The origins of Bingola
The designer
Bingola was invented by David Latimer. David has an academic background covering Information Technology, Economics, Mathematical Statistics and Environmental Science. He is qualified to understand the mathematical probability of letters appearing in words and to write the advanced programs to identify balanced tickets.
His career has included business development, energy management, tourism and events. He is a published tourism author. He has designed several social games to promote tourism and adventure in the outdoors.
The idea for Bingola
During the COVID-19 pandemic period from late 2019 to 2021, when international tourism was impossible, David became a full-time carer for an elderly person, including being an occasional participant at a community centre.
It was during this time, the idea for Bingola was born. David discovered most games for seniors were either very traditional games or games for children. There were no games for seniors that presumed they were more educated and experienced that the generations that had gone before. There was an opportunity to improve traditional games for more sophisticated players.
Proving the game
Since the opening up David has evolved the game of Bingola and proven the mathematics behind the balanced tickets. It has been tested in a range of social situations. Bingola has been auto-tested by specialised computer programs, running millions of games to directly prove the game is fair and always resolves properly.
Using his extensive computing, environment and business acumen, David has also created a process to produce Bingola in Australia at the lowest possible price. It is so cost efficient, most organisations would end up paying more in paper and ink to print it out themselves.
The innovation of Bingola
If Bingola seems like a minor variation of games you already know, let's review what makes Bingola innovative. Unlike Bingo, the game requires more than a random number generator. There's complex mathematics behind every ticket, as we explain below.
Numeric vs Alphabetic Bingo
A popular game is Bingo with numbers, where 1 to 90 is called out in random order. In some countries, the range is 1 to 75. Bingo works fairly because the chance of any number being called is always the same. Any random Bingo ticket has the same probability of winning as any other ticket. Bingo is a fair game, but limited to numbers.
An alternative game is alphabetic bingo, but some letters, like R and N, appear more often than others, like X and Z. Because not all letters are equal, alphabetic Bingo tickets played in schools are either all the same, or they have different probabilities to win. While it's helpful for very young children to learn their ABC's, alphabetic Bingo is not a fair or interesting competition for older children or adults.
The calculations
Bingola is innovative because it solves the fairness problem when words are being called out. Some letters are more frequently used than others.
The first step in making sure that Bingola is fair was to calculate the frequency of letters in the Bingola dictionary. We find out exactly often the letters from A to Z appear in a word of a particular dictionary.
The second step was to calculate how the probability of both letters and combinations of letters affect the outcome of each turn and the whole game. By using combinations of letters, there are more possibilities that just the 26 letters of the alphabet.
Each Bingola ticket has a unique combination of letters. Some letters are more common than another. Our system is able to find a balanced combination of common and uncommon letters. Using complex mathematics our system can always ensure an ideal balance of letters and letter combinations that gives no player an unfair advantage.
Probability System
The production of Bingola tickets involves a sophisticated probability system. The complex formula is simplified to a P-number.
There are billions of possible Bingola tickets and millions of those tickets satisfy a particular P-number value. Only those ticket from the pool with the same P-number are printed. This means each printed ticket has an equivalent chance to win any particular game.
The system has been tried and tested. Our automated trials have shown the resultant probabilistic distribution is equivilant to a numeric Bingo system. This means if a particular ticket is played millions of times with randomised wordlists, it will win approximately the same number of times as any other ticket.
If every ticket has the same chance to win, why is there usually a single winner? This is due to the random wordlist. When you toss a coin on average there's a 50-50 chance of heads or tails, however on a particular throw it can only be heads or tails.
In Bingola, a similar thing occurs. Our probabilistic formula is based on the whole dictionary, however only a few of those words will appear at the top of the word list of a particular game. Since a wordlist is random, a particular letter may be more frequent than average, while another letter less frequent. As nobody knows which words will appear in the list, nobody knows which letters will come up first.
In summary, Bingola is made fair because each printed ticket is mathematically calculated to have the same level of success. Other combinations are not printed. For an equitable game, the organiser simply hands out tickets with the same P-number.
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