Thread Rating:
and the odds is 108.
what is the edge?
The probability for EXACT SCORE is very closed to 0.44%.
So the edge is over 52%.
Live keno is horrible.
editQuote: LiberLaiEXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.
and the odds is 108.
what is the edge?
Crystal Math and my BF are correct
Sally
Quote: mustangsallyAn exact calculation is very easy in Excel using a few different methods.
Using the binomial coefficients formula
link found here.
https://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.
silly
Quote: LiberLaiEXACT 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
If the smallest number > 31, the smallest sum >= 32 + 33 + ... + 51, which is 830.
Quote: KeyserBasically Keno is like going to the horse track.
It smells the same? Is that what you mean?
silly
Quote: KeyserBoth are basically carnival games. The house edge is so high for both that nobody can hope to win in the long run.
There is no house edge at the racetrack. The track takes a takeout (like a rake in Poker), and all the bettors bet against one another (parimutuel betting, like a cardroom). The takeout is what eats your lunch.
In short, horse racing is a suckers bet. Virtually every casino game has much better odds.
But,let's back to the question
what is Keno 810's house edge? how to calculate it?
Quote: qeqeqeyes,that'right.
But,let's back to the question
what is Keno 810's house edge? how to calculate it?
A simulation is good enough for this game and I don't think there is any need to calculate it.
A perfect score occurs about 0.43% of the time. If it pays 108 to 1, the return is about 46.5% with a house edge of 53.5%.
Quote: mustangsallyedit
Crystal Math and my BF are correct
Sally
So I and Crystal Math are correct once again ?
Quote: qeqeqeyes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?
There is no easy solution that I know of. Sometimes, even in gaming, a simulation is the best we can do.
using full version Wolfram Alpha or MathematicaQuote: qeqeqeyes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?
it should be this for sum=810
A/B (simple part)
where:
A = Coefficient[Product[1 + x*y^i, {i, 1, 80}],x^20 y^810]
B = C(80,20)
x^20 y^810 means
x^20 is drawing 20 distinct values without replacement
y^810 is the sum
that number before x^20 y^810 (say 15 x^20 y^810)
would be 15 ways for draw 20 and sum=810
of course it is probably closer to
15,201,859,411,512,400 x^20 y^810
just guessing (as I do not have full versions of WA or M
and R does not really support this. maybe there is a package for it)
found this (for more reading)
How many ways are there to get a specific sum
ok
had some time to kill off before hitting the mall
Sally
in Mathematica in above postQuote: qeqeqeyes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?
or in Pari Gp (free)
prod(i=1, 80, 1 + x*y^i);
I used GP (took split second to calculate and print to a file)
answer (find x^20 = 20 draws without replacement and y= the sum)
exactly
15542763534960598 / 3535316142212174320 [ from C(80,20) ]
about = 0.0043964281862597251250724239977180641876
here be the results
example: 3*y^1407
3 ways to get the sum=1407 (and sum=213)
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house edge should now be easy
back to eating
Sally
For 20 numbers the standard deviation is 20^.5 * σ * (60 / 79 ) ^.5 = 90.
So the expected value is 810 +/- 90. The probability mass function for the value 810 is 0.00443.
So:
1 / (σ * (60 / 79 * 20 * 2 * pi)^.5) = 0.00443.
I thought I would add this to a webpage so anyone can view or inspect.Quote: mustangsallyhere be the results
I never have seen this info (keno 80 draw 20 sums) published as exact results.
Can't say that anymore
I am certain I am NOT the 1st to do this.
https://sites.google.com/view/krapstuff/keno
approximations in Excel are close enough for me
Sally