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## Poll

 I'm stumped too. 2 votes (16.66%) This is easy, Wiz. 3 votes (25%) Just accept the simulation and move on. 2 votes (16.66%) I have some ideas, let me work on it. 3 votes (25%) I don't understand the question No votes (0%) How do I convert HEIC files to JPEG? 1 vote (8.33%) I recommend the International Car Forest 1 vote (8.33%) When are you going to analyze River Hold 'Em? 1 vote (8.33%) Total eclipse reminder 04/08/2024 4 votes (33.33%) I liked the Big Bang Theory ending. 2 votes (16.66%)

12 members have voted

Wizard
Administrator
Joined: Oct 14, 2009
• Threads: 1332
• Posts: 21942
May 22nd, 2019 at 7:05:53 PM permalink
Here is my new page on this topic, Keno Sums. I welcome all comments and corrections on it.

Again, thank you to all who contributed to this topic!
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary

Joined: Sep 6, 2014
• Threads: 19
• Posts: 1682
May 22nd, 2019 at 7:39:58 PM permalink
Thanks for your work on this... I didn't check through the math, but it seems weird that the return for exactly 810 is about half of every other bet.

ETA: You seem to have the number of combinations correct.. must be accurate... weird.
Wizard
Administrator
Joined: Oct 14, 2009
• Threads: 1332
• Posts: 21942
May 22nd, 2019 at 9:44:10 PM permalink
Quote: rsactuary

Thanks for your work on this... I didn't check through the math, but it seems weird that the return for exactly 810 is about half of every other bet.

I figure that's because the payout is larger. More risk to the casino to offer it.
It's not whether you win or lose; it's whether or not you had a good bet.
Klopp
Joined: Mar 10, 2020
• Threads: 7
• Posts: 16
March 11th, 2020 at 12:07:52 PM permalink
An insightful approximate solution can be given. The probability distribution of the sum of the 20 keno balls can be very closely approximated by a normal distribution with expected value 810 and standard deviation 97.2.
In chapter 9 of the book Surprises in Probability written by Henk Tijms a more general situation is considered: a lottery in which r different numbers are randomly drawn from the numbers 1 up to s. Then the sum of the drawn numbers has an approximate normal distribution with expected value r(s+1)/2 and as standard deviation the square root of r(s+1)(s-r)/12 provided that s is not too small . An insightful and useful result.
Last edited by: Klopp on Mar 11, 2020

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