Ultimate Software for Horse Racing Trifectas, OTW Wagering
By Ion Saliu, Founder of Equestrian Mathematics, Trifectas Programming Science
0. Introductory Notes to the Ultimate Horse Racing Software for Trifectas (Triactors); Download, Install, Run
ULTIMATE HORSE RACING ~ version 2.0 ~ April 2017 ~ software category 5.3.
- This package is definitely the ultimate, never-to-be-duplicated software for horse racing where the trifecta wager is available (i.e. the top 3 finishers in a race). Specific data files of past races or past winning numbers make possible for the programs in this grand application to work at any horse race track in the world, live or at off-track wagering (OTW).
- Downloading this collection of high-power programs requires the special Ultimate Software membership. It is available only to members who paid for the Permanent Software Download subscription. Click on the top banner to learn the terms, conditions, and availability.
- Your membership page has clear instructions on downloading, installing, and running the software. All Ultimate Software applications are available for download from your membership page. In addition, you can download a special software utility to work with data files efficiently.
The presentation of the four menus and their applications and functions is next. The programs themselves have their own menus. The menus in all my programs are self-describing, but there are also specialized pages with more detailed information.
I. Main Menu: Data Files, Reports, Strategies, Trifecta Generators
This menu comprises the most important programs and functions of the Ultimate Horse Racing Trifecta Software bundle. There is a sine qua non step: Create the data file of past races or past winning horse numbers. You already know and fulfilled this step as a user of BrightH3: High-Powered Trifecta Software for Horse-Race Betting.
There is also a visual tutorial, with plenty of screenshots, applicable to all my software for lottery and horse racing:
- Lottery Software Visual Manual (the fundamental steps apply also to trifecta software).
T: Tutorial Online
It takes you to this Web page via your default Web browser. The online information is always up to date, as it is much prompter to edit a Web page than rewriting a manual bundled with the software.
E: MDIEditor Lotto
Starts the separate GUI application MDIEditor And Lotto WE (for 64-bit Windows). The 32-bit OS version can be run from menu #3.
Functions I, E: Edit Data Files
The history file or data file is always saved in text (ASCII) format and consists of the 3-horse numbers recorded in previous races as winners. You can create the file simply by typing the winning numbers race by race - one trifecta result per line.
- The data file must have exactly 3 horse numbers per line. The numbers must be separated by one or more blank spaces. You can also use commas , as the field separators. The universal field separator should be the blank space.
- The final step is to format the race results (the lines in your horse data files).
Here is an example of the contents of my file for the Kentucky Derby horse race after formatting (D-Ke20.CLN, included):
16 4 3 (race #1, or the most recent)
19 6 5 (2nd recent race)
16 19 13 (3rd recent race)
4 2 10
8 16 2
…
… all the way down to the last line in the file, representing the oldest race result (winning 3-horse numbers).
I created a specialized piece of software to maximize the efficiency of working with data files: LotteryData. Please visit the following link, as it also deals with the important topics of lottery strategies and the winning reports:
S: Sort Data Files
The program formats nicely the pick 3, pick-4 and horse racing files as in the sample above. The lines are not sorted in ascending order as the position counts in horse races.
This task can be also performed specifically for Horse Racing Trifecta data files in Super Utilities, option T = Sort or Add-up Data Files. I always use the LotteryData utility mentioned above.
For additional useful information, read:
- MDIEditor Lotto WE: Lottery Software Manual, Book, ebook, Help
- Help on Software for Lottery, Lotto, Gambling: Download, Install, Run, Maintain Results Files
- State Lottery, Lotto Drawings, Results, Past Winning Numbers: Online, over Internet.
After creating, updating, and formatting the data files, one more important operation is required: concatenation of the real data file with a simulated data file.
The concatenation is done in Super Utilities, option M = Make/Break/Position, then Make, then option 1 or 2: Make DH3 from DATA-H3 and SIM-H3. DH3 is the final data file the software needs to generate reports, strategies, combinations (trifectas), etc.
- This version of the Ultimate Horse Software requires a Dh3 data file of at least 130000 (one hundred thirty-thousand) races (lines of 3 winning horse-numbers).
Here is the best procedure for creating the SIM-H3 and DH3 files to meet the size requirement of 130000 (one hundred thirty-thousand) races (lines). Simply run Super Utilities (SoftwarePickH3), option S = Files (SIM-H3, count lines). Generate 130000 straight trifecta sets. You'll have a SIM-H3 file in seconds.
** It is of the essence to use only randomized SIM files. Do not use, under any circumstances, SIM files in lexicographical order! Otherwise, the winning reports (W, MD) will turn into big headaches! Some filters will be so unusually high that several columns will run into one another. The Check Strategy functions will NOT run any longer **
W: Winning Reports (WH3, MDH3 Files)
The creation of the winning reports, is of paramount importance. Press W to generate the reports.
- S = Super reporting (WH3.x and MDH3.x): a DH3 file against itself (like in the lotto software)
- Type 200 (or more) for the length of each report. Type DH3 for the name of the data file, and the default for total races to analyze.
- Type or accept the defaults WH3.1 to WH3.6 and MDH3.1 to MDH3.6 for the report names.
The 6 + 6 W/MD report files will show a number of parameters or FILTERS. Based on the reports, you feed the trifecta generating program (L or R, main menu) with the filters. The process of setting filter values is known as strategy selection.
For more information, read:
- MDIEditor Lotto WE: Lottery Software Manual, Book, ebook, Help
- Filtering, Filters in Lottery Software, Lotto Software
- Lotto, Lottery Software Tutorial - "My kingdom for a good tutorial!"
- Software to Create Reports for Lottery Strategies.
O: Sort Filter Reports by Column
The program sorts the WH3, MDH3, GRH3, DEH3, FRH3, SKH3 reports by column, helping the user see more easily the filters — e.g. filters of wacky values (very low, or extremely high).
The sorting is done by type of winning reports. The program also offers the correct choices (correct names) for filters (columns) to sort on.
For more information, read:
C: Check Strategies (Filter Settings)
The function analyzes the 6 + 6 W/MD reports to establish any type of strategy, between minimum and maximum values. The strategy report will show how many times a particular horse-racing strategy hit in past races. In other words, we check how a collection of filter settings would have fared in the past.
The program also creates the strategy files in the correct format (error-free). The strategy files are named STH3.000 (default). You need to remember the ST file names! It is a very good idea to create a simple text file where you record various horse racing strategies: ST names and what the strategies are based on.
** Potential errors when checking for strategies.
#1: Do NOT use SIM files in lexicographical order. Always shuffle all your SIM files.
#2: Do NOT mix different race formats in your data files; that includes the file with your real races and your SIMulated files.
#3: Sometimes some filters can get way, way out of range. The value can be wider than what I planned as the maximum length for that particular filter. I wanted the reports to be as readable as possible.
If #3 happens, the strategy checking functions will trigger errors. You can fix the error by opening your winning reports one by one in the text editor. You will notice that two neighboring columns are no longer separated by at least one blank space.
The culprit is the number in the column which is no longer aligned with numbers above and below. You need delete one (very rarely more than one) character at the end of that lengthy number. Make sure that there is one blank space between the numbers in the two columns and that they are properly aligned in the respective columns. Here is a visual example:
1234 23
12345123 = strategy-checking error
Corrected W/MD file:
1234 23
1234 123
Repeat the procedure with all your trifecta winning reports, as necessary. **
H: Strategy Hits in the Past
The program generates straight trifectas for situations when a particular strategy (as in the STH3*.* files) hit in the past races. The program needs an input file created by StrategyH3 (the previous function). The input file consists of the race IDs for the hit situations. Otherwise, the user will manually input the filter settings and the races IDs (the ID is the line # when the strategy hit).
L: Lexicographic Straight Trifectas
Option R: Randomized Straight Trifecta Sets
This is the ultimate goal of LotWon software: Generate winning combinations. We keep records of past races (maintain data files), then analyze the data files and generate the winning reports. Then, we analyze the W reports and select filter values for our horse racing strategies. We finally apply the strategies to the combination (set) generators.
Each trifecta generating program has several functions of its own.
* L - Program name: LexicoH3 – it generates horse racing trifecta straight sets in lexicographical order. That is, the program starts the generation at lexicographic index #1 (1, 2, 3) and ends at the last index in the specific race (e.g. 20 19 18 in a Kentucky Derby 20-horse race).
Functions in this program:
N = Normal Lexicographic - NO ranges - NO favorites
- generates every trifecta in the 3-horse race, from lexicographical index #1 to the last index.
1 = 1 favorite number - NO ranges
- generates every trifecta, from lexicographical index #1 to the last index; also, each and every combination will contain one favorite number chosen by the software user.
2 = 2 favorite numbers - NO ranges
- generates every trifecta, from lexicographical index #1 to the last index; also, each and every trifecta will contain two favorite numbers chosen by the software user.
3 = 3 favorite numbers - NO ranges
- generates every trifecta, from lexicographical index #1 to the last index; also, each and every trifecta will contain three favorite numbers chosen by the bettor.
R = Combinations between positional RANGES
- generates every horse trifecta by positional ranges; e.g. numbers in 1st position between 1 and 3; numbers in 2nd position between 5 and 9; numbers in 3rd position between 16 and 20.
P = PURGE an output file of combinations
- takes an output trifecta file previously generated and eliminates additional sets by applying further filtering.
* R - Program name: CombineH3 – it generates horse racing trifecta straight sets in randomized manner. That is, the program starts and ends the generation anywhere in the trifecta matrix, instead of lexicographically.
Functions in this program:
0 = NO favorite numbers, NO shuffle
- generates randomized trifectas, without any favorite numbers, or clusters (shuffled combinations).
1 = 1 favorite number - NO shuffle
- generates randomized trifecta straight sets; also, each and every random set will contain one favorite number chosen by the software user.
2 = 2 favorite numbers - NO shuffle
- generates randomized horse racing trifecta combinations; also, each and every random trifecta will contain two favorite numbers chosen by the horse racing bettor.
3 = 3 favorite numbers - NO shuffle
- generates randomized horse racing trifecta sets; also, each and every random combination will contain three favorite numbers chosen by the user.
S = SHUFFLE numbers (all horse numbers in the race format)
- The function generates, for example, 10 horse numbers in one cluster or group, 3 numbers per each line; i.e. a horse-racing game will have clusters of 4 lines (straight sets), 3 numbers per line; the last line will repeat 2 numbers from previous lines.
- If you select 9 as number of horses per race, this option will generate perfect 3x3 Sudoku squares. You can generate millions of 3x3 Sudoku matrices, save them, then use them to manually fill Sudoku puzzles. Be forewarned that about one trillion distinct 3X3 Sudoku squares are possible!
- Since a staggeringly huge amount of distinct (unique) clusters is possible, we must employ filters. The filters will restrict drastically the number of clusters generated. Patience is needed as we deal with possibly trillions of clusters.
* Both programs above have two super functions before the combination generation starts:
- S = Super generating
- F = Fixed generating.
* Both horse racing programs above have two more functions that also eliminate unwanted 3-number sets (triactors):
- inner filters (they eliminate around 95% of all straight sets - enable it rarely);
- LIE elimination: You noticed that, more often than not, your horse racing output files do NOT have winning numbers - not 3 straight winners, not 3 boxed winners, not even 2-number winners. You can open the LIE file and generate trifectas that do NOT contain groups of numbers existent in the LIE file.
For more information, read:
U: Super Utilities
This piece of software bundles several utilities for horse-race wagering. Each sub-program in turn has several features of its own.
S = Files (SIM-H3, Count Lines)
- Simulate a SIM-H3 file
- Count lines in text files.
D = Duplicates: Strip and Wheel
- The function retrieves the input data, finds duplicate lines, and eliminates them.
F = Frequency Reporting by Digit
- The sub-program counts how many times each horse number came out in the specified range of past races. Then, it plots a skip chart - number of races between hits. Also, the function saves to files the most frequent pairings (BESTH3) and the least frequent pairings (WORSTH3).
W = Check for Winners
- The function checks for groups of 3 winning horse numbers in two manners:
1) an OUTPUT file against a data file with real draws
2) POOLS of numbers against a data file with real horse races results (past winning trifectas).
This function is the recommend method to check if your output files had any winners in past races, especially the races when you played the trifectas.
T = Sort or Add-up Data Files
- Nicely formats your horse racing trifecta files horizontally; plus, sorts in ascending order vertically, by multiple columns. The recommended method is the one I use. I referred to it at the beginning of this section: the LotteryData utility.
- Add-up the numbers in each trifecta in a data file to sum-totals. The recommended method is performed by the standalone application Sums presented in the next section (menu #2).
G = Generate Combinations, Favorites, Least-Number-Groups
- The function generates trifectas lexicographically. You can play favorite numbers: 1, 2, 3; or NO favorites. You can also eliminate (least) singles and pairings. This function does not require a data file of past races.
M = Make/Break/Position (DH3, Positional Ranges, Break Long Lines to Trifecta Straight Sets)
- Make DH3 without LEASTH3
- Make DH3 with LEASTH3
- Make DH3 with LEAST & BESTH3
- Break 3+ horse numbers to 3-number lines
- Generate trifectas by positional ranges (positional limits).
1 = Singles Rundown
- Calculate the frequency of every single in a format (e.g. 10 horse numbers);
- sort the singles by frequency in descending order;
- create a least single file (singles that have not come out in the specified range of races).
2 = Pairs Rundown
- Calculate the frequency of every pair (pairing) in a horse racing format;
- sort the pairs by frequency in descending order;
- create a least pairing file (pairs that have not come out in the specified range of races).
This important piece of Horse Racing software is amply presented on its dedicated page:
- Lottery Software for Singles, Pairs, Triples, Quadruples, Quintuples, Sextuples.
The next three functions — D, N, M — represent valuable new software, highly requested by members of the Super Forums.
D: Dedicated LIE Elimination (LieID)
This program applies the LIE elimination feature introduced in the BRIGHTh3 lottery software, specifically the combination generators. The main function generates the reports showing the levels of the ID filters for both the pairings and number frequencies.
For ample information, you definitely want to read:
N: LIE StriNgs (LieStringsH3)
The program shows the horse races as strings of skips, high/low, odd/even, decades, last numbers — to be used in the LIE elimination strategies. The string report files are to be used as INPUT to combination generating (G), with the filters being fed automatically. The output files are then used as LIE files in the combination generators (e.g. LexicoH3).
For ample information, you definitely want to read:
M: Markov Chains, Pairs, Followers
This complex piece of software deals with the famous Markov chains, random pairing, trendy number frequencies (.e.g. hot, cold horse numbers).
II. Menu #2: Skips, Delta, Lottery Decades, Last Digits, Wheels
D: Deltas
This is another important addition to the grand collection Ultimate Horseracing Software. The delta application shows the horse races as strings of deltas or differences between adjacent numbers. The program creates first the delta report for a data file (results). The program also generates trifectas based on user-input deltas.
For ample information, you definitely want to read:
S: Skips, Decades, Last Digits, Frequencies
The program shows the horse races as strings of skips, high/low, odd/even, increase/decrease from previous draw. The program also generates reports for horse-number decades, last digits, and a report of frequencies from 3 groups: hot, mild, cold. You can use the skips, high/low, odd/even, decades, last digits, frequencies as filters in the trifecta (triactor) generators or the purge function. The software can check if or when a strategy hit in the past. The Strategy Hits function reports how many sets a particular horse-racing strategy would have generated in winning situations.
For amplified information, you definitely want to read:
Q: Skips & Frequency Groups-Only
The program shows the horse races as strings of skips and frequencies. Both parameters are divided into 3 groups of numbers: hot, warm, cold. You can use the skips and frequency groups as filters, or generate trifectas for the LIE Elimination strategy.
This application is similar to function S = Skips, Decades, Last Digits, Frequencies. The skips, however, are divided in 3 groups, rather than dealing with them number by number. Please read the pages referred to above.
H: Wheels from Files
This program takes an input file of trifectas and converts the sets to k of 3 as lottery wheel format - from 1 of 3 to 3 of 3; also, a number of combinations can be input in a random manner, without any wheeling.
The function is useful if you want to reduce the number of trifectas in an output file previously generated. For example, you generated hundreds of combinations in CombineH3 (function R = Random on main menu) with light filtering; you want to play only a handful of triactor combinations that have no more than k numbers in common (as in lotto wheeling); evidently, you settle for a lower-tier prize, if available.
Read more details:
F: Rank Horse Numbers by Frequency
This program generates frequency reports two ways: 1.- Regardless of position; 2.- Position by position. The horse numbers are ranked by frequency in descending order, from hot, to mild, to cold.
This multi-game application is amply presented on its dedicated page and in other specialty materials:
K: Create Lottery, Horse Racing Skip Systems
This program creates lottery and horse-racing systems based on two or three consecutive skips; the most recent skips make it into a particular system.
This multi-game application is amply presented on its dedicated page and in other specialty materials:
M: Sum-up Horse Data Files
The application calculates the amount of trifectas that add-up to a sum-total. It also calculates the sums of each race in data files, plus root sum, and standard deviation. You can generate such combinations (triactors) and save them. The program creates summary reports for the game: Every sum-total and its amount of trifectas, plus percentages... and much more.
See:
V: Verify Data Files
This program parses the horse racing data files to make sure they comply with the format required by this much-envied type of software. It is highly recommended to check your data files periodically to make sure they are error-free — because errare humanum est.
For more information, read:
C: Check Winners
Check for winning numbers in output files against real race-results files. The trifectas to play were saved first to output text files by the arrangements generators.
This task can be also performed specifically for horse racing trifecta data files in Super Utilities (main menu), option W = Check for Winners = the best method.
T: Cross-Checking Lottery Strategies
The app writes to disk the lines of specified indexes in a file, usually a strategy file created by the function C = Check Strategies (main menu). You created the W*.* files in the Command Prompt software. You also generated the statistical reports in MDIEditor And Lotto WE. You then created the strategy file for the Stats function in MDIEditor Lotto. You want to see the same line numbers in WS*.* files for a more comprehensive horse racing strategy; i.e. possibilities to reduce even more the output to play.
Read more:
U: Text File Reverser
G: User's Groups, O/E, L/H, Sums
This is a big trifecta program that works with groups of horse numbers: odd, even, low, high, frequency groups, sums.
The application has many functions and its own Web page.
Please read the dedicated presentation:
III. Menu #3: Generate Sets, Pairings, Under/Over Strategies, Boxed Trifectas
* Axiomatic one, some of the functions below represent standalone programs. Other functions belong to older programs, but the names of the functions were less obvious to some software users. For example, several users asked me how to generate horse racing trifectas from groups or pools of horse numbers. There are no programs with relevant names. Instead, these functions are well represented in large programs that provide a wide variety of functions. In this particular example, the trifecta generators from pools or groups of numbers belong to the Super Utility software.
N: 3-Number Sets from Pools of Horse Numbers
Generate horse racing trifecta sets from pools or groups of numbers.
Program name: SoftwarePickH3 (Super Utilities on main menu), option M: Make/Break/Position.
The groups of horse numbers can be listed in files, in one line or multiple lines. For example, SkipSystem created for you a pool of numbers. The file in text format consists of one line of 7 numbers. You want to generate trifectas from those 7 numbers. Total of straight trifectas from 7 numbers: 7 * 6 * 5 = 210. In SoftwarePickH3, you select option M: Make/Break/Position. Then, option Break, then option 2 = All 3 Numbers Equally.
The same function can also generate trifectas from multiple lines of 3+ numbers each. For example, you had 10 lines, for each number of your horse race; each line has 6 other numbers, as the best pairs of each of the 10 numbers.
You can apply in this function a powerful filter: the Least feature. Actually, you will eliminate all pairings in a special file WORSTH3 created by the same Super Utility (option F: Frequency). It is recommended now, in strong terms, to use WORSTH3 instead of LEASTH3.
For in-depth information, study:
P: 3-Number Sets by Positions
Generate horse racing trifectas from 3 lines of numbers representing the 3 positions in a trifecta.
Program name: SoftwarePickH3, option M: Make/Break/Position.
You can generate straight trifectas based on positions or positional ranges (positional limits). If you run the statistical functions of my software, you will see that the numbers are strongly biased regarding the position. You can read at SALIU.COM a lot about ranges or positional ranges. You will see living proof that the horse numbers follow the Fundamental Formula of Gambling (FFG). Each position has numbers based on the FFG median.
You can apply in this function a powerful filter: the Least feature. Actually, you will eliminate all pairings in a special file WORSTH3 created by the same SoftwarePickH3 (option F: Frequency).
For best information, read:
- Lotto, Lottery Software, Excel Spreadsheets: Programming, Strategies, Positional Ranges
- Lottery Skip Systems: Lotto, Powerball, Mega Millions, Euromillions, Horse Races
- Analysis of Best Ranges for Lotto Number Frequency, Lottery Pairs, Pairings.
F: 3-Number Combinations from 3 Frequency Groups
Generate trifectas based on frequency: hot numbers, mild numbers, and cold numbers. Run first the Frequency Reporting module, and then the straight sets generator (lexicographic or random).
Program name: SkipDecaFreqH3 (function D: Deltas, menu #2), options: L = Combinations, Lexicographic; R = Random Combinations. Then, select the screen pertaining to the filters based on the 3 horse-number frequency groups.
Read further:
D: 3-Number Sets by Decades
Generate horse racing trifecta sets decade by decade. The following 5 "decades" are possible in this version of the software: 1-4, 5-8, 9-12, 13-16, 17-20.
Program name: SkipDecaFreqH3, options: L = Combinations, Lexico; R = Random Combinations. Then, select the screen pertaining to the filters based on the horse-number decades.
Please read much more:
G: Pairing Reports, Custom Grids, Straight Trifectas
The program plots the horse racing report of horse-number-pairings. It also builds a custom grid consisting of pairings chosen by the user. For example, the user can build a grid with pairing rank #8 and pairing rank #9 (instead of only #1 and #2 as in the wonder grid). You will notice that pairs #6+#7, or #7+#8, or #8+#9 come out with good frequency. You want to play them after a number of skips.
The Custom Grid will generate trifectas to 2 output files similar to the output files in Make/Break/Position in Super Utilities.
I noticed in my horse-racing real data file that pairing ranks #6 and #7 performed very well in generating hits for the very next race. Also, 2-way combinations of pair-ranks #1, #6, and #7 fared very well (from one race to the next).
The program also finds the pairings that have not come out within a range of races (function F, like the W reporting in the main menu). Then, function G generates trifectas for the missing pairings by setting the TWO filter.
Finally, the C function will check the 2 output files to see how they fared in the past (100 or 200, etc.) races.
This program can be useful also in conjunction with the LIE (reversed) strategy feature present in all trifecta generators. The pairings do not lead to winning straight sets the very next race (draw), far more often than not.
Program name: PairGridH3.
Replaces: SkipPairH (still in the package — just type its name at the command prompt, after eXiting the main menu).
For valuable information, read:
U: Under/Over Strategies
A special trifecta generator based on the FFG median. Two FFG medians are considered (for 10 horses):
R: Boxed & Random Trifectas
The program generates trifecta combinations either boxed or random. Usual filters can be applied, although they behave differently for the boxed generation. That's so because our results (real races) are always in straight trifectas format.
By the way, the following is the best method of record-keeping. Record only results from races with 9 or more horses, but do NOT write numbers greater than 10! If the results have numbers greater than 10, discard the race. Play only in races with 9 or more horses, as the payouts are much more favorable to wagering (bigger payouts, especially for longshot trifectas). Exception: I play up to 20 horse numbers in big races, such as the Kentucky Derby. Open the D-Ke20.CLN file, which has all the results in history, up to year of grace 2015. I deleted, however, 2 races with numbers larger than 20.
Program name: BoxRandomH3.
For more details, read:
IV. Menu #4: Specialty Programs for Probability, Odds, Combinatorics, Lexicographical Order, Wheeling
S: Super Formula, Definitive Probability, Statistics, and Gambling Software
Super Formula is the definitive software for statistics, probability, odds, gambling mathematics... and much more. The functions are grouped in 12 categories. Each software category has its own detailed sub-categories. This unique application grew from the request by many people to create software to automate the calculations in the Fundamental Formula of Gambling (FFG). FFG discovered the most fundamental elements of theory of probability and also the Universe: The relation between the degree of certainty (DC), probability p, and number of trials N.
There is ample information of the dedicated page:
D: Birthday Paradox Strategies
I had written an original essay touching a few issues of creating winning systems from the Birthday Paradox, or the probability of repetition (duplication). Such systems would apply to games of chance such as lottery, horse racing, roulette... and more. There are lottery players and gamblers who now realize how important the probability of repetition is.
Can such mathematical knowledge be applied to gambling, especially lottery or horse-racing? I was skeptical when I first heard about it and was asked about it. The difficulty of achieving thorough understanding of this phenomenon was caused by a parameter I call number of elements. Indeed, the roulette numbers repeat. You can see them all the time, if the casinos turn on the electronic displays known as the marquees. But is there a rule, a mathematical formula that enables us to calculate the repeat probability?
I thought more deeply on this repetition fact. For example, I look at a sequence of 8 roulette numbers as an eight-element string. The degree of certainty is better than 50% that such string should contain one repetition (duplication). One of the eight numbers should be a repeat with a 50-50 chance. The same is true about horse races. In this case, the element is the index of the combination (or set) drawn.
I studied some real data: Lottery drawings and roulette spins. I was somehow surprised to discover that repetition occurs close to that cutoff point of the 50-50 chance! I should also point out that the strength of the analysis and system creation is stronger at the beginning of the game. For lottery and lotto, the beginning is clear: A game starts with the first race of a game format.
Program names: Collisions, BirthdayParadox.
For specialty information, study:
P: Generate All Possible Types of Sets
This software generates ALL possible types of sets: Exponents, permutations, arrangements, combinations - and Powerball, Mega Millions, Euromillions combinations. The software generates the sets in lexicographical order or randomly. The sets can be numerical or be composed of words (text).
The horse racing trifectas belong to the arrangements category (the order or position counts; the arrangements, like the combinations, cannot have duplicate elements).
For specialty information, visit:
- Combinatorics: Permutations, Combinations, Factorial, Exponents Generate
- Comprehensive Generating: Exponents, Permutations, Arrangements, Combinations, Powerball, Mega Millions, Euromillions, Horse Racing.
R: Shuffle or Randomize Elements
Shuffle trifecta files (text files); then go to the line equal to the probability median (FFG = 50%). The program can also shuffle numbers in a highly randomized manner. There is a plethora of randomization functions in this program!
For specialty information, read:
L: Software for Lexicographical Order
The program finds the lexicographical order (index, or rank) of a given set and conversely finds the set for a specified index (rank, or numeral, or lexicographic order). Applicable to these set types: Exponents, permutations, arrangements, combinations, Powerball (5+1), Euromillions (5+2) combinations.
For specialized information, read:
B: Generate Combinations inside FFG Median Bell
This multi-game software generates sets in the FFG median zone and inside the bell (Gauss) curve. The program can be used for: pick-3 4 lotteries, horse racing, lotto-5, -6, -7, Powerball, Mega Millions '5+1', Euromillions '5+2', roulette, sports betting, soccer pools.
For specialized information, read:
F: Lexicographically-Index File
This program takes a horse data file (results) and adds indexes (ranks) to the corresponding trifectas in the file. The indexes are calculated based on the combination lexicographical order or index for that race format.
For in-depth coverage, read:
O: Probability, Odds Calculator
The probability software calculates all the odds of any many games, including Powerball, Mega Millions, Euromillions, Horse Racing games. For example, the odds for 10 horses in the race:
V: Universal Combination Generator
Lotto and horse-racing software generates combinations for absolutely any type of lottery game, plus horse racing exactas (top 2 finishers), trifectas, superfectas (top 4 finishers), etc. Specifically to this program: the combinations can be generated in steps. That is, the user has the choice to generate combinations with constant gaps or skips between them. For example, starting at the very top of a combination set (the lexicographical order #1), then step 90, the following sets generated will have lexicographic order #91,…, and so on, to the very last combination in the set (e.g. trifecta 20 19 18).
Read all the details:
G: Wonder-Grid Checking for Horse-Number Pairings
The program checks the past performance of the GRIDH3 files. The program starts a number of races back in the DATA-H3 file and creates 3 GRIDH3 files: for 10, 20, and 30 races. Each range of analysis N creates its own report file (ChkGridH3.*).
It can be used well in conjunction with the LIE (reversed lottery strategy) feature in the combination generators. The wonder grid skips more races compared to the winning situations.
For more details, read:
K: Wonder-Grid Pairs, Statistical Reports
This program creates all the statistical files for 3-race ranges - calculated by the FFG. The files have the extensions 1 to 3 in their names. The following files are created: FREQH3, PAIRSH3, GRIDH3, BESTH3, WORSTH3, LEASTH3. GRIDH3 has each number plus its 2 top pairs; BESTH3 = the top (N-1)/3 pairs; WORSTH3 has the worst (N-1)/2 pairs; LEASTH3 has the pairs with a frequency equal to 0. At the end, the program combines all GRIDH3.* BESTH3.*, WORSTH3.*, LEASTH3.* to GRIDH3, BESTH3, WORSTH3, LEASTH3.
This program is useful in conjunction with the LIE (reversed) strategy feature present in all horse output generators. The pairings do not lead immediately to winning trifectas more often than not.
For more details, read:
H: Play-Last-N-Draws as a Lottery Wheel
The horse racing utilities check for winning numbers in files of real race results. A data file will be checked against itself as if playing the last N races before the current one. For example, check the wins when I play the last 12 draws in a 5/43 lotto game. The odds of 2 of 5 are 1 in 12 as calculated by the OddsCalc super program. How many 2 of 5 hits (and other hits) will be recorded if playing in 100 future 5/43 lottery drawings?
View:
U: Old Horse Racing Utilities
This piece of horse-racing software was superseded by Super Utilities (option U in the main menu). Just nostalgia, I guess! O tempora! O mores!
Program name: UtilH32.
You might want to read:
Resources in Horse Racing: Theory, Software, Systems, Betting
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