The odds of Powerball are calculated for two dependent lotto games. The first part of the game, 5 of 69, has a total of 6 types of odds, from 0 of 5 to 5 of 5. The second part of the game has two types of odds, from 0 of 1 to 1 of 1. The following is a rundown of the Powerball probabilities (odds):
The odds calculated as EXACTLY in a Powerball game 5/69 AND 1/26: 0 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 1.53 0 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 38.32 1 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 3.68 1 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 91.98 2 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 28.05 2 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 701.33 3 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 579.76 3 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 14,494.11 4 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 36,525.17 4 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 913,129.18 5 of 5 in 5 from 69 AND 0 of 1 in 1 from 26 = 1 in 11,688,053.52 5 of 5 in 5 from 69 AND 1 of 1 in 1 from 26 = 1 in 292,201,338
The probability to win the jackpot is 1 in 292,201,338. Evidently, the Powerball game offers far fewer prizes than the total number of odds elements.
The new Powerball game required an update to the online odds calculator and random generator. I upgraded both ActiveX controls, especially as of employing the superior innate filtering for lotto games, including Powerball.
The Powerball_6 module generates optimized combinations for Powerball, the same way as for the other lotto games (except for Keno). The pick, horses, roulette and sport betting combinations are not optimized. The generating online control generates now 1000 combinations instead of 100. As I have stated many times, the more lotto combinations generated, the higher the probability to win (degree of certainty to hit the jackpot). According to the Fundamental Formula of Gambling (FFG), the chance to hit is lower in the beginning. We must run closer to the FFG median to have the highest winning chance.
It did take a very long time to get the FFG median by generating just 100 lottery 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 Powerball combinations. Chances are they were not winners. But you didn't play them either, so you saved money. A higher number of repetitions get you closer to that highly elusive winning combination (worth over half billion dollars sometimes).
There is no lotto strategy that I specifically designed for Powerball. But you can apply the general lotto and lottery strategy I present on the main strategy page. You can divide Powerball in two lotto games: One game draws five numbers, the other draws two numbers. It is similar to the Mega Millions or Euromillions-type of games. I present Powerball-type strategies based on the first five regular lotto numbers.
The mathematics of lotto and lottery, including Powerball, is founded on the Fundamental Formula of Gambling:
In the Fundamental Table of Gambling (FTG) there is a column p=1/8 that describes exactly a lotto game drawing 6 winning numbers from a field of 48 numbers. 6 divided by 48 is 1/8 or 0.125. That's how you calculate the probability p, when considering one lotto number at a time. If the Powerball game draws 5 regular lotto numbers from a field of 69 numbers, the individual probability is equal to 5/69. That is very important parameter. It is thoroughly analyzed at this Web site, specifically on the main page dedicated to lottery strategies.
You only need 3 values for the degree of certainty DC: 50%, 75%, 90%. The parameter DC = 50% is fundamental. It represents the probability median. You can substitute the other two, or you can add other parameters, if you wish.
Click here to download a Command Prompt mathematical program that does all the calculations: SuperFormula, option F = FFG. The super software boasts dozens of probability and statistics functions. The program allows you to calculate the number of trials N for any degree of certainty DC. Plus, you can also calculate the very important binomial distribution formula (BDF) and binomial standard deviation (BSD). This lotto software program also calculates several types of Powerball odds, lottery probabilities based on hypergeometric distribution probability.
In 55% of the wins, an individual Powerball regular number repeats after 8 draws, for p = 5/53. We call the cutoff value FFG median. The lottery strategy based on the FFG was first presented in 1997. In the most basic lotto Powerball strategy, the user would run the frequency reporting in Ion Saliu's lottery software known as LotWon, SuperPower and MDIEditor Lotto. The statistical reports show each lotto number and its skips.
The skip represents the number of drawings between two hits (wins). The lotto player would look at the current skip of every Powerball regular number. The player then selects the skips between zero and 8, for example. That is a total of 9 values for a skip. The user would end up with some 15 to 25 Powerball regular numbers. In the final step, the player would wheel the numbers by applying a reduced lottery system (lotto wheel).
You can download from this site powerful software that analyzes the skips for the Powerball game: SkipSystem. Open the two reports (SKIPPb.1 and SKIPPb.2) in a text editor, like MDIEditor Lotto. You may want to set the font to Courier 10 point. The report #2 can be of valuable help to you! Read also: Necessary Updates to the Pick Lottery, Lotto and Roulette Skips Software.
The most powerful software capable of handling the game of Powerball is known to the world as MDIEditor Lotto. It has specific functions that crunch the Powerball: statistical reporting (frequency and skips), filter analysis, and optimized combination generator. Read the comprehensive guide to MDIEditor and Lotto. Steps in menu: Lotto, then Powerball 5+1, then type of Powerball combination generating.
This site offers also the best, bar none, Powerball random numbers generator and odds calculator. The engines are online ActiveX controls you can run at any time — freely, of course! Not to mention that the Powerball combinations are optimized based on statistical parameters. You won't find such feature anywhere else.
Other valuable resources include the past results, drawings of Powerball from the beginning of the lottery game and statistical reports of the Powerball lotto numbers ranked by frequency.
• Nota bene – If you do not see the two controls (online applications) as the image in section 1, please follow the instructions on the dedicated page:
Probability, Odds Calculator, Random Combinations Generator.
• Version 7.0 of the super generator employs superior inner filtering for lotto games, including Powerball. 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.
The first graphic shows the Top 10 Powerball numbers ranked by frequency regardless of position.
The Powerball 5/69 & 1/26 Numbers Ranked by Frequency File: C:\Powerball\DATA-PB Drawings Analyzed: 85 Date: 07-28-2016 Frequency norms based on probabilities: 7.25% & 3.85% R E G U L A R Numbers P O W E R B A L L S Rank Regular # Hits Percentage Powerball Hits Percentage 1 32 12 14.12% 6 6 7.06% 2 40 12 14.12% 10 6 7.06% 3 64 12 14.12% 25 6 7.06% 4 12 11 12.94% 3 5 5.88% 5 69 11 12.94% 17 5 5.88% 6 62 10 11.76% 9 5 5.88% 7 23 10 11.76% 5 4 4.71% 8 52 10 11.76% 18 4 4.71% 9 47 9 10.59% 19 4 4.71% 10 27 9 10.59% 21 4 4.71%
The second graphic shows the Top 10 Powerball numbers ranked by frequencies position by position.
The Powerball 5/69 & 1/26 Numbers Ranked by Frequency - By Position File: C:\Powerball\DATA-PB Drawings Analyzed: 85 Date: 07-28-2016 Rank Position 1 Position 2 Position 3 Position 4 Position 5 Number Hits % Number Hits % Number Hits % Number Hits % Number Hits % 1 2 8 9.41% 12 6 7.06% 32 5 5.88% 59 6 7.06% 69 11 12.94% 2 3 7 8.24% 25 6 7.06% 40 4 4.71% 52 5 5.88% 64 10 11.76% 3 5 7 8.24% 27 6 7.06% 41 4 4.71% 60 5 5.88% 68 7 8.24% 4 4 6 7.06% 28 5 5.88% 25 3 3.53% 54 4 4.71% 62 7 8.24% 5 11 6 7.06% 23 4 4.71% 29 3 3.53% 46 3 3.53% 67 6 7.06% 6 10 5 5.88% 20 3 3.53% 31 3 3.53% 47 3 3.53% 63 5 5.88% 7 12 5 5.88% 22 3 3.53% 15 3 3.53% 50 3 3.53% 57 4 4.71% 8 14 5 5.88% 30 3 3.53% 33 3 3.53% 31 3 3.53% 65 4 4.71% 9 7 4 4.71% 32 3 3.53% 34 3 3.53% 32 3 3.53% 66 4 4.71% 10 16 4 4.71% 40 3 3.53% 37 3 3.53% 58 3 3.53% 52 3 3.53%
View the charts showing the sums or sum-totals with the respective amount of combinations for this American multi-state lottery game: Powerball Sums chart. The unique lottery and lotto software to plot the sum charts is Sums.
In this year of grace 2016, I just assembled all Command Prompt programs I've written that work with Powerball. I know, you've worked with virtually all of them for years. To make things easier and more efficient, I created an integrated package in the manner of the Bright software packages. The main screen is a familiar one:
The registered members of this website already know how to download, install, and run my Command Prompt software. For newcomers: You need register first. Then, you start by creating a New Folder on your C:\ drive; e.g. (my real-life example: C:\PBall). You download the compressed package Powerball to the C:\PBall directory. Click on Powerball to decompress in the same folder. And then click on README.TXT to... read the sine qua non information.
Actually, all the facts you need to know will be available to you as soon as you register to download my software. There is an informative membership page that also hosts all the links to downloading all my software. You might face an extra layer of security ("Not redirecting properly"): You just click that ubiquitous Try Again button.
No doubt, MDIEditor Lotto is a lot more comprehensive when working with the Powerball game. Still, there are some very useful utilities in this Powerball bundle. The most notable program in this Command Prompt collection is Skip System (function: K = Create Powerball systems based on skips). You can also Sort the data file of past results (function S); plot all Powerball sums and generate all combinations for a particular sum-total (G); create meaningful reports regarding the frequencies of the regular numbers and Power Balls (F); etc.
There are many more functions. They will not be mention here in order to keep this Web page reasonably short. All programs in the Powerball are adequately presented on every Bright bundle. For openers: Best Lotto Software for 6 Numbers Lottery Games.
The old-timers might still prefer working in MDIEditor Lotto only. I don't. I always start in Powerball. It does have direct links to MDIEditor Lotto. I created my data file (past results, drawings, past winning numbers) at the command prompt.
Powerball is also faster in creating the much-needed SIMulated data files. This latest package has the file of real drawings for the current Powerball game format: 5 from 69 AND 1 from 26. File name: DATA-PB (as of July 27, 2016). You create the simulated file of "drawings" in function U = Super Utilities, the function 1 = Simulate Drawings. Best to name the file SIM-PB. I created over 2.2 million random draws. I should have created more (I probably will). The today's computers are so much faster (and faster still by the year). I'll keep things as they are for a while because I'm pursuing some Powerball strategies. You can test if your PC is up to the challenge. Try generating a SIM-PB file of 10 million combinations — best to do it at the command prompt. The U = Super Utilities program (Lotto2Games51) is presented in more detail on its dedicated page: Lottery Software for Powerball, Mega Millions, SuperLotto.
Now, let's return to MDIEditor Lotto. I'll show you just one example of devising and running Powerball strategies. You always keep your data file up-to-the date. Then, you concatenate the real-results file with the simulated file. You can do it at the command prompt or in MDIEditor Lotto. In Powerball: U = Super Utilities, then M = Make/Break/Position (function 1). In GUI: Data, Make DP5; files: DATA-PB, SIM-PB, result-file D-PB.
The screenshot below shows a real-life strategy for the latest Powerball game format. The strategy file is included in the package you downloaded (StratPB-Ion1K). The pivot (key) filter is ION1 = 1000. FYI: The filter eliminates all combinations in the last 1000 Powerball drawings based on deltas. The deltas are simply differences between adjacent lottery numbers in real drawings (I want to keep this page shorter... and also preserve my secrets, axiomatic one!)
As you can see on the screenshot, our strategy hit 49 times in the past 100 Powerball drawings (only 85 of them are real-life at the time of this writing... but this ratio will always hold true as an average). The strategy has a very good skip median: 0. It means, in over 50% of all winning cases, the strategy hits in consecutive Powerball drawings. If combined with skips of 1 draw in-between, our strategy hits preponderantly in consecutive draws, or skipping just one drawing.
The parameter at the bottom of the filter-input file reads Eliminate the last 2,296,267 draws. It is the entire amount of the D-PB data file. That filter is determined separately in MDIEditor Lotto. Menu bar, Filters, then Past Draws. I haven't seen Powerball combinations repeating within 2,296,267 drawings. Yes, it could happen now and then, but very rarely. That's why I just said to test your computer prowess and generate, say, 10 million random combinations (simulated draws).
The more Powerball simulated drawings you can use, the better. The software generator spits out lots and tons of unnecessary Powerball combinations. That slows down the generator in a beneficial way. I wrote on my website of situations from my past lottery history. Looks like I had a significantly higher success at hitting the lottery when the personal computers were so much more primitive. O tempora! O mores! I always get mellow when rereading these two pages: History of My Lottery, Lotto Experience with Software, Systems, Strategies + Randomness, Degree of Randomness, Degrees of Certainty, Generate True Random Numbers.
This Powerball game isn't a slouch. It is far, far, and far easier to win lottery games covered by the Bright and especially Ultimate software packages. We got to be as shrewed as imaginable when playing Powerball. No doubt, as you read in Section 2, my theory improves the lotto odds in the neighborhood of sevenfold just by playing numbers that show skips under the FFG median. In the case of applying the Powerball strategy presented here, the odds remain still IONospheric (high). We need to generate lots and lots of Powerball combinations repeatedly. Mathematically — and nobody can disprove the following law — the degree of certainty (winning chance) is low in the first round of random combinations generated (even millions of them). The more random combinations generated (number of trials), the higher the chance to win.
You generate random-filtered Powerball combinations in MDIEditor Lotto: Menu bar, Lotto, Powerball 5+1, Optimized Powerball. You can Open a strategy you already discovered and saved (e.g. StratPB-Ion1K, included in the package). Don't forget to fill in the always-empty Eliminate the last ... draws field. You can also check the Enable the inner filters (they are validated about 3 out of 4 drawings). And, of course, you can always edit the filter-input form by changing any of the fields (text boxes). You would do so based on your analysis if the current filter report. Menu bar, Filters, Powerball 5+1.
Let the function run for an hour first. Press Stop! on the menu bar, then Stop! again, and Stop! once more. Notice how many combinations were generated. Repeat the procedure several times. You might want to repeat the combination generating process over several days (between the Powerball official drawings).
It is best to select Powerball combinations to play from the bottom of the generation file (usually named Optimized Powerball after you clicked Stop! three times).
You can also save hundreds of combinations at the end of several runs. Put all them combos in one text file. Then, you can select randomly an amount of lines from the file you just saved. You do that in the command prompt mode, function W = Wheels from files. Enter the input file (the one that you just saved), how many lines to randomly input from, and the name of the output file. The output file holds the Powerball tickets you want to play.
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