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Theoritical Math Problem - progressive JoB

#1

Set up:

Standard 9/6 JoB with a progressive royal. Meter rate 1%. Bank of 20
machines. The royal resets at 4000 coins.

There are 2 groups of 10 people who play this bank of machines. They both
play perfect strategy for the given progressive level.

The first group starts playing with the progressive at reset and plays until
the progressive gets to 5200 coins. If the progressive is hit before 5200
coins they continue to play until it gets to that level. Once it hits 5200
the second group starts playing on the other 10 machines and play until the
progressive is hit. Once it is hit by either group the second group gets up
and leaves until the 5200 threshold is reached again. The first group
continues to play regardless of level.

Questions:

How does this impact the royal cycle for each group?

As the meter climbs, the royal cycle gets shorter for both groups because "perfect strategy" dictates drawing for the royal more frequently.

Which group has a shorter royal cycle?

The second group will have a shorter royal cycle since they're always adjusting their strategy for a 5200-coin or higher royal.

Which group will hit more royals?

The first group, because they're playing more hands.

What is the expected cycle for each group?

I'll leave this to someone with lots of time on their hands.

Dan

···

"Tony Dubnik" <tdubnik@alltel.net> wrote:

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

#2

"Tony Dubnik" <tdubnik@...> wrote:
>Set up:
>
>Standard 9/6 JoB with a progressive royal. Meter rate 1%. Bank of

20

>machines. The royal resets at 4000 coins.
>
>There are 2 groups of 10 people who play this bank of machines.

They both

>play perfect strategy for the given progressive level.
>
>The first group starts playing with the progressive at reset and

plays until

>the progressive gets to 5200 coins. If the progressive is hit

before 5200

>coins they continue to play until it gets to that level. Once it

hits 5200

>the second group starts playing on the other 10 machines and play

until the

>progressive is hit. Once it is hit by either group the second

group gets up

>and leaves until the 5200 threshold is reached again. The first

group

>continues to play regardless of level.
>
>
>Questions:
>
>How does this impact the royal cycle for each group?

As the meter climbs, the royal cycle gets shorter for both groups
because "perfect strategy" dictates drawing for the royal more
frequently.

Agree.

>Which group has a shorter royal cycle?

The second group will have a shorter royal cycle since they're

always

adjusting their strategy for a 5200-coin or higher royal.

Agree.

>Which group will hit more royals?

The first group, because they're playing more hands.

Not sure I agree with this one, Dan. If the first group gets a
royal on less than 50% of the resets, then we know the second group
is hitting more royals. (because one of the 2 groups is hitting a
royal on every reset.)

For the RF to reach 5200, 1200 has to be added to the meter. 1200/
(1%*$5) = 24000 hands. So if the first group has better than a 50%
of hitting a royal in 24000 hands, then they will hit more royals
than the 2nd group.

If the first group does NOT adjust it's strategy, then it would take
27997 hands to have a 50% chance of hitting a royal. (because (1-
0.002476%)^27997 = 50%). If it takes 27997 hands to have a 50%
chance of hitting a royal, then the chance of a royal in 24000 hands
is less. It is 45%. So if the first group does not adjust its
strategy, the 2nd group would hit more royals.

However, the assumption was that the first group DOES adjust its
royal strategy. I don't know if those adjustments are enough to
drop number of hands required for a 50% chance of a royal from 27997
to 24000 (and thus give the number-of-royals edge to the first
group).

You might be right, Dan, it's just not obvious to me. There are
probably not many adjustments until the meter rises substantially,
so my guess would be that the 2nd group gets more royals.

>What is the expected cycle for each group?

I'll leave this to someone with lots of time on their hands.

Agree!

--Dunbar

···

--- In vpFREE@yahoogroups.com, Dan Paymar <Dan@...> wrote:

#3

You might be right, Dan, it's just not obvious to me. There are
probably not many adjustments until the meter rises substantially,
so my guess would be that the 2nd group gets more royals.

Once the royal hits $5200, each group has a 50% chance of hitting it.

#4

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...>
wrote:

>You might be right, Dan, it's just not obvious to me. There are
>probably not many adjustments until the meter rises substantially,
>so my guess would be that the 2nd group gets more royals.

Once the royal hits $5200, each group has a 50% chance of hitting it.

Yikes, I totally misread the problem. I thought the first group,
clearly masochists, got up and left as soon as the royal reached
$5200. That's the only scenario, strange as it would be, in which the
question "which group get more royals?" makes any sense.

Thanks for pointing out what should have been clear to me in the first
place, Tom.

--Dunbar

#5

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...>
wrote:

>You might be right, Dan, it's just not obvious to me. There are
>probably not many adjustments until the meter rises substantially,
>so my guess would be that the 2nd group gets more royals.

Once the royal hits $5200, each group has a 50% chance of hitting it.

Yikes, I totally misread the problem. I thought the first group,
clearly masochists, got up and left as soon as the royal reached
$5200. That's the only scenario, strange as it would be, in which the
question "which group get more royals?" makes any sense.

Thanks for pointing out what should have been clear to me in the first
place, Tom.

--Dunbar

The way you read it would have made it more interesting. It was
written rather wordily (a word that I've never used before and at
which I'm surprised that my spell-checker didn't "flag" it). All Tony
needed to say was that group 1 always plays and group 2 only plays if
it's more than $5200. The way you read it, which group hits more
royals does sound debatable.

#6

There are a total of 15 machines in high limit - 10 along the north wall under the meter displays, and 5 in a circular group near the south end.
   
  The games available and EV at reset are:
   
  8/5 JOB (97.3%), 8/7 BP (98.0%), 9/5 DDB (97.9%), and 9/6 DB (97.8%).
   
  Progressive amounts by denomination:
   
  $1: $4,017.67
  $2: $8,284.44
  $5: $20,079.50

···

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#7

In the span of about 2 hours of Friday night, there was a $20 NSU royal and a $5 JoB royal, and one guy hit deuces twice within FIVE HANDS on $2 NSU. No such luck for this reporter, but it was interesting to see that many hits in such a short time. BTW, the casino was PACKED.

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#8

In the span of about 2 hours of Friday night, there was a $20 NSU

royal and a $5 JoB royal, and one guy hit deuces twice within FIVE
HANDS on $2 NSU. No such luck for this reporter, but it was
interesting to see that many hits in such a short time. BTW, the
casino was PACKED.

I wonder who that could be... :wink:

···

--- In vpFREE@yahoogroups.com, vpfree2006 <vpfree2006@...> wrote:

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