Wizard
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Wizard 
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March 21st, 2012 at 8:34:58 AM permalink
This is a keno variant I noticed yesterday on a Game King machine. Here are the rules.

1. Player picks 2 to 10 numbers out of 80.
2. Game picks three numbers from the 70 to 78 unchosen numbers and marks them with eggs.
3. Game picks 20 numbers out of 80.
3. If 2 eggs are hit, player win is multiplied by 4.
4. If 3 eggs are hit, player win is multiplied by 8.
5. In addition, if 2 or 3 eggs are hit, the game draws 3 extra balls.
6. Player is paid according to the base pay table below.



Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
Catch 0 0 0 0 0 0 0 0 0 0
Catch 1 1 0 0 0 0 0 0 0 0
Catch 2 3 2 1 1 0 0 0 0 0
Catch 3 0 20 4 2 1 1 1 0 0
Catch 4 0 0 50 5 5 3 2 2 1
Catch 5 0 0 0 88 55 10 4 4 2
Catch 6 0 0 0 0 500 110 20 15 10
Catch 7 0 0 0 0 0 1000 200 120 60
Catch 8 0 0 0 0 0 0 2000 500 250
Catch 9 0 0 0 0 0 0 0 2000 1000
Catch 10 0 0 0 0 0 0 0 0 2000


What is unclear to me is what happens if the get hits two eggs on the initial 20 ball draw, and then hits the third egg with the three extra balls. Does the player with 4X or 8X. Here is what the rules say:

Quote: rules


If two eggs are hit, all wins pay 4X. If three eggs are hit, all wins pay 8X! Two or more hit eggs on a winning card awards three extra balls!



I tend to think that the game would still pay 4X. Based on that assumption for the pick-10 game I get a return of 93.4114% for the pick-10.

Would anyone up for a math challenge care to confirm or refute that?
It's not whether you win or lose; it's whether or not you had a good bet.
DJTeddyBear
DJTeddyBear
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March 21st, 2012 at 8:58:48 AM permalink
I'm inclined to agree with you, that it will still do a 4X multiplier.

However, considering how rarely that will happen, maybe they'll be generous?

Frankly, if you're planning on creating a WoO page for this, I think you should calculate the edge both ways, as well as state the odds of it actually happening.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
s2dbaker
s2dbaker
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March 21st, 2012 at 10:08:41 AM permalink
I won $70 on a Caveman Keno game at Dotty's. If you want to find out about that multiplier issue, just play it. Heck, I was just killing some time.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
CrystalMath
CrystalMath
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March 21st, 2012 at 10:28:07 AM permalink
I'm always up for a math challenge.

I calculated the return both ways. Turns out that both are feasible. Looks a bit odd to me, though, because I would not expect to see a 97.3% keno, much less a 99.0% keno if you look at the 9 spot game. But, I would expect the help screen to clearly indicate which draws count toward the multiplier, so without a disclaimer on the help screens, I tend to think that the second game is how the game works.

Player is awarded multipliers based only on the first 20 draws.
Spots Marked Return
2 0.887757812
3 0.929734822
4 0.912414647
5 0.924574006
6 0.916688735
7 0.929466186
8 0.937256048
9 0.972962771
10 0.934113907


Player is awarded multipliers based on any eggs hit, with either with the first 20 draws or the 3 extra draws.
Spots Marked Return
2 0.903975771
3 0.9466015
4 0.928930666
5 0.941349123
6 0.933075619
7 0.946124812
8 0.954121691
9 0.990311769
10 0.950684901
I heart Crystal Math.
CrystalMath
CrystalMath
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March 21st, 2012 at 10:40:47 AM permalink
Quote: Rules


If two eggs are hit, all wins pay 4X. If three eggs are hit, all wins pay 8X! Two or more hit eggs on a winning card awards three extra balls!



Based on these rules, I have changed my oppinion. The rules state that only a "winning card" will get three extra balls. So, you would not get additional balls if you hit only two eggs but none of your marked spots. Based on this, I have come up with new returns, and I think it is the second one since the rules don't specify whether or not the 3 extra draws can increase your multiplier. These returns look much more normal for an IGT keno game, plus they are more consistent across the marked spots.


Player is awarded multipliers based only on the first 20 draws.
Spots Marked Return
2 0.847924228
3 0.863133828
4 0.863656371
5 0.866315366
6 0.866445463
7 0.867018706
8 0.864888873
9 0.866761486
10 0.864497242


Player is awarded multipliers based on any eggs hit, with either with the first 20 draws or the 3 extra draws.
Spots Marked Return
2 0.863032537
3 0.878263762
4 0.878877291
5 0.881489195
6 0.881579823
7 0.882045464
8 0.879805963
9 0.881317345
10 0.879256766
I heart Crystal Math.
marksolberg
marksolberg
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March 21st, 2012 at 10:41:18 AM permalink
The game is paid on the final count of number and eggs hit, so I would say it would be 8x even if the third egg is hit during the three extra numbers.

Mark
marksolberg
marksolberg
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March 21st, 2012 at 10:48:14 AM permalink
Challenge winner is CrystalMath using his final table.

Mark
Wizard
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Wizard 
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March 21st, 2012 at 11:03:21 AM permalink
Thanks CM for the outstanding and rapid results! Indeed, I was awarding the extra balls for hitting 2 or more eggs always. I'll have to go back and fix that.

Quote: marksolberg

The game is paid on the final count of number and eggs hit, so I would say it would be 8x even if the third egg is hit during the three extra numbers.



Not to say you're wrong, but how do you know?
It's not whether you win or lose; it's whether or not you had a good bet.
marksolberg
marksolberg
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March 21st, 2012 at 11:08:37 AM permalink
Quote: Wizard

Not to say you're wrong, but how do you know?



I looked at the par sheet.

Mark
Wizard
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Wizard 
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March 21st, 2012 at 11:10:42 AM permalink
Quote: marksolberg

I looked at the par sheet.



Good answer.
It's not whether you win or lose; it's whether or not you had a good bet.

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