Do Some Bingo Cards Win More than Other Cards? - An Experiment There are theories that predict more winable bingo cards; namely Tippett and Grandville Theories. These seem like plausible theories made by respected mathematicians. This is an experiment to see if some cards win more often than other cards. I play bingo in a club. There are twenty to fifty players. I noticed that you must win in at least twenty five turns. I wrote a computer program to make bingo cards and play with them; this is easy for a computer which is very mathematical. I was able to play 1000 games a second with my home computer. I count the wins in less than 26 as a measure of quality. I play 1000 cards 1000 times each. I compare these cards to a master list with high scoring cards. I replace lower scoring cards with higher scoring cards. In this way, I get the highest scoring cards concentrated on a master list. Regular cards win about 80 times in 1000 tries. The master list boosted wins to 108 wins per 1000 games. I use a number seed to make cards so I can make a card again. What I did to see if cards win more was to use the master list cards to play again and see there winability then. I played 530 million games to make a master list of 1000 top winning cards. However; when I played with these top cards again, they proved to be no better than a randomly made card. This seems to indicate that all bingo cards have an equal chance of winning and no card is any better than any other card. In this product I include: the program, the master top scoring card list, the top scoring list when used again, more details about the program. If cards did show more winability, I would have pursued a reason for this - different last digits, average near the mean as the bingo theories indicate they should be like. My explanation to this project is this: A card may score very high by chance. That is, a card may win more times in 1000 trials by chance. Every 1000 cards, a few may excel by chance. It is like winning a lottery. If you win a lottery, than does not mean you are more likely to win another lottery again. You have an equal chance to win another lottery as anyone else. I am sure this is not the final word on this matter and some other thing may come up, but this is solid evidence against bingo theories. Paul Skittone 2023

Vocabulary Word Version: The inadvertent misconception made by the casino in its ads that its spa facilities are a free compliment to people checked into its hotel rooms was decried by people when they went to the spa and were told there is a $100 dollar entrance charge even to those in the hotel. Simplified Version: The unintentional impression made by the casino in its ads that its spa amenities are a free addition to people checked into its hotel rooms was disapproved of by people when they went to the spa and were told there is a $100 entrance charge even to those in the hotel. Paraphrase: The casino ran an ad showing its spa. It made it look like this was part of the deal when you went there and got a room. This was not done on purpose. People complained when they went to the spa and were told there is an additional $100 dollar entrance fee even to those in the hotel.

VOCABULARY STORY: Discerning people enumerated the discordant amounts of actual discounts disclosed in a court case and the promised discounts in deceptive ads by a cruise ship company. SIMPLIFIED STORY: Alert people listed the different amounts of actual reductions in prices revealed in a court case and the promised cuts in tricky ads by a cruise ship company. PARAPHRASE: A court case was brought against a cruise ship company. It was claimed that it was wrongfully offering lower prices that it did not honor. Those following the story closely counted all the difference in the advertised prices and the actual prices charged.

WHY AM I WRITING MORE VOCABULARY STORIES: I am embarking on writing yet more vocabulary stories; I already have 1000 similar stories on TES. So, I should explain the reasons for offering these to you: My common word stories are a flop. Not many people want those. But many people have looked at and have downloaded my fancy vocabulary stories. (It is a thrill to see my work go all around the world!) There is a continuing desire for fancy vocabulary learning; these words have earned their way in the world! It also seems that certain subjects attract interest in themselves. The new format with 5 words is quick, easy and clear. WHAT THESE STORIES CAN BE USED FOR: Vocabulary words can be used for do nows. You can challenge students or yourself to make A story out of 5 fancy words. It is easy and gets easier with practice. Paraphrasing stories, makes it clear that you know what the words mean. Short interesting stories can delightfully made by cleaver minds. There can be different takes on the same set of words. You can add a paraphrase to rephrase the ideas to make the story clearer; not stilted by the need to get words used. I feel energized to write these stories. Words are flexible enough to serve as a medium to express ideas I am currently thinking about. For example; I really went to a casino spa that was shockingly charging $100 dollars extra to its hotel guests; this found itself into story 1. I hope you use my word sets and stories to improve your vocabulary and thinking - to keep your gray matter in the pink, along with me. Paul Skittone

New vocabulary story 3 CAN YOU MAKE A STORY CONTAINING THESE FIVE WORDS?: PLAUSIBLE POLARIZE OMINOUS DEBUNK PLACATE MY VOCABULARY STORY: There are many plausible ominous theories about the Kennedy Assassination that have polarized American society ever since 1963. To placate conspiracy theorists and debunk their ideas, many government documents have been declassified. SIMPLIFIED STORY: There are many believable alarming theories about the Kennedy Assassination that have torn American society ever since 1963. To calm conspiracy theorists and discredit their ideas, many government documents have been declassified. PARAPHRASE: The Kennedy Assassination has been controversial ever since it happened in 1963. There are shocking theories that many people believe. Government documents have been declassified in an attempt to disprove many of these ideas and satisfy critics.

New vocabulary story 4 CAN YOU MAKE A STORY CONTAINING THESE FIVE WORDS?: POLEMICAL PONDEROUS OBTUSE OFFICIOUS OBSTINATE MY VOCABULARY STORY: Many people find the polemical writing of Marx ponderous and obtuse. He is also obstinately officious in his desire to change the world. SIMPLIFIED STORY: Many people find the argumentation writing of Marx heavy, awkward and difficult. He is also unreasonably bent on offering his services in his desire to change the world. PARAPHRASE: The works of Marx rub many people the wrong way. He is tedious and difficult. He continually rants about advice to turn the world inside out; which seems totally unreasonable.

How many syllables are in the English language? A learned professor says 15,000; however; he uses uncommon words and dubious sound combinations. Here is my list using common words. It is under 5,000 syllables.

DO ALL BINGO CARDS HAVE THE SAME ODDS OF WINNING? A WAS TO SEE Bingo is a game of frustration. You get a card with 25 numbers on it; five to a row. The rows are picked from these ranges: ROW 1 1-15 ROW 2 16-30 ROW 3 31-45 ROW 4 46-60 ROW 5 61-75 Other people get cards too. Numbers are called out at random from 1 to 75. If one of your numbers is called, you cover it. You win if you’re the first one to have five numbers in a row, including diagonals; so there are twelve ways to win. My first reaction to this game was extreme boredom; then I got into it. If you believe in luck, or somehow think you have a better card, then it is interesting. Someone said to me there are lucky numbers that win more. There are at least two theories claiming some numbers or combinations of numbers win more. I was curious. I wrote a BASIC computer program to find the answer: Are there better BINGO cards than win more often? My BASIC program can play about 1000 games a second. I made random cards and played with them automatically. I found the number of times a card won in 1000 game trials before the 25th number was called. It seemed to me that, that is the number you usually have to win by to win. I saved the data for each card; amount of wins before the 25th number is called. I then used the same cards to run a second 1000 game trial for each card. I saved this data. I got an average for both lists; the average number it took cards to win. Then I compared the two lists, looking for consistency; that is in both trials, where card that were better in trial 1, better in trial 2. The final result of this was around 25% That is, cards that were better in trial 1 were also better in trial 2. This shows that cards have an equal chance of being better than average in two games trial of 1000 games each. 25% chance of these outcomes: in both trials a card was above average in both trials a card was below average in trial 1 a card was above average and in trial 2 below average in trial 2 a card was below average and in trial 1 below average CONCLUSION: Bingo cards have an equal change of being better at winning. DISCUSION: It is disappointing to find this result, but confirms the laws of statistics. If you just look at the list of wins, some cards do excel and sometimes they excel both times. However; overall, in 1000 games, this does not hold true. I think I will also test for extremely good cards. That is, do cards that are much better in one trial win more often in a second trial. THE END

THE BASIC MATH EVALUATOR and COURSE explained The math product I offer, Basic Math Evaluator and Course, is special to me. I was a Speech Improvement Teacher in a high school in the 1990’s. My students always failed a basic math course that was offered to them in place of the regular course. The way they were taught was degrading and ineffective. This hurt me because I was poor in math in high school in a similar way. I resolved to write a program with my new found BASIC programming skills. The staff of my school was cooperative and supportive. The program, as you see it, was the result of this effort. It can be used in a course. Problems can be presented so that several types of problem appear in a sequence. Students must recall how to do them again and again. Because they work individually, tutoring in place is possible. After a test, the program shows you a list of the skills you know and don't know based on your answers. We had great success with this approach. The program has been upgraded to work with BBC BASIC for Windows and has three variations of questions. The problem of images was cleaverly side stepped by presenting images as pictures, instead of being generated each time. With modern computers and the internet, it is now available to you! Thank-you TES, Thank-you Russell! (BBC BASIC creator). I hope you use it and it’s ideas will be adopted.

Do you want to run multiple choice tests with students working together? The Testing Machine allows students to enter multiple choice answers together using one prepared keyboard. The Testing Machine was sought after by the founders of machine learning. This invention uses a standard computer and keyboard to accomplish this task. Because computers have buffers, several keystrokes can be reacted on that are close together. This makes it possible for several students t use on computer. This is useful for teachers working in small groups. A full explanation is included in the program.

AN ENGLISH WORD LIST Many attempts have been made to list a complete list of common English words. Here is mine. It took one year to compile. It is 17,000 words long. THE RULES I have tried to make it short but inclusive Any word that I have never heard or seen has been left out. I have usually only included one form of a word: government not governmental. THE REASONS FOR A COMMON WORD LIST Not to say I climbed it because it was there but such a project should be done; that is, any word you can think of is (or should be) on this list. I guess it is useful to learn English. It does display the richness of English; how any idea can be communicated. A BIOGRAPHY Such a list is a reflection of the interests and activities of the compiler. English peoples have participated in all the interests and activities of mankind. New words are continuously entering (and leaving) the “list”. I myself at 73 years old have many interests on an introductory level; without being boring and tedious. A spelling program is possible - a w then you see the word can be read, you can attempt a spelling, word. AVAILABLE AND FREE So here it is. Amazing how it fits in such a small space.

How are your basic math skills? This product has sixteen tests to find out. It then gives your an evaluation of your skills. You can pick questions on these topics to improve your abilities.

This is a writing exercise. It will get you to creatively write a story. Make a story from this list, using at least ten words: (I have included my story answer, with a paraphrase of it.) transfusion yule romanesque debris her inherent shinner fillet meteor burmese salient verbiage odd fascism accost whiplash bib gibe napalm formica THE AMERICAN HOSPITAL The American hospital was in an odd Romanesque building in the French town of Arl, during World War Two; the fight against fascism. Nurse Bell made her way through the debris that was inherent to war. An occasional meteor came out of the German salient, causing injuries. They gave transfusions, treated whiplash and napalm burns. During Christmas 1944, they had a giant Yule log in the fireplace to cheer the troops. The American hospital was in an odd tenth century building in the French town of Arl, during World War Two; the fight against the Nazis. Nurse Bell made her way through the wreckage is a part of war. An occasional shooting star came out of the German forward position, causing injuries. They gave blood, treated auto accidents and chemical burns. During Christmas 1944, they had a giant festive log in the fireplace for the troop’s moral. I never would have writing this story without the word prompts.

This is a writing exercise. It will get you to creatively write a story. Make a story from this list, using at least ten words: (I have included my story answer, with a paraphrase of it.) tape controversy stuff celibacy eat cull caucus gospel waxen goat korean perspicacious animate divination tawny fort brazen coroner mindset flake WHAT THE KOREAN WAR GENERAL DID There was an animated controversy during the Korean war. It was investigated by a congressional caucus which culled information from tapes. They said a general lived in a safe fort, eating to stuff himself with rich food. At the same time, he had a mindset to feed troops into battle without regard. The coroner said many deaths could have been avoided with a more perspicacious attitude. There was an lively scandal during the Korean war. It was explored by a congressional committee which drew information from recordings. They said a general lived in a secure strong place, eatting to fill himself with rich food. At the same time, he had an attitude to send troops carelessly into battle. The death investigator said many casualties could have been avoided with a more cautious strategy.

Basic computer language was first brought out in 1963 to allow ordinary people to program computers; before this only specialists could do this and the language was very difficult. When computers became cheap and widely available in the 1980’s, BASIC was part of the package. There are many versions of BASIC based on the same concepts. Commands are listed in order to tell the computer what to do. These commands are the program and can be saved. BASIC is similar to English and has command words based on what the word does. These are many books and web sites on this topic for beginner programmers. Programming is a satisfying endeavor you can get better in. You can write simple programs to do games and tasks. Here are some of the main key words: These simple commands and be combined into complex programs of actions the computer can do again and again. DOWN LOAD this product to see some essential words and ideas.

PLANNING AND WRITING A COMPUTER PROGRAM Computers are awesome and BASIC language makes this vast power available and easy. But, what should you write? It should do something, answer something. I’ve been playing BINGO. Someone claimed there are lucky numbers. At least two theories claim there are better numbers and configurations that win more. DOWN LOAD THE PRODUCT TO SEE THE WHOLE ARTICLE

This is a writing exercise. It will get you to creatively write a story. Make a story from this list, using at least ten words: (I have included my story answer, with a paraphrase of it.) tape controversy stuff celibacy eat cull caucus gospel waxen goat korean perspicacious animate divination tawny fort brazen coroner mindset flake SAINT STEPHAN THE FIRST MARTYR Saint Stephan was the first martyr. He denounced devination in an animated way, causing controversy in the pagan city. To tempt him, he was asked to eat brazen goat offered to idols that the pagans stuff themselves with. He grew waxen and began preaching the gospel with a firm mindset and refused; so they killed him. Saint Stephan was the first person killed for the faith. He condemned fortune-telling in an lively way, causing a commotion in the pagan city. To catch him up, he was asked to eat grilled goat offered to pagan gods that the pagans gorge themselves with. He grew pale and began preaching the gospel with a steady attitude and said no; so they killed him.

PLANNING AND WRITING A COMPUTER PROGRAM PART 2 It is not good to give up too easily. Are there better bingo card configurations? There are theories that say yes! So, if there are such cards you can look for them. What I’m doing is this: Have a computer program to: Make 1000 cards. Play 1000 games with each card. Get a rating number for each card. Have a list of better cards. Compare the new cards with the cards on the second list. Replace cards on the second list if it is rated lower than a new card. Progress: The original rating was 80. After 130 trials, the average rating is now 102.5. It takes around 20 minutes per trial and the computer is working. If the super cards are used and get only a beginner type rating, it is another sign that all cards are equal in their ability to win. This could be that in only 1000 games, a card can get lucky and win more even if it’s ability to win is only average. What I think: All cards are the same, but who knows?

This is an exercise to use common words randomly picked to make a story. This is a writing exercise. Random words force you to write some odd topics! You would not think of these things otherwise. These words are picked from my 17000 common word list. I provide a paraphrase into alternate words. THE BEAUTIFUL MIND The Beautiful Mind is about a zany man who is able to shunt all his mind into making meticulous equations. Pivotal to this story is how the guy was compatible to this sort of thing. He was able to hop on a math project and get with it. He was not interested in cookies or nosegays or funny limericks, just math. It was a morass and after a while, he could not pronounce his own name, being mortal. When he could not pay the remittance on his room, he was found there as crazy as a loon. The Beautiful Mind is about a odd man who is able to turn over all his mind into making elaborate equations. Central to this story is how the guy was suitable to this kind of thing. He was able to go on a math project and get with it. He was not interested in sweets or flowers or funny poems, just math. It was a mess and after a while, he could not say his own name, being human. When he could not pay the rent on his room, he was found there

In Rome, at the junction of two main roads is a stadium, the Colosseum. It is surrounded by flora - pines. In ancient Rome, the law was inconsistent. If you collaborated with the State, you were just chastised for offenses; if not you were classified as an enemy. If you gainsayed an official or were delinquent with your mortgage, you were handed over. Teams of gladiators decapitated people on the guillotine between bout as light entertainment. In Rome, at the crossing of two main roads is an arena, the . Colosseum It is surrounded by plants - pines. In ancient Rome, the law was two tiered. If you were in with the State, you were just mildly scolded for offenses; if not you were identified as an enemy. If you criticized an official or were behind with your payments, you were handed over. Gangs of gladiators beheaded people on the block between fights as light entertainment.