Written on September 12, 2002.

The page * Probability, Odds, Formulae, Algorithm, Software Calculator* presents the mathematics and logic of calculating the odds for various games of chance.

The page * Software and formulae to calculate lotto odds using the hypergeometric distribution probability* gives more details on calculating the lotto odds for various prizes.

I wrote software to calculate the odds or probabilities for many situations. The free programs in point are presented briefly on this page.

• OddsCalc.exe calculates the odds of any lotto game, including power ball and keno. If the game draws 6 winning numbers, the program calculates the odds from '0 of 6' to '6 of 6'. Of course, '6 of 6' represents the jackpot case.

• ODDS.EXE calculates the lotto odds using the 'hypergeometric distribution probability'. The odds are calculated as *'k of m in n 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 player can choose to play a pool of 10 favorite numbers. What is the probability to get '4 of 6 in 10 from 49'? The odds: '1 in 90'.

• SuperFORMULA.EXE does the calculations for the * Fundamental Formula of Gambling* as presented at

That is, calculate the number of trials

The program can reverse the above and calculate the degree of certainty

It also handles the

The program displays the factorials (!) of the parameters used by the binomial distribution:

Also, the program calculates the standard deviation applied to binomial events:

“A most useful scientific tool!”; “Unmatched theory of probability software, bar none!”, many users exclaim.

These programs only work on Intel/Microsoft Windows platforms. Regretfully, the users of Apple computers cannot use my software. The only thing they can use is my lottery and gambling ActiveX control. The online number generator can generate combinations for a wide variety of games of chance. It can also calculate the odds or probability of such games of chance. The online control performs also some of the calculations of FORMULA.EXE. There is another restriction, however. The 'IonSaliuGen' online ActiveX control only runs in Microsoft Internet Explorer version 4 or later! It shouldn't be a bid deal, though. Microsoft Internet Explorer is easily available as a freebie. Download your free copy of MSIE5 or later from the home page.

Apple Mac computers users can run the online generator and odds calculator right here, on this webpage.

Here is that great device at your fingertips: the best lottery, lotto, gambling combination random number generator you can find online! This powerful online application handles any type of lotto and lottery games: pick-3, pick-4, lotto-5, lotto-6, lotto-7, Powerball (both 5+1 power ball and 6+1 power ball), horseracing (both trifecta and superfecta), Keno; plus, the queen of casino games: roulette; plus, sports betting, the American way. The ActiveX control also calculates the odds in lotto games, including PowerBall and Keno, following the official method used by the lottery commissions.

• Version 6.0 of the ActiveX control generates 1000 combinations in a text box. The combinations can be saved to files, using the "Save" button. The text box is a capable online editor: select, copy, cut, paste, undo, select font, edit, print, save to file… The control buttons boast now “tool tips” – a useful feature for newcomers. And that's just for starters!

The online application calculates also the binomial standard deviation—a very important parameter of randomness. The binomial standard deviation is especially useful with the normal probability rule and Gauss curve (bell).

The ActiveX control sports an often-requested team-combination generator applicable to the American betting system. The player can choose between two teams to win a bet, based on a point spread or just “pick 'em”. The player must first create “game files” consisting of the competing teams. Additional info is available in the input boxes and the main text box.

The "Roulette" option applies now my "Free Winning Roulette System #2", as presented on the "Roulette" page and the "Message Board". The last three columns are what is all about.

"D1&2" means the 1st dozen (1 to 12) in combination with the 2nd dozen (13 to 24). "D1&3" means the 1st dozen (1 to 12) in combination with the 3rd dozen (25 to 36). "D2&3" means the 2nd dozen (13 to 24) in combination with the 3rd dozen (25 to 36). A + (plus) sign indicates a hit, a – (minus) sign indicates a loss. You can count how many + a specific 2-dozen group encountered in 100 spins. Is it above or below the standard deviation? Follow the ideas in the free system #2… You can also see how the + and – move within 1000 spins.

There are important statistical reports at the end of the roulette file. The file shows also the “seed” used for the random generation. It is far more ranging than the “timer” seed used previously. Therefore the randomization follows more closely the “natural” randomness. This feature is of use to computer programmers. Read more on my approach to randomization: * "Randomizing: An Art of Scientific Philosophy, Science of Philosophical Art, Philosophy of Artistic Science, Art of Philosophical Science, Science of Artistic Philosophy, Philosophy of Scientific Art ©"*. It has the source code of a Visual Basic function:

Read also the best gambling approach to even-money type of bets (including baccarat and blackjack):

The following types of lotto games are covered specifically: 5-number loto games, lotto 6, lotto 7, Powerball, and Euro Millions. The generators generate optimized generations! That is, specific built-in filters screen out combinations with very low probability of appearance. Some players would spend their lives playing combinations like 1,2,3,4,5,6. Live 9 lives only to find out that thousands other players have played the same type of wacky combination!

The Keno combinations are not optimized.

The grand generator also handles the digit lottery games pick-3 and pick-4. Horse racing combinations are also generated in the manner of a pick 3 lottery game (trifecta combinations). The pick combinations are not optimized (no innate filters enabled).

The generating ActiveX control generates now 1000 combinations instead of 100. As I have stated many times, the more combinations generated, the higher the probability. According to FFG (Fundamental Formula of Gambling), the chance to hit is lower in the beginning. We must go closer to the FFG median to have to highest winning chance. It did take a very long time to get the FFG median by generating 100 combinations at a time. Now, the generator offers better time compression. Think about it as saving money. You ran the generator for a few thousand combinations. Chances are they were not winners. But you didn't play them either, so you saved money.

The best location in the combination file is in the FFG median zone. You can visually approximate the area using the scroll bar: It's somewhere in the middle. I have become convinced of the bias towards the FFG median zone by analyzing a lot of real life cases. Among other fields, I analyzed two full seasons of the NFL (the pro football league in the US). Read * Winning Combinations Come Predominantly Inside FFG Median Bell*.

For industrial-strength software that crunches the lottery and horse racing, use the all-powerful MDIEditor and Lotto WE. Read also a plethora of articles dealing with the mathematics and practice of gambling, lottery, lotto. Use the native search engine of this web site. Check also the directory of (almost) all pages that this site consists of: * Statistics Stats Main Pages*.

• IonSaliuGenerator, version 7.0, January 2005 — The Best Random Numbers, Combinations Generator.

• Version 7.0 of the super generator implements superior inner (innate) filtering for lotto games, including Keno, Powerball, Mega-Millions, Euro-Millions. The Saliusian filters are founded on the most significant parameters of probability theory and statistics. You'll notice on your lotto cards. The patterns follow more closely the patterns of real lottery drawings.

Just take 10+10 lottery cards (grids). Mark the last 10 drawings on 10 lotto grids. Put an "R" (for real) on the back of the grids, so that nobody can see the marks. Next, run the super generator, say, 21 times. Scroll to the middle of the combination file. Take any 10 combinations you want. Mark them on the other 10 lotto grids. Put a "G" (for generate) on the back of the grids, so that nobody can see the marks. Mix up the lotto cards, without seeing the back marks. Look at the grids. Pick 5 or 10 of them. You'll be around 50% between the cards showing the real lottery draws and the cards plotting the randomly generated lotto combinations. Read more on the patterns plotted by real-life lottery drawings on lotto cards (matrix):

* Geometric, regular patterns on lotto play slips, cards, grids*.

Resources in Theory of Probability, Mathematics, Statistics, Combinatorics, Software.

See a comprehensive directory of the pages and materials on the subject of theory of probability, mathematics, statistics, combinatorics, plus software.

Standard deviation: Basics, mathematics, statistics, formula, software, algorithm.

Calculate: Median, degree of certainty, standard deviation, binomial, hypergeometric, average, sums, probabilities, odds.