Software calculates odds for any lottery with hypergeometric probability formula.

Software to Calculate Probability (Odds) for Lotto, Powerball, Mega Millions, Euromillions, SuperLotto Plus, Keno, Horse Racing

By Ion Saliu,
Founder of Lottery Mathematics, Founder of Gambling Mathematics

Learn how to best calculate lotto odds, lottery probability.

I. The Software to Calculate Probabilities (Odds) For Any Lotto
II. Calculating Lottery Odds Based On Hypergeometric Distribution Probability
III. Calculating the Probabilities (Odds) of Regular Lotto Games and Keno
IV. Calculating the Probabilities (Odds) of 5+1 Lotto Games: Powerball, Mega Millions, California SuperLotto Plus
V. Calculating the Probabilities (Odds) of 5+2 Lotto Games: Euromillions
VI. Calculating the Probabilities (Odds) of Horse Racing
VII. The Reversed Problem: Probability to NOT-Win
VIII. Resources in Theory of Probability, Mathematics, Statistics, Odds, Software

Odds Calculator is the software to calculate lottery probabilities, odds lotto, lottery, Powerball.

• OddsCalc.EXE ~ version 6.01, October 2012 ~ free software to calculate odds (probabilities) for any lotto, Powerball, Mega Millions, Euromillions, CA SuperLotto, Keno, Horse Racing.

The best probability software to calculate lotto odds or chances is OddsCalc.

Using hypergeometric distribution formula to calculate all lotto odds, as exactly and at least.

2. Calculating Lottery Odds Based On Hypergeometric Distribution Probability

Two decades ago, I started writing software to calculate the odds or probabilities for many situations, especially lottery games. I had never found what I wanted out there. Doing it manually, even using a handheld calculator was tedious and testing. Even if knowing most formulas, it is NOT an easy task! Not to mention that some situations have no formulas! Just think of situations like probability to win at least or at most M in N trials or probability NOT to win. I honestly believe I cover the largest territory in this domain!

OddsCalc.EXE calculates the probabilities (odds) of any lotto game, including Powerball, Mega Millions, CA SuperLotto, Euromillions, Keno, and even horse racing. If the lotto game draws 6 winning numbers, the program calculates the odds from 0 of 6 to 6 of 6. Furthermore, the probability is calculated from two perspectives: as exactly and as at least.

The software calculates the lotto probability using the hypergeometric distribution probability. The odds are calculated as k of m in p from N. More clearly, let's suppose a lotto 6/49 game. The lottery draws 6 winning numbers. The player must play exactly 6 numbers per ticket. But the lottery player can choose to play a pool of 10 favorite lotto numbers. What is the probability to get 4 of 6 in 10 from 49? The odds: 1 in 90.

The general hypergeometric formula for the as exactly case:

                                   C(n, k)
P(m of k in s from n) = ----------------------------
                                        C(s, m) * C(n-s, k-m)

The hypergeometric distribution probability formula has restrictions. Some cases are impossible; e.g. exactly 1 of 6 in 10 from 10.

My lotto software “runs” the extra mile and puts together multiple cases and does calculate precisely the odds as at least situations.

How to calculate all regular lotto odds and Keno lottery probability odds.

3. Calculating the Probabilities (Odds) of Regular Lotto Games and Keno

Most common lotto games draw 6 winning numbers most commonly from a field of 49 numbered balls. OddsCalc.EXE does handle such lottos, plus games that draw 4 winning numbers, or 5, or 7 winning numbers, etc. You can calculate the odds for countless situations, such as 39 from 49 or 50 from 55, etc.

Again, there are situations when the players select pools of numbers which are larger than the amount of winning numbers drawn in the game. There are lottery syndicates that can afford to play 18 or 20-number pools. In fact, they asked me to calculate the odds for a lotto game in Australia that allowed the players to mark 20 numbers on their play-slips (instead of 6). Of course, that play requires huge amounts of money (there are 38760 lotto combosnations to play!) Nonetheless, this incredible lotto software can easily calculate the odds for all possible situations.

The program requires just a few parameters. They are easy to understand and explained in detail on the input screens. Say, you want to calculate all possible odds for a 6-49 lotto game, with no pool of extra numbers (i.e. calculate the odds for a 6-number pool, exactly the number of winning lotto numbers drawn by the lottery commission). The biggest lotto number: 49; How many lotto numbers per combination: 6; How many lotto numbers in the pool: 6.

The best probability software to calculate lotto odds for 6-49 games are Bright programs.

The calculations are saved to disk files only. All names start with Od; the text files can be opened in Notepad or any text editor. In this case: OdL49-6.6; easy mnemonics!

 The odds calculated as EXACTLY in a lotto game '49/6/6':

 0 of 6 in 6 from 49  = 1 in 2.29 
 1 of 6 in 6 from 49  = 1 in 2.42 
 2 of 6 in 6 from 49  = 1 in 7.55 
 3 of 6 in 6 from 49  = 1 in 56.66 
 4 of 6 in 6 from 49  = 1 in 1032.4 
 5 of 6 in 6 from 49  = 1 in 54200.84 
 6 of 6 in 6 from 49  = 1 in 13983816 


 The odds calculated as AT LEAST in a lotto game '49/6/6':

 0 of 6 in 6 from 49  = 1 in 1 
 1 of 6 in 6 from 49  = 1 in 1.77 
 2 of 6 in 6 from 49  = 1 in 6.62 
 3 of 6 in 6 from 49  = 1 in 53.66 
 4 of 6 in 6 from 49  = 1 in 1013.03 
 5 of 6 in 6 from 49  = 1 in 53991.57 
 6 of 6 in 6 from 49  = 1 in 13983816 

And here is that Tattslotto case when the players are allowed to mark 20 numbers on the playing cards: 45/6/20 (we never use the bonus numbers — bonus, bogus!)

 The odds calculated as EXACTLY in a lotto game '45/6/20':

 0 of 6 in 20 from 45  = 1 in 45.99 
 1 of 6 in 20 from 45  = 1 in 7.67 
 2 of 6 in 20 from 45  = 1 in 3.39 
 3 of 6 in 20 from 45  = 1 in 3.11 
 4 of 6 in 20 from 45  = 1 in 5.6 
 5 of 6 in 20 from 45  = 1 in 21.01 
 6 of 6 in 20 from 45  = 1 in 210.14 


 The odds calculated as AT LEAST in a lotto game '45/6/20':

 0 of 6 in 20 from 45  = 1 in 1 
 1 of 6 in 20 from 45  = 1 in 1.02 
 2 of 6 in 20 from 45  = 1 in 1.18 
 3 of 6 in 20 from 45  = 1 in 1.81 
 4 of 6 in 20 from 45  = 1 in 4.33 
 5 of 6 in 20 from 45  = 1 in 19.1 
 6 of 6 in 20 from 45  = 1 in 210.14 

The Keno odds are calculated by the same option: L = Standard Lotto and Keno. The parameters: 80/10/20 for the most common Keno format.

The best lotto odds software to calculate lottery probabilities for Keno.
 The odds calculated as EXACTLY in a lotto game '80/10/20':

 0 of 10 in 20 from 80  = 1 in 21.84 
 1 of 10 in 20 from 80  = 1 in 5.57 
 2 of 10 in 20 from 80  = 1 in 3.39 
 3 of 10 in 20 from 80  = 1 in 3.74 
 4 of 10 in 20 from 80  = 1 in 6.79 
 5 of 10 in 20 from 80  = 1 in 19.44 
 6 of 10 in 20 from 80  = 1 in 87.11 
 7 of 10 in 20 from 80  = 1 in 620.68 
 8 of 10 in 20 from 80  = 1 in 7384.47 
 9 of 10 in 20 from 80  = 1 in 163381.37 
 10 of 10 in 20 from 80  = 1 in 8911711.18 


 The odds calculated as AT LEAST in a lotto game '80/10/20':

 0 of 10 in 20 from 80  = 1 in 1 
 1 of 10 in 20 from 80  = 1 in 1.05 
 2 of 10 in 20 from 80  = 1 in 1.29 
 3 of 10 in 20 from 80  = 1 in 2.09 
 4 of 10 in 20 from 80  = 1 in 4.72 
 5 of 10 in 20 from 80  = 1 in 15.47 
 6 of 10 in 20 from 80  = 1 in 75.57 
 7 of 10 in 20 from 80  = 1 in 570.52 
 8 of 10 in 20 from 80  = 1 in 7059.54 
 9 of 10 in 20 from 80  = 1 in 160439.97 
 10 of 10 in 20 from 80  = 1 in 8911711.18 

Calculating charts of lotto probabilities, lottery odds for Powerball, Mega Millions, Super-Lotto.

4. Calculating the Probabilities (Odds) of 5+1 Lotto Games: Powerball, Mega Millions, California SuperLotto Plus

In this example, we calculate the odds for the Powerball game at the time of this writing (October 2012): 5 regular numbers from a field of 59 AND 1 Power Ball from a field of 35.

This function software calculates lotto odds for regular numbers in Powerball, Mega Millions.

This function of probability software calculates odds for Power Balls, Mega Balls.
 The odds calculated as EXACTLY in a Powerball game
 '59/5/5 AND 35/1/1':

 0 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 1.63 
 0 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 55.41 
 1 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 3.26 
 1 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 110.81 
 2 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 20.78 
 2 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 706.43 
 3 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 360.14 
 3 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 12244.83 
 4 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 19087.53 
 4 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 648975.96 
 5 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 5153632.65 
 5 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 175223510 


 The odds calculated as AT LEAST in a Powerball game 
 '59/5/5 AND 35/1/1':

 0 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 1 
 0 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 35 
 1 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 2.72 
 1 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 95.03 
 2 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 19.06 
 2 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 667.21 
 3 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 343.35 
 3 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 12017.25 
 4 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 18473.75 
 4 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 646581.22 
 5 of 5 in 5 from 59  AND  0 of 1 in 1 from 35  = 1 in 5006386 
 5 of 5 in 5 from 59  AND  1 of 1 in 1 from 35  = 1 in 175223510 

Charts of probability, lotto odds for Euromillions lottery game.

5. Calculating the Probabilities (Odds) of 5+2 Lotto Games: Euromillions

In this example, we calculate the odds for the Euromillions game at the time of this writing (October 2012): 5 regular numbers from a field of 50 AND 2 Star Numbers from a field of 11.

The best lottery odds software to calculate lotto probabilities for regular numbers in Euromillions.

OddsCalc is lottery odds software to calculate lotto probabilities for Star numbers in Euromillions.
 The odds calculated as EXACTLY in a Euromillions game
 '50/5/5 AND 11/2/2':

 0 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 2.65 
 0 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 5.3 
 0 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 95.38 
 1 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 4.35 
 1 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 8.69 
 1 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 156.42 
 2 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 22.81 
 2 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 45.62 
 2 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 821.22 
 3 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 326.97 
 3 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 653.94 
 3 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 11770.89 
 4 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 14386.64 
 4 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 28773.28 
 4 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 517919.11 
 5 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 3236994.44 
 5 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 6473988.89 
 5 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 116531800 


 The odds calculated as AT LEAST in a Euromillions game 
 '50/5/5 AND 11/2/2':

 0 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 1 
 0 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 2.89 
 0 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 55 
 1 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 2.36 
 1 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 6.84 
 1 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 129.91 
 2 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 13.94 
 2 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 40.34 
 2 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 766.53 
 3 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 209.24 
 3 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 605.69 
 3 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 11508.18 
 4 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 9375.04 
 4 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 27138.29 
 4 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 515627.43 
 5 of 5 in 5 from 50  AND  0 of 2 in 2 from 11  = 1 in 2118760 
 5 of 5 in 5 from 50  AND  1 of 2 in 2 from 11  = 1 in 6133252.63 
 5 of 5 in 5 from 50  AND  2 of 2 in 2 from 11  = 1 in 116531800 

Lottery Odds Calculator can be extended to any lotto games drawing numbered balls from two chambers.

6. Calculating the Probabilities (Odds) of Horse Racing

In this example, we calculate the odds for the most famous horse race: The Kentucky Derby. We do the calculations for superfectas (top 4 finishers) and a field of 20 horses.

The best odds software to calculate probabilities for horse racing trifectas, superfectas.
 1.a. The odds calculated as EXACTLY in horseracing - STRAIGHT bet '20/4/4':

 0 of 4 in 4 from 20  = 1 in 63.89 
 1 of 4 in 4 from 20  = 1 in 207.64 
 2 of 4 in 4 from 20  = 1 in 969 
 3 of 4 in 4 from 20  = 1 in 7267.5 
 4 of 4 in 4 from 20  = 1 in 116280 

 1.b. The odds calculated as EXACTLY in horseracing - BOXED bet '20/4/4':

 0 of 4 in 4 from 20  = 1 in 2.66 
 1 of 4 in 4 from 20  = 1 in 8.65 
 2 of 4 in 4 from 20  = 1 in 40.38 
 3 of 4 in 4 from 20  = 1 in 302.81 
 4 of 4 in 4 from 20  = 1 in 4845 



 2.a. The odds calculated as AT LEAST in horseracing - STRAIGHT bet '20/4/4':

 0 of 4 in 4 from 20  = 1 in 46.2 
 1 of 4 in 4 from 20  = 1 in 166.83 
 2 of 4 in 4 from 20  = 1 in 848.76 
 3 of 4 in 4 from 20  = 1 in 6840 
 4 of 4 in 4 from 20  = 1 in 116280 

 2.b. The odds calculated as AT LEAST in horseracing - BOXED bet '20/4/4':

 0 of 4 in 4 from 20  = 1 in 1.92 
 1 of 4 in 4 from 20  = 1 in 6.95 
 2 of 4 in 4 from 20  = 1 in 35.36 
 3 of 4 in 4 from 20  = 1 in 285 
 4 of 4 in 4 from 20  = 1 in 4845 

How about lotto odds of NOT winning situations – e.g. NOT even 3 of 6 in lottery?

7. The Reversed Problem: Probability to NOT-Win

All the calculations above referred to the odds to win or the probabilities to win. How about the lotto probabilities to NOT-Win? The answer is simple in simple cases. For example, coin tossing. The probability to win with heads is 0.5; the probability to NOT-Win with heads is 1 - 0.5 = .5.

In lotto games, however, the situations are much more complex. Therefore, the calculations are more complicated. Let's use a common example, as it refers to “the most famous lotto wheel in the world”: 49 numbers, 3 of 6 minimum guarantee, in 163 lines (combinations). That wheel guarantees at least 1 combonation with a 3 of 6 win — no denial about that. On the other hand, if we generate 163 random 6-number lotto combinations, we are NOT guaranteed to win 3 of 6 every time. In fact, if we randomly generate 13,983,816 combinations for a 6-49 lotto game, the degree of certainty to get the winning combination is 63.2%. The phenomenon is known as Ion Saliu's Paradox of N Trials.

Let's say we randomly generate 100 combinations for a 6-49 lotto game. What is the degree of certainty that none of the combinations will contain 3 or more winning numbers? In the first step, we run OddsCalc.EXE. The odds calculated as AT LEAST in a lotto game 49/6/6:
3 of 6 in 6 from 49 = 1 in 53.66;

In the next step, we need to run SuperFormula.EXE function M = At Most M successes in N trials. Parameters: 2 = The program calculates p, then 1, then 53.66, then 0, and then 100. We can see that the opposite of at least 3 of 6 is at most 3 of 6, 0 successes in 100 trials. That is, every combination in our 100-line block will register 0, or 1, or 2 winning lotto numbers — but NO 3 or more winners. Or, we can get the same result for 1 in 53.66 for exactly 0 successes in 100 trials. Either way, the lotto odds are 15.24% or 1 in 6.56 trials. We'll notice that, on average, we will not hit 3 or more winning numbers every 7 lottery drawings or so IF we play 100 random combinations.

These calculations are valuable in conjunction with the LIE elimination function in my lotto software.

Resources in software calculator of probability, odds for lottery and lotto.

8. Resources in Theory of Probability, Mathematics, Statistics, Odds, Software.
See a comprehensive directory of the pages and materials on the subject of theory of probability, mathematics, statistics, combinatorics, plus software.

Software calculates accurately lottery probability, lotto odds for any game and prize.

You found the best software calculator for all lottery and lotto games in the world.

| Home | Search | New Writings | Odds, Generator | Contents | Forums | Sitemap |

This is the best Web site of lotto odds calculators.