, total pool of numbers for 5/39 is 69,090,840.

To calculate the opportunities, simply multiply the the total number of chances that you have together (in this case it is referred to as 5! or 5 factorial).

Since you pick 5 numbers, the opportunities equal 5 x 4 x 3 x 2 x 1 = 120.

Therefore, the odds of winning all 5 of the numbers in a 5/39 lottery is = pool/opportunities = 69,090,840/120 = 575,757. 

That is, you have 1 chance out of 575,757 chance of getting all 5 numbers correct in a 5/39 lottery.

Using the above method of calculation for lower number wins, you can see that your odds are as follows:

All 5 of 5 winning numbers      1 in 575,757
Any 4 of 5 winning numbers    1 in 3,387
Any 3 of 5 winning numbers    1 in 103
Any 2 of 5 winning numbers    1 in 10 

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Pick 3 Game: Statistics and a Winning Lottery System

In Pick 3, there are one thousand numbers consisting of three individual digits from 0-0-0 through 9-9-9 populated from the digits 0123456789.

We call numbers with three unique digits “Unmatched” 1-2-3.
We call numbers with two unique digits “Doubles” 1-2-2.
We call numbers with one unique digit “Triples” 2-2-2.

Breaking down the One Thousand Pick-3 numbers we find . . .

Unmatched: 720 Straight numbers = 72% percent = 120 Boxed.
Doubles: 270 Straight numbers = 27% percent = 90 Boxed.
Triples: 10 Straight numbers = 1% percent = no Boxed.

The game pays for numbers correctly predicted and played as “Straight” which means the digits are drawn in the exact order as played. And “Box” which means the same digits as drawn, but in any order. For example, if 2-1-2 were drawn you would have had to play 2-1-2 to win Straight or one of 1-2-2, 2-1-2, 2-2-1 to win Box. Box pays a third to a sixth of Straight because Unmatched numbers have six ways of positioning the digits, Doubles have three. Triples, there is only Straight.

Unlike the larger Pick-5 and Pick-6 games, the Box prize is not a consolation for having the correct digits in the wrong order. It is a totally separate play independent of the Straight play. Some states allow the front or back Pair to be played “Straight” these are also totally independent plays.

Because the Pick-3 digits are pictured as “numbers” 0123456789 we can treat these identifiers as if numbers for the purpose of a further breakdown into “Odd” and “Even” configurations.

Odd = 1 3 5 7 9
Even = 0 2 4 6 8

All the numbers fall into four groups based on Odd/Even.

All Odd 0-2-4 = O-O-O = 125 numbers = 12.5% = 35 Box = A group
All Even 1-3-5 = E-E-E = 125 numbers = 12.5% = 35 Box = B group
More Odd 1-3-4 = O-O-E = 375 numbers = 37.5% = 75 Box = C group
More Even 0-2-3 = E-E-O = 375 numbers = 37.5% = 75 Box = D group

The A group

There are 35 pure Odd Box numbers. There are 5 Triples.
111, 333, 555, 777, 999
There are 10 Unmatched Odd Box numbers.
135, 137, 139, 157, 159, 179, 357, 359, 379, 579
There are 20 Double Odd Box numbers.
113, 115, 117, 119, 133, 155, 177, 199, 335, 337, 339, 355, 377, 399, 557, 559, 577, 599, 779, 799

The B group

There are 35 pure Even Box numbers. There are 5 Triples. 000, 222, 444, 666, 888
There are 10 Unmatched Even Box numbers. 024, 026, 028, 046, 048, 068, 246, 248, 268, 468
There are 20 Double Even Box numbers.
002, 004, 006, 008, 022, 044, 066, 088, 224, 226, 228, 244, 266, 288, 446, 448, 466, 488, 668, 688

The C group

There are 75 leaning toward Odd numbers.
Unmatched 50
013, 123, 134, 136, 138, 015, 125, 145, 156, 158, 017, 127, 147, 167, 178, 019, 129, 149, 169, 189, 035, 235, 345, 356, 358, 037, 237, 347, 367, 378, 039, 239, 349, 369, 389, 057, 257, 457, 567, 578, 059, 259, 459, 569, 589, 079, 279, 479, 679, 789
Doubles 25
011, 112, 114, 116, 118, 033, 233, 334, 336, 338, 055, 255, 455, 556, 558B, 077, 277, 477, 677, 778, 099, 299, 499, 699, 899

The D group

There are 75 leaning toward Even numbers. Unmatched 50
012, 023, 025, 027, 029, 014, 034, 045, 047, 049, 016, 036, 056, 067, 069, 018, 038, 058, 078, 089, 124, 234, 245, 247, 249, 126, 236, 256, 267, 279
128, 238, 258, 278, 289, 146, 346, 456, 467, 489, 148, 348, 458, 478, 489m 168, 368, 568, 678, 689
Doubles 25
001, 122, 144, 166, 188, 003, 223, 344, 366, 388, 005, 225, 445, 566, 588, 007, 227, 447, 667, 788, 009, 229, 449, 788, 889

How to make a winning lottery system

Buying all one thousand combinations Straight for a dollar per play would cost $1000 and return $500.

Buying all 210 Boxed combinations for a dollar per play would cost $210 and return either $80 for Unmatched or $160 for a Double.

Buying all 120 Unmatched Box combinations for a dollar per play would cost $120 and return $80 two times in three.

Buying all 90 Doubles Boxed combinations for a dollar per play would cost $90 and return $160, but you can only expect Doubles to be drawn one time in three to four draws.

To make a Pick-3 system work, the system author has to setup conditions where a series of correct choices by the user will result in a win. In other words, the choices you make will determine whether you win or lose.

In this system there is one to four choices to be made correctly in order to profit at Pick-3.

  1. The first choice is whether to play today at all. This is the only way to deal with days when there is no clear path. It is always better not to play then to lose as the difference doesn’t have to be made up out of future wins. It’s hard to recover when losing negates the value of future wins, so don’tplay when the signs don’t point to a group: A, B, C, D.
  2. The second decision is whether unmatched or doubles will be drawn. As you can see, we can quickly eliminate a lot of numbers when we decide to play only unmatched or only doubles.
  3. The third choice allows for ignoring the second decision if choice isn’t clear and requires one of the four groups be chosen for play, the: A, B, C, or D group.
  4. The forth choice can be skipped if groups A or B were chosen, but should be applied if either C or D is expected to contain the winning number and the second decision was skipped. The forth choice is to eliminate one or two digits out of the ten. This means you don’t play any number containing those digit(s), thus 15 - 30 numbers are eliminated out of the 75.

Other rules to follow:

The usual charting methods should be applied tracking the four groups’ skips and hits in the hopes of determining which is due in the next draw. You don’t have to pick between unmatched and doubles, but the profits improve when you do so correctly.

The digits should be tracked so the dead numbers can be eliminated when necessary.

Tracking will demonstrate that you shouldn’t play the same group back to back. They will occasionally come in that way, but you want to play what happens most often, not occasionally.

Doubles tend to come in clusters, watch for a series of 3-5.

Unmatched draws to end with several Doubles.

All Odd or all Even are due an average of 1 in 8 to 10 draws.

Two digits repeating are due an average of 1 in 8 to 10 draws.

A Double repeating its two digits averages 1 in 20-25 draws.

Triples are expected once every 99 draws, see if they either hit more often in your game or return with a second hit within a third of the time they were out since their last draw. Sort of a leap frog effect to watch for.

If positive about doubles being due, play all three of their variations Straight at a dollar each for a $500 win.

If you find you can’t seem to win often enough to be useful, either you aren’t trying hard enough or it’s a game you shouldn’t be playing.  Don’t forget this.

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A Winning Pick 3 Strategy - Keypad based

One interesting strategy for winning Pick 3 is one that relies on keypad patterns. Keypads are like the numeric key pad on the right hand side of your computer keyboard. Many people feel that keypad patterns are profitable way to play the Pick 3 lottery and beat it.

The Keypad System only works for 3 unique numbers so it is only to be used on days all different digits are drawn (0-1-2).  Itdoes not work when doubles (0-2-2) or triples (2-2-2) are drawn.  You are advised not to play the Keypad System on days doubles or triples are due.

A standard computer keypad looks something like this . . .

 

The winning numbers are derived from the following winning keypad patterns:

Corners 16 numbers
Upper Left  (7854) 7-8-5 8-5-4 5-4-7 4-7-8
Upper Right (8965) 8-9-6 9-6-5 6-5-8 5-8-9
Lower Left  (4521) 4-5-2 5-2-1 2-1-4 1-4-5
Lower Right (5632) 5-6-3 6-3-2 3-2-5 2-5-6

V’s 8 numbers
Left  V’s 7-5-1 8-4-2
Upper V’s 7-5-9 4-8-6
Right V’s 9-5-3 8-6 2
Lower V’s 1-5-3 4-2-6

Bent L’s 16 numbers
Left  L’s 7-8-6 4-5-9 4-5-3 1-2-6
Upper L’s 7-4-2 8-5-1 8-5-3 9-6 2
Right L’s 9-8-4 6-5-7 6-5-1 3-2-4
Lower L’s 1-4-8 2-5-7 2-5-9 3-6-8

Horizontal 3 numbers
Across 7-8-9 4-5-6 1-2-3
Vertical 3 numbers
Down 7-4-1 8-5-2 9-6-3

Criss Cross 2 numbers
Criss 1-5-9
Cross 7-5-3

With the Zero
Down 4-1-0 5-2-0
Corner 1-2-0
L 6-3-0 3-2-0

There are fifty-three keypad patterns in all.

Compare the keypad patterns to any month of your Pick-3 game’s history and you will find multiple winning hits every time.

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Man beats lottery: Two times in 3 months!

When he won in the February 22, 2008, Mega Millions drawing, he joked with Virginia Lottery officials, “I’ll see you next time.” Little did he know, there really would be a next time.

Three months later, the same lucky lottery player was back at Lottery headquarters with another Mega Millions ticket worth $250,000.

When asked about his amazing luck, Mr. Branch replied, “I really can’t explain it!”

Mr. Branch matched the first five numbers in the May 20, 2008, Mega Millions drawing. He bought the winning ticket at Hull Street BP/Amoco, located at 8211 Hull Street Road in Richmond.

The winning numbers for that drawing were 2-14-26-32-41 and the Mega Ball was 32.

The win occurred just two days before Mr. Branch and his wife celebrated their fourth wedding anniversary with a trip to Myrtle Beach.

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Lottery Games

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