Thread Rating:

LiberLai
LiberLai
Joined: Jul 9, 2012
  • Threads: 2
  • Posts: 3
July 9th, 2012 at 1:26:58 AM permalink
EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?
LiberLai
LiberLai
Joined: Jul 9, 2012
  • Threads: 2
  • Posts: 3
August 3rd, 2012 at 1:16:55 AM permalink
I have wrote a simulation program myself.

The probability for EXACT SCORE is very closed to 0.44%.

So the edge is over 52%.
CrystalMath
CrystalMath
Joined: May 10, 2011
  • Threads: 8
  • Posts: 1827
August 3rd, 2012 at 8:15:02 AM permalink
I agree with your simulation.
I heart Crystal Math.
pokerface
pokerface
Joined: May 9, 2010
  • Threads: 12
  • Posts: 514
August 3rd, 2012 at 8:19:44 AM permalink
seems the edge is comparable with other keno bets
winning streaks come and go, losing streak never ends.
CrystalMath
CrystalMath
Joined: May 10, 2011
  • Threads: 8
  • Posts: 1827
August 3rd, 2012 at 8:36:47 AM permalink
I actually get closer to .43%, but who's counting when the edge is crazy like this.

Live keno is horrible.
I heart Crystal Math.
mustangsally
mustangsally
Joined: Mar 29, 2011
  • Threads: 25
  • Posts: 2463
August 3rd, 2012 at 9:15:22 AM permalink
Quote: LiberLai

EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?

edit
Crystal Math and my BF are correct
Sally
I Heart Vi Hart
CrystalMath
CrystalMath
Joined: May 10, 2011
  • Threads: 8
  • Posts: 1827
August 3rd, 2012 at 9:26:22 AM permalink
Quote: mustangsally

An exact calculation is very easy in Excel using a few different methods.

Using the binomial coefficients formula
link found here.
http://wizardofvegas.com/forum/questions-and-answers/math/9660-probability-of-fair-die-equaling-sum-of-20/2/#post143909
It is the sum of 10 calculations


This is the same as asking the prob of a sum of 810 rolling 20d80 dice (20 - 80 sided die, or one 80 sided die rolled 20 times)

I get 0.383395%

In Excel,
there may be a few rounding errors,
I would have to use a high precision program on my other computer for an exact value)
this looks very close ;)

115,292,150,460,685,000,000,000,000,000,000,000,000 / 442,024,848,215,333,000,000,000,000,000,000,000


One could also use the posted Wizard's method or even the generating function I showed in an earlier thread.
(I think, when I have more time, I will use the Wizards method and see if there are no rounding errors)

A HE formula like this one
=((((Payoff to 1)+1)*P)-1)*100

108 to 1 payoff (but you said the odds are 108, that should be a 107 to 1 payout)
shows a =((((108)+1)*0.383395%)-1)*100 = -58.20989698% edge

107 to 1 payoff (but you said the odds are 108, that should be a 107 to 1 payout)
shows a =((((107)+1)*0.383395%)-1)*100 = -58.59329242% edge

I agree, over 50% house edge
Hey just about all State Lotteries are this bad, but people do hit the Lottery, just not me yet.

Sally



Actually, in keno, 20 numbers are drawn from a pool of 80, so all of the numbers must be unique and it is not like rolling 20 80 sided dice, where the numbers can be repeated.
I heart Crystal Math.
mustangsally
mustangsally
Joined: Mar 29, 2011
  • Threads: 25
  • Posts: 2463
August 3rd, 2012 at 9:32:39 AM permalink
removed
silly
I Heart Vi Hart
mustangsally
mustangsally
Joined: Mar 29, 2011
  • Threads: 25
  • Posts: 2463
August 3rd, 2012 at 10:13:13 AM permalink
Quote: LiberLai

EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?



http://static.mansion88.com/microsites/m88/Keno/kenoRules_en.html

I do not know much yet about Keno, looks to be a simple game.

The 810 total is used in other bets as shown in the linked page.
(my guess the 810 is the mode)

I am sure this is easy to calculate without a simulation as all Keno is basic math.
well, using the right formulas

Looks like a good "Ask the Wizard" question
I Heart Vi Hart
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 95
  • Posts: 4332
August 3rd, 2012 at 10:57:51 AM permalink
Sounds more like a "brute force" problem, although you don't have to check every possible combination of 20 numbers out of 80.

If the smallest number > 31, the smallest sum >= 32 + 33 + ... + 51, which is 830.

  • Jump to: