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
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