Calculate Lotto, Lottery Odds Based On Hypergeometric Distribution Probability

Written by Ion Saliu on October 1, 2001- revised November 14, 2001.

Ion - Good to see you have recovered your senses.

One of the main advantages of newsgroups is that when someone (including me sometimes) begins to stroll down the wrong trail (mathematically that is), that there are others here that can help straighten one out.

P.S. Maybe someday I may show you how to *REALLY* play roulette with my "Sorry_it_is_not_for_sale" roulette system.

Royce Penny
Royce Penny's Money Machine

Royce:
Axiomatic one, good to see you, too, have recovered your senses. I no longer see those disturbing C(0,5) and 'combination sequence number'!

As of roulette: Are you the same Canadian who sent me some info on his roulette software? Maybe you want to show me your roulette system. I don't think I want to explain to you my system. But, of course, you can see me playing. Unfortunately, the conditions in the U.S. are not proper for gambling. Many people are afraid now to go to casinos. There are too many unknown persons in there. We all heard about terrorists frequently meeting in Las Vegas prior to September 11. I thought the Canadian casinos might be a better destination now. If you are the same person who sent me roulette info, let me know. We might have the opportunity to see each other's systems.

May Almighty Number give you always the most favorable Probability, and Odds, and Payouts! And thus your pocket shall not be empty, as your mouth is never empty of words.

Ion Saliu

Ion,

you have won a jackpot, ... inside you. Now you can admit many hypothesis to explain why you have not seen these conclusions before. Perhaps many guys here told you that 1in6 is different from 6in49 but your creative mind couldn't let you read/hear/see that. But, what really mind here is this tread you wrote. We cannot put our ideas without defending them, ... like a dog defends "his" owner. Sometimes we don't own our ideas, they own us. But now you got out as a owner of your mind and with a honest position.

Frank

Franc José:
Axiomatic one, I was hesitant to respond to your post. Some people might have suspected I asked you to put up nice words for me. Of course, you said what you wanted to say on your own. But you know the computing beast . . .
Moreover, I feel far more comfortable in an adversarial environment. I feel less comfortable in a sincerely in-your-face-nice environ. I still feel better in an in-your-face-nice-but-really-adversarial-behind-your-back environ. I am at my best in a sincerely in-your-face-adversarial environment. If it's about say-differently-and-I-kick-ass, don't hide it. The computing beast civilization named humanity benefited from it cosmically more than any other species. Only humans have the privilege to kick ass. Other species cannot do that. The lions, for example, can only go for the jugular. Had they been able to KA, their imperial palaces would display human statues at the gates as symbols of ferocious force...

Portuguese is not my mother tongue; it's my aunt tongue. I can't speak it. Yet I felt I knew Portuguese reading your post. I felt I know Chinese, and English, and Russian, and Arabic, and Fowuru, and any tongue, reading your post. Maybe some asked themselves (or the AHs asked you via email): “What the heck English wass that?” The answer: It is human communication. Great thought: “Sometimes we don't own our ideas. Our idea possesses us. It pushes us into leaving no stone unturned.”

May Almighty Number give you always the righteous count of consonants, and vowels, and syllables, and words. And thus your speech shall not be too short in any language, or too long in any dialect. For all the glory is in Number.

Ion Saliu

Axiomatic ones, I wrote software to do all lotto odds calculations, fast and accurately:
Scientific Software: Mathematics, statistics, probability, combinatorics, odds, algorithms.

The software in this group is one of the best ever and highly unique. The programs deal with theory of probability; calculating odds for various games of chance, perform statistical functions (e.g. standard deviation, binomial distribution, hypergeometric distribution, etc.) There are also programs that perform tasks in combinatorics. The software calculates and generates permutations, combinations and everything else as far as the number sets are concerned.

OddsCalc 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 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'.

See also the resource Random Generator, Odds Calculator in the foother of most webpages at SALIU.COM.

• Download Software: Science, Mathematics, Statistics, Lexicographic, Combinatorial to calculate formulas, odds, probability.

Lists the main pages and links to the best in theory of probability, combinatorics, statistics, mathematics. The very original formulas and theories are always backed by specific computer programs. The computers are so much faster and more accurate than the humans!

• Previous post: Official Lotto Odds Correctly Calculated as EXACTLY, not AT LEAST.

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Comments:
: : Calculate lotto, lottery odds based on hypergeometric distribution probability. Ion Saliu on "Hypergeometric distribution: Calculate lotto, loto, loteria, lottery odds, probabilities based on hypergeometric distribution probability." Axiomatic one, please read an analysis of Hypergeometric distribution: Calculate lotto, loto, loteria, lottery odds, probabilities. Great thought: "Sometimes we don't own our ideas. Our idea possesses us. It pushes us into leaving no stone unturned." The purpose of this page is to better organize the materials on probability and odds. Probability starts with logic. There is a set of N elements. A simple example of sets and favorable elements: there are 10 balls in a jar; 5 of the 10 balls are red; what is the probability to extract one red ball from the jar? There 5 favorable cases in a total of 10 elements; the probability is 5/10 = ½ = 0.5.The easiest case is coin tossing. What is the probability (odds) of heads in one coin toss: 1 / 2 = 0.5. The probability can be also understood as expected number of successes in one trial. That formulation makes it easier to understand why probability can never be higher than 1: no event can have more than one success in one try! There are many instances when the formulation of probability is reversed and expressed as This is known as the odds against: the odds against one point face in dice rolling are 5 to 1. Some also use the formula n in N to express the so-called favorable odds. It all comes down to calculating the two fundamental elements of the probability formula. I always start with calculating total elements in the set or total possible cases. Then I figure out number of favorable cases. 'Total possible cases' is self-evident sometimes; there are 2 and only 2 cases in coin tossing: heads and tails. The cube has exactly 6 faces. The favorable cases are also easy to figure out. There is one favorable case in coin tossing: either heads OR tails. Calculating the two fundamental elements of the probability formula is very difficult sometimes. The calculations create a lot of controversy at times. The way we look at the probability or odds can get very tricky. Is it the odds of EXACTLY n in N" or "the odds of AT LEAST n in N"? In general, there are formulas for calculating the total number of cases and number of possible cases. The binomial distribution probability formula is widely used in instances of "the odds of EXACTLY n in N". for example, the probability of getting EXACTLY 5 heads in 10 coin tosses is 24.61% or '1 in 4.06'. There are 1000 total possible cases in pick-3 lottery, the straight bet being considered, from 0 (000, in fact) to 999. Only one 3-digit combination is drawn, therefore the winning probability is 1 / 1000 (0.001). The lottery commission says "the odds are 1 in 1000", or "1000 to 1". The best in Hypergeometric distribution: Calculate lotto, loto, loteria, lottery odds, probabilities based on hypergeometric distribution probability. There are 10000 total possible cases in pick-4 lottery, the straight bet being considered, from 0 (0000, in fact) to 9999. Only one 4-digit combination is drawn, therefore the winning probability is 1 / 10000 (0.0001). The lottery commission says "the odds are 1 in 10000", or "10000 to 1". Calculating the odds at horse-racing is also tricky. We know only statistically that the bettors pick the winner in around 45% of the races. We can also use mathematical formulae to calculate the probability or the odds for certain horseracing wagers. The probability of winning straight trifecta is '1 in N * (N-1) * N(-2)' , where N represents the number of horses in the race. For example: the odds of a straight trifecta in a 12-horse race are '1 in 12 x 11 x 10' = '1 in 1320'. The probability of boxed trifecta is 6 times better; the order of the top three finishers is not important. We can arrange 3 numbers (horses) in 3! = 1x2x3 = 6 ways regardless of order. The lotto games are much more diverse. The diversity widens when the 'power ball' games are taken into account. The lottery commissions set the odds as exactly k of m. Exactly is the operative word here. I thought it was at least. The odds calculated as at least k of m lead to very different values. The most certain element in calculating the lotto odds is total possible cases. It is known as total number of combinations C(n, k). The combination formula is widely accepted, expert or not. I wrote software to do all the calculations, accurately and freely: ODDS.