vpFREE2 Forums

A video keno puzzzler

#1

I spend a considerable amount of time analyzing games. I'm always looking to add a play to my repertoire. Most of the work goes for naught but I do come up with a gem every once and awhile.

It's these type of video keno games that I think are the wave of the future in advantage play. I see more and more of them these days. They can't be fully analyzed by existing commercial software. Here's what this 8-SPOT video keno play looks like:

PAYSCALE

8 of 8.............800
7 of 8.............160 + 2% METER
6 of 8.............19
5 of 8.............11
4 of 8.............4
3 of 8.............1

I know how to do the math for the payscale with a calculator, pen and pad, but Bob pointed out to me about a month ago that the Wizard of Odds has a keno analyzer on his website. That saves me a lot of time.

So the payscale came up 81.6246%. The first thing I did was cull out the payback for hitting a solid 8, putting the number at 81.277%. I don't like the extreme longshots figuring into these types of plays.

But there is another segment to the game. A game within the game. The player picks his/her numbers. When you hit the start button STARS jump out onto 7 randomly picked numbers. The machine picks change every game while the player can just keep playing the same numbers.

When you hit a pay with your numbers and at least 4 of the 7 machine picks hit you go into a bonus round. To come up with the frequency of going into the bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.

I first calculated the frequency for 7 of 15 and how many permutations would be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8 and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled out the extreme longshots and put the frequency at 70.26 games for getting into the bonus round.

When you make such a catch the game goes to an alternate screen. There are 20 doors with money prizes behind each. You get to pick the doors. The prizes are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8 have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

15 of the doors allow you to pick again. 5 of the doors, while still awarding a money prize, have a stop sign behind them. When you pick one of them the bonus round is over and you return to the main game.

At first glance I figured to average 4 picks. But this may not be true. On the first pick you are 15 to 5 to keep picking. But if you are succesful there the next pick is only 14 to 5 to keep picking, 13 to 5, etc.

I've never done this kind of math before so I'm looking for any and all opinions on what the exact frequency of picks would be.

Thanks in advance.

#2

Mickey,

I imagine the frequencies can be expressed as a "continued fraction" that would give rise to an elegant solution. However, the determination of the frequency with which you successfully are allowed to pick "n" doors in the bonus round yields nicely to brute force.

Set up a spreadsheet with the following columns:

B: "Stop Doors"
C: "Other Doors"
D: "Total Remaining Doors"
E: "P(Stop)
F: "Conditional P(Stop)"
G: "P(Cum)",

where:

"Cumulative Pick" identifies the pick for which you're calculating the probability of stopping at (1,2,3 ... 16)

"Stop Doors" is the number of stops remaining when initiating that pick (a constant of 5)

"Other Doors" are the non-stops, starting at 15 and declining to 0.

"Total" is the sum of "Stop Doors" and "Other"

"P(Stop)" = "Stop Doors"/"Total Rem Doors" is the probability of hitting a Stop on this pick, = 5/20 to start with, increasing to 1

"Conditional P(Stop)" represents the cumulative probability of hitting a Stop on the "nth" Pick, and is the product "P(Stop) for this pick * "Conditional P(Stop) for the prior pick.

"P(Cum)" is a check sum on the Conditional P(Stop) column, which, if accurately entered, should total 1 at the bottom.

···

A: "Cumulative Pick"

-------

Multiplying (A) by (F) and summing the results will give the Exp(Picks). I get exactly 3.5.

I imagine you slapped your head 2 sec into this explanation, Mickey.

- H.

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

I spend a considerable amount of time analyzing games. I'm always looking to add a play to my repertoire. Most of the work goes for naught but I do come up with a gem every once and awhile.

It's these type of video keno games that I think are the wave of the future in advantage play. I see more and more of them these days. They can't be fully analyzed by existing commercial software. Here's what this 8-SPOT video keno play looks like:

PAYSCALE

8 of 8.............800
7 of 8.............160 + 2% METER
6 of 8.............19
5 of 8.............11
4 of 8.............4
3 of 8.............1

I know how to do the math for the payscale with a calculator, pen and pad, but Bob pointed out to me about a month ago that the Wizard of Odds has a keno analyzer on his website. That saves me a lot of time.

So the payscale came up 81.6246%. The first thing I did was cull out the payback for hitting a solid 8, putting the number at 81.277%. I don't like the extreme longshots figuring into these types of plays.

But there is another segment to the game. A game within the game. The player picks his/her numbers. When you hit the start button STARS jump out onto 7 randomly picked numbers. The machine picks change every game while the player can just keep playing the same numbers.

When you hit a pay with your numbers and at least 4 of the 7 machine picks hit you go into a bonus round. To come up with the frequency of going into the bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.

I first calculated the frequency for 7 of 15 and how many permutations would be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8 and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled out the extreme longshots and put the frequency at 70.26 games for getting into the bonus round.

When you make such a catch the game goes to an alternate screen. There are 20 doors with money prizes behind each. You get to pick the doors. The prizes are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8 have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

15 of the doors allow you to pick again. 5 of the doors, while still awarding a money prize, have a stop sign behind them. When you pick one of them the bonus round is over and you return to the main game.

At first glance I figured to average 4 picks. But this may not be true. On the first pick you are 15 to 5 to keep picking. But if you are succesful there the next pick is only 14 to 5 to keep picking, 13 to 5, etc.

I've never done this kind of math before so I'm looking for any and all opinions on what the exact frequency of picks would be.

Thanks in advance.

#3

I did an expected value computation. That is find the probability of each of 16 possibilities. Then multiply the number of "doors" times its probability and add up the 16 terms. I did it quickly and certainly have round off errors and probably other errors. My probably flawed answer was 3.5 doors. The most likely event is 4 doors but I have the average of 3.5.

···

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

I spend a considerable amount of time analyzing games. I'm always looking to add a play to my repertoire. Most of the work goes for naught but I do come up with a gem every once and awhile.

It's these type of video keno games that I think are the wave of the future in advantage play. I see more and more of them these days. They can't be fully analyzed by existing commercial software. Here's what this 8-SPOT video keno play looks like:

PAYSCALE

8 of 8.............800
7 of 8.............160 + 2% METER
6 of 8.............19
5 of 8.............11
4 of 8.............4
3 of 8.............1

I know how to do the math for the payscale with a calculator, pen and pad, but Bob pointed out to me about a month ago that the Wizard of Odds has a keno analyzer on his website. That saves me a lot of time.

So the payscale came up 81.6246%. The first thing I did was cull out the payback for hitting a solid 8, putting the number at 81.277%. I don't like the extreme longshots figuring into these types of plays.

But there is another segment to the game. A game within the game. The player picks his/her numbers. When you hit the start button STARS jump out onto 7 randomly picked numbers. The machine picks change every game while the player can just keep playing the same numbers.

When you hit a pay with your numbers and at least 4 of the 7 machine picks hit you go into a bonus round. To come up with the frequency of going into the bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.

I first calculated the frequency for 7 of 15 and how many permutations would be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8 and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled out the extreme longshots and put the frequency at 70.26 games for getting into the bonus round.

When you make such a catch the game goes to an alternate screen. There are 20 doors with money prizes behind each. You get to pick the doors. The prizes are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8 have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

15 of the doors allow you to pick again. 5 of the doors, while still awarding a money prize, have a stop sign behind them. When you pick one of them the bonus round is over and you return to the main game.

At first glance I figured to average 4 picks. But this may not be true. On the first pick you are 15 to 5 to keep picking. But if you are succesful there the next pick is only 14 to 5 to keep picking, 13 to 5, etc.

I've never done this kind of math before so I'm looking for any and all opinions on what the exact frequency of picks would be.

Thanks in advance.

#4

Wow! Thanks, Harry. Thanks, Robert. I'm going to practice the math until I get it down pat. I think it will be awhile before I get a play on this game. It's still new and the meters are still low. It's an individual progressive but on lots of machines. It looks like I'll have to find one where the 7 of 8 has missed about 5.5 cycles to put it on a playable number. Even then it wouldn't be anything to write home about. The bet is just 50 cents. But I can crank out about 1500 games per hour.

A miss of 5.5 cycles would put 7 of 8 paying a little more than the solid 8, about $420. It would be about a 4.5% edge at that point--with the meter thrown in. About a $35 an hour play. With the number of machines involved I think eventually I'm going to find a few plays at this game.

Thanks again. Take care.

#5

Probably flawed? You and Harry posted your answers at the same minute, so you and he were probably working independently, and, without looking at either of your messages, losing my virginity at using Excel spreadsheets, I did it essentially the way Harry described and came up with the same answer, so I'd be very surprised to discover that it wasn't right.

4 being the most common number? Wouldn't 1 be, with each additional number being somewhat less likely?

···

----- Robert <merg17@hotpop.com> wrote:

I did an expected value computation. That is find the probability of each of 16 possibilities. Then multiply the number of "doors" times its probability and add up the 16 terms. I did it quickly and certainly have round off errors and probably other errors. My probably flawed answer was 3.5 doors. The most likely event is 4 doors but I have the average of 3.5.

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

>

> I spend a considerable amount of time analyzing games. I'm always looking to add a play to my repertoire. Most of the work goes for naught but I do come up with a gem every once and awhile.

>

> It's these type of video keno games that I think are the wave of the future in advantage play. I see more and more of them these days. They can't be fully analyzed by existing commercial software. Here's what this 8-SPOT video keno play looks like:

>

> PAYSCALE

>

> 8 of 8.............800

> 7 of 8.............160 + 2% METER

> 6 of 8.............19

> 5 of 8.............11

> 4 of 8.............4

> 3 of 8.............1

>

> I know how to do the math for the payscale with a calculator, pen and pad, but Bob pointed out to me about a month ago that the Wizard of Odds has a keno analyzer on his website. That saves me a lot of time.

>

> So the payscale came up 81.6246%. The first thing I did was cull out the payback for hitting a solid 8, putting the number at 81.277%. I don't like the extreme longshots figuring into these types of plays.

>

> But there is another segment to the game. A game within the game. The player picks his/her numbers. When you hit the start button STARS jump out onto 7 randomly picked numbers. The machine picks change every game while the player can just keep playing the same numbers.

>

> When you hit a pay with your numbers and at least 4 of the 7 machine picks hit you go into a bonus round. To come up with the frequency of going into the bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.

>

> I first calculated the frequency for 7 of 15 and how many permutations would be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8 and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled out the extreme longshots and put the frequency at 70.26 games for getting into the bonus round.

>

> When you make such a catch the game goes to an alternate screen. There are 20 doors with money prizes behind each. You get to pick the doors. The prizes are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8 have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

>

> 15 of the doors allow you to pick again. 5 of the doors, while still awarding a money prize, have a stop sign behind them. When you pick one of them the bonus round is over and you return to the main game.

>

> At first glance I figured to average 4 picks. But this may not be true. On the first pick you are 15 to 5 to keep picking. But if you are succesful there the next pick is only 14 to 5 to keep picking, 13 to 5, etc.

>

> I've never done this kind of math before so I'm looking for any and all opinions on what the exact frequency of picks would be.

>

> Thanks in advance.

>

[Non-text portions of this message have been removed]

#6

Agree the most common answer or "mode" is 1. The "median" is 3.

If there are S "stop" doors and G "go" doors, the general answer for the mean on
a problem of this nature is (G + S + 1)/(S + 1) for S >=1 and just G if S = 0.
The special case identified here is indeed (15 + 5 + 1)/(5 + 1) = 3 1/2.

···

________________________________
From: Tom Robertson <007@embarqmail.com>
To: vpFREE@yahoogroups.com
Sent: Sun, April 3, 2011 4:51:51 PM
Subject: Re: [vpFREE] Re: A video keno puzzzler

Probably flawed? You and Harry posted your answers at the same minute, so you
and he were probably working independently, and, without looking at either of
your messages, losing my virginity at using Excel spreadsheets, I did it
essentially the way Harry described and came up with the same answer, so I'd be
very surprised to discover that it wasn't right.

4 being the most common number? Wouldn't 1 be, with each additional number
being somewhat less likely?

----- Robert <merg17@hotpop.com> wrote:

I did an expected value computation. That is find the probability of each of 16
possibilities. Then multiply the number of "doors" times its probability and
add up the 16 terms. I did it quickly and certainly have round off errors and
probably other errors. My probably flawed answer was 3.5 doors. The most
likely event is 4 doors but I have the average of 3.5.

--- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@...> wrote:

>

> I spend a considerable amount of time analyzing games. I'm always looking to
add a play to my repertoire. Most of the work goes for naught but I do come up
with a gem every once and awhile.

>

> It's these type of video keno games that I think are the wave of the future
in advantage play. I see more and more of them these days. They can't be fully
analyzed by existing commercial software. Here's what this 8-SPOT video keno
play looks like:

>

> PAYSCALE

>

> 8 of 8.............800

> 7 of 8.............160 + 2% METER

> 6 of 8.............19

> 5 of 8.............11

> 4 of 8.............4

> 3 of 8.............1

>

> I know how to do the math for the payscale with a calculator, pen and pad,
but Bob pointed out to me about a month ago that the Wizard of Odds has a keno
analyzer on his website. That saves me a lot of time.

>

> So the payscale came up 81.6246%. The first thing I did was cull out the
payback for hitting a solid 8, putting the number at 81.277%. I don't like the
extreme longshots figuring into these types of plays.

>

> But there is another segment to the game. A game within the game. The
player picks his/her numbers. When you hit the start button STARS jump out onto
7 randomly picked numbers. The machine picks change every game while the player
can just keep playing the same numbers.

>

> When you hit a pay with your numbers and at least 4 of the 7 machine picks
hit you go into a bonus round. To come up with the frequency of going into the
bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.

>

> I first calculated the frequency for 7 of 15 and how many permutations would
be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8
and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled
out the extreme longshots and put the frequency at 70.26 games for getting into
the bonus round.

>

> When you make such a catch the game goes to an alternate screen. There are
20 doors with money prizes behind each. You get to pick the doors. The prizes
are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8
have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

>

> 15 of the doors allow you to pick again. 5 of the doors, while still
awarding a money prize, have a stop sign behind them. When you pick one of them
the bonus round is over and you return to the main game.

>

> At first glance I figured to average 4 picks. But this may not be true. On
the first pick you are 15 to 5 to keep picking. But if you are succesful there
the next pick is only 14 to 5 to keep picking, 13 to 5, etc.

>

> I've never done this kind of math before so I'm looking for any and all
opinions on what the exact frequency of picks would be.

>

> Thanks in advance.

>

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]

#7

--- In vpFREE@yahoogroups.com, "Rick E. Percy" <ricke.percy@...>
You are right. I worked too fast and looked at the wrong column of numbers

wrote:

···

Agree the most common answer or "mode" is 1. The "median" is 3.

If there are S "stop" doors and G "go" doors, the general answer for the mean on
a problem of this nature is (G + S + 1)/(S + 1) for S >=1 and just G if S = 0.
The special case identified here is indeed (15 + 5 + 1)/(5 + 1) = 3 1/2.

________________________________
From: Tom Robertson <007@...>
To: vpFREE@yahoogroups.com
Sent: Sun, April 3, 2011 4:51:51 PM
Subject: Re: [vpFREE] Re: A video keno puzzzler

Probably flawed? You and Harry posted your answers at the same minute, so you
and he were probably working independently, and, without looking at either of
your messages, losing my virginity at using Excel spreadsheets, I did it
essentially the way Harry described and came up with the same answer, so I'd be
very surprised to discover that it wasn't right.

4 being the most common number? Wouldn't 1 be, with each additional number
being somewhat less likely?

----- Robert <merg17@...> wrote:
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>I did an expected value computation. That is find the probability of each of 16
>possibilities. Then multiply the number of "doors" times its probability and
>add up the 16 terms. I did it quickly and certainly have round off errors and
>probably other errors. My probably flawed answer was 3.5 doors. The most
>likely event is 4 doors but I have the average of 3.5.

>

> --- In vpFREE@yahoogroups.com, "Mickey" <mickeycrimm@> wrote:

> >

> > I spend a considerable amount of time analyzing games. I'm always looking to
>add a play to my repertoire. Most of the work goes for naught but I do come up
>with a gem every once and awhile.
>

> >

> > It's these type of video keno games that I think are the wave of the future
>in advantage play. I see more and more of them these days. They can't be fully
>analyzed by existing commercial software. Here's what this 8-SPOT video keno
>play looks like:

> >

> > PAYSCALE

> >

> > 8 of 8.............800

> > 7 of 8.............160 + 2% METER

> > 6 of 8.............19

> > 5 of 8.............11

> > 4 of 8.............4

> > 3 of 8.............1

> >

> > I know how to do the math for the payscale with a calculator, pen and pad,
>but Bob pointed out to me about a month ago that the Wizard of Odds has a keno
>analyzer on his website. That saves me a lot of time.
>

> >

> > So the payscale came up 81.6246%. The first thing I did was cull out the
>payback for hitting a solid 8, putting the number at 81.277%. I don't like the
>extreme longshots figuring into these types of plays.

> >

> > But there is another segment to the game. A game within the game. The
>player picks his/her numbers. When you hit the start button STARS jump out onto
>7 randomly picked numbers. The machine picks change every game while the player
>can just keep playing the same numbers.
>

> >

> > When you hit a pay with your numbers and at least 4 of the 7 machine picks
>hit you go into a bonus round. To come up with the frequency of going into the
>bonus round I looked at it like it was a 15-Spot with 1 way of 8 and 1 way of 7.
>

> >

> > I first calculated the frequency for 7 of 15 and how many permutations would
>be 3 of 8 and 4 of 7. Then 8 of 15 and how many permutations would be 3 of 8
>and 5 of 7, and 4 of 8 and 4 of 7. I went on up the line with this but culled
>out the extreme longshots and put the frequency at 70.26 games for getting into
>the bonus round.
>

> >

> > When you make such a catch the game goes to an alternate screen. There are
>20 doors with money prizes behind each. You get to pick the doors. The prizes
>are multiples of the bet, 1X, 2X, 3X, and 4X. Seven of the doors have 1X, 8
>have 2X, 3 have 3X and 2 have 4X. Average pick is 2X.

> >

> > 15 of the doors allow you to pick again. 5 of the doors, while still
>awarding a money prize, have a stop sign behind them. When you pick one of them
>the bonus round is over and you return to the main game.
>

> >

> > At first glance I figured to average 4 picks. But this may not be true. On
>the first pick you are 15 to 5 to keep picking. But if you are succesful there
>the next pick is only 14 to 5 to keep picking, 13 to 5, etc.
>

> >

> > I've never done this kind of math before so I'm looking for any and all
>opinions on what the exact frequency of picks would be.

> >

> > Thanks in advance.

> >

>

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[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]