## Poll

2 votes (16.66%) | |||

3 votes (25%) | |||

2 votes (16.66%) | |||

3 votes (25%) | |||

No votes (0%) | |||

1 vote (8.33%) | |||

1 vote (8.33%) | |||

1 vote (8.33%) | |||

4 votes (33.33%) | |||

2 votes (16.66%) |

**12 members have voted**

May 22nd, 2019 at 7:39:58 PM
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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.

ETA: You seem to have the number of combinations correct.. must be accurate... weird.

May 22nd, 2019 at 9:44:10 PM
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Quote:rsactuaryThanks 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.

March 11th, 2020 at 12:07:52 PM
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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.

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