Hey Tengaged! I wanted to do the math for the tengaged lottery in its current state to show what the odds of winning truly are.
TL;DR: Odds of winning the lottery jackpot is 1/10626 (0.00941%).
Getting 3/4 numbers is 1/506 (0.198%).
Getting 2/4 numbers is 1/46 (2.174%).
The odds of any one person winning the lottery each drawing is about 1/85 (1.176%).
I have outlined the mathematical methods used below in the image, but essentially in statistics, drawing a specific number of items in no particular order from a larger group is called a combination. If these numbers needed to be drawn in order, it would be called a permutation. There is a specific formula used to calculate the odds of drawing a certain combination, but it can be easily simplified for smaller numbers such as the ones used in the tengaged drawing.
Essentially, 4 numbers are drawn. On the first one, you have 4 chosen numbers available out of a possible 24 total. Assuming one of your numbers is drawn, on the next drawing you have 3 remaining chosen numbers out of a possible 23. Continue this with 2/22 and 1/21, and multiply all 4 probabilities together to get 1/10626.
Similar logic is used to calculate the probability of getting only 3 numbers correct, you just don't need to include the final 1/21 probability. Even though 4 numbers are drawn, one can be incorrect so we only need 3 probabilities multiplied together here to get correct answer, which is 1/506. *Note that this probability includes the possibility of getting the fourth number correct.
Finally, using the data from the first couple lottery blogs, I am assuming about 125 people on average will enter the lottery. This means, assuming every person who enters is picking a unique set of numbers, we can multiply 1/10626 by 125 to get 125/10626. This number simplifies to about 1/85, which means if 125 people enter a lottery, there is still only a 1.176% chance that the lottery will have a winner. Obviously if more than 125 people enter, this number will be bigger.
One last fun fact: If you enter every single lottery up to #7365, there is a 50% chance that you will have never won any of them. (Math: (1-(10625/10626)^7365)*100 = 50%)
Please let me know if I have made any mistakes, I calculated this at 2am after a bout of insomnia! I hope this is enlightening to you all, and thanks to everyone who read this far!
TL;DR: Odds of winning the lottery jackpot is 1/10626 (0.00941%).
Getting 3/4 numbers is 1/506 (0.198%).
Getting 2/4 numbers is 1/46 (2.174%).
The odds of any one person winning the lottery each drawing is about 1/85 (1.176%).
