There is a number of pages at this Web site that many old-timers had not been aware of. Most visitors land at such pages from search engines or other referring domains. I had not announced those pages properly, via the Newest Writings (see footer of all pages).
I introduce in this category pages with popular features, especially requested in search engines:
~ NFL results, scores (and schedule);
~ The results, past drawings, past winning numbers for the following multi-jurisdictional lottery games: Powerball, Mega Millions, Euromillions.
In addition to publishing the results, the resources also handle some useful statistical reports.
The NFL schedule and results pages presents the schedule for the entire season, then the Results (scores) of all games one week at a time. The resource presents also an interesting stat: The average score of the week.
There are very complex statistical reports for the multi-jurisdictional lottery games. The reports show the frequency of each lotto number in absolute terms and relative terms (percentages). The percentages relate immediately to the theoretical probability of appearance for a lotto number. The frequency in absolute terms is harder to make sense of. You need to divide the frequency to total number of drawings to get an idea of the performance of a lotto number.
It is well known that each lotto number has a probability equal to every other number. The appearance (statistical fact) is a totally different matter. There is a discrepancy in frequencies. The discrepancy is very significant in the short run (a short span of analysis). The discrepancy tends to get uniform in the very long run, percentage-wise. But the long run is very, very long.
Look at this statistical report for a real-life lotto game: Pennsylvania lottery Cash 5 (5 of 39):
Lotto 5/39 Numbers Ranked by Frequency: Pennsylvania Lottery Cash 5.
In the short-term scenario (100 draws analyzed), the discrepancy is wide: frequencies range from 5% to 18%. The long-term scenario consists of 4155 drawings in the game (the draws are real). The discrepancy is far smoother: From 11.67% to 14.8%. The extremes are much closer to the norm (theoretical probability): 5/39 = 12.82%. The 4155 draws in the history amounts to over 532 times the number of drawings required for one hit. So, the long run is really huge to get uniformity. A comparison to a lotto 6/49 game, considering the frequency of 6-number combinations. The long run would amount to 500 times 14 million (over 7 billion or 7 milliard drawings or draws).
Does it sound familiar to you, axiomatic one? It does to me. All human beings, therefore all civilizations, have had the tendency to achieve uniformity, to get closer to a (currently unformulated) norm — over the long run. It took Home sapiens a very long run (measured in millions of years or billions of weeks) to get separation from the kin-beasts. The humans (Homo sapiens branch) were Saliu-absolutely at the same norm some 50 thousand years ago.
The painful discrepancies started some 5000 years ago (that's not the illusory age of Earth in biblical terms). The discrepancy (gap) got closest during the cold war. The discrepancy tends to NORM if humanity span tends to infinity. Acceptable uniformity should be reached during this millennium (the third, III, following Caesar's calendar). Absolute uniformity will not, and shall not, be reached — ever. That's a great quality for Homo sapiens. No other species has ever benefited from inequality to the same high level as the humans. Don't all the birds of the same feather look the same, do the same, survive the same, and die the same — way?
Let us always take advantage of discrepancies or gaps. And off to the races we go. The short-term range of analysis (real parpaluck) leads to unmistaken biases. The player can take advantage of short-term report spans. The same type of analysis for roulette shows very clear and strong facts.
You can perform such statistical analyses at any time. Just download and run that incredulously great piece of statistical lottery software: FrequencyRank.
Resources in Lotto, Lottery: Theory, Mathematics, Software
Lists the main pages and links to the best lottery, lotto, software, systems, and wheels. It's all about winning lotto, lottery systems, including for pick digit lotteries, Powerball, Mega Millions, Euromillions, Keno.
Resources in Theory of Probability, Mathematics, Statistics, Combinatorics
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!
Resources in Blackjack, Baccarat: Theory, Mathematics, Basic Strategy
Lists the main pages and links to the best blackjack, baccarat, software, systems, and strategies. It's all about winning blackjack, baccarat systems, including the famed Basic Strategy.
Resources in Roulette: Theory, Mathematics, Super Strategy
Lists the main pages and links to the best roulette, software, systems, and strategies. It's all about winning roulette systems, including the famed Super Roulette Strategy.
Resources in Horseracing: Theory, Mathematics, Software
Lists the main pages and links to the best horse racing, software, systems, and strategies. It's all about winning horse racing systems, including the generating of trifectas.
Resources in Sports Betting: Theory, Mathematics, Excel Spreadsheet
Lists the main pages and links to the best sports betting, software, systems, strategies. It's all about winning sports betting systems, including the generating of parlays.