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Question re Wizard of Odds Analysis

#1

The Wizard of Odds ran an analysis regarding a recent Suncoast promotion with a second royal being paid double. His analysis assumed you got to play until you hit 2 royals rather than real world conditions; nevertheless I can't reconcile my logical and his numerical analysis.

http://wizardofodds.com/askthewizard/249

His analysis indicated that best play was to use one strategy for the average royal value, and his computer's values bear him out. Logically I assume that 2 strategies with differing values of the royals would be employed, since the machine plays no differently after the first RF is attained. I assumed his "error" was undervaluing the first RF since it also leads to an increased expectation for a second RF. Therefore I tried using his #, 1500x, for the value of the first RF and 2000x for the second. To my surprise, the expectation was lower that way. The only explanations I can think of are: (i) his numbers are based on total expectations based on 2 RFs being attained exactly at the cycle # (and perhaps the expectation per hand would be higher if a shorter cycle were applicable for the second royal) or (ii) there is something amiss in the computer generated numbers.

I would kindly appreciate the input of some of the probability aces on this board.

David

#2

Clearly the same strategy must be played the entire time, since the game
ends when you hit two royals. It doesn't matter if the first royal pays 0,
1000, or 1500 coins. The only thing that matters is you win 3000 coins at
the end.

That being said, the analysis isn't complete. It's true that playing the
1500-coin strategy gives you the best ER per hand (assuming you always can
play until you hit). However, the 1000-coin strategy leaves you with more
money at the end (about 18 more coins, so $180 if it's a $2 game). So if you
have nothing better to do when the play is over, you might prefer to play
the 1000-coin strategy.

Even if the first royal wasn't necessary -- if the offer was simply a double
pay on your first royal (and no more) -- the 1000-coin strategy would still
leave you with more money.

Cogno

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com] On Behalf
Of David
Sent: Monday, April 12, 2010 11:11 AM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Question re Wizard of Odds Analysis

The Wizard of Odds ran an analysis regarding a recent Suncoast
promotion with a second royal being paid double. His analysis assumed
you got to play until you hit 2 royals rather than real world
conditions; nevertheless I can't reconcile my logical and his numerical
analysis.

http://wizardofodds.com/askthewizard/249

His analysis indicated that best play was to use one strategy for the
average royal value, and his computer's values bear him out. Logically
I assume that 2 strategies with differing values of the royals would be
employed, since the machine plays no differently after the first RF is
attained. I assumed his "error" was undervaluing the first RF since it
also leads to an increased expectation for a second RF. Therefore I
tried using his #, 1500x, for the value of the first RF and 2000x for
the second. To my surprise, the expectation was lower that way. The
only explanations I can think of are: (i) his numbers are based on
total expectations based on 2 RFs being attained exactly at the cycle #
(and perhaps the expectation per hand would be higher if a shorter
cycle were applicable for the second royal) or (ii) there is something
amiss in the computer generated numbers.

I would kindly appreciate the input of some of the probability aces on
this board.

David

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#3

Strategy should only be changed after hitting the first royal if
there's uncertainty about hitting the second royal. He's looking it
the play holistically, so that it doesn't matter what each royal pays,
but only what the total pays. As is the case with progressives, the
cost of hitting the jackpot needs to be incorporated to attain the
maximum value. Even after hitting the first royal, the second royal
shouldn't be valued at 2000, since hitting it has the drawback of
ending the play. In the same way that hitting the first royal
increases the value of hitting the next one, hitting the second royal
decreases the value of hitting the third one. Yes, the expectation
per hand while playing for the second royal is maximized by a strategy
that assumes it pays 2000 and doesn't take into account the fact that
hitting it will end the play. The "best play" is debatable. He's
maximizing the value per hand of the play as a whole, but the value of
the play as a whole is, as Steve Jacobs frequently emphasized,
maximized by a strategy that assumes the royal is break even. For 9/6
Jacks or Better, strategy would assume a $1 royal pays $4880, not
$6000, for example.

···

The Wizard of Odds ran an analysis regarding a recent Suncoast promotion with a second royal being paid double. His analysis assumed you got to play until you hit 2 royals rather than real world conditions; nevertheless I can't reconcile my logical and his numerical analysis.

http://wizardofodds.com/askthewizard/249

His analysis indicated that best play was to use one strategy for the average royal value, and his computer's values bear him out. Logically I assume that 2 strategies with differing values of the royals would be employed, since the machine plays no differently after the first RF is attained. I assumed his "error" was undervaluing the first RF since it also leads to an increased expectation for a second RF. Therefore I tried using his #, 1500x, for the value of the first RF and 2000x for the second. To my surprise, the expectation was lower that way. The only explanations I can think of are: (i) his numbers are based on total expectations based on 2 RFs being attained exactly at the cycle # (and perhaps the expectation per hand would be higher if a shorter cycle were applicable for the second royal) or (ii) there is something amiss in the computer generated numbers.

I would kindly appreciate the input of some of the probability aces on this board.

David

#4

I would play the first roy as regular. The second roy, I would play as a 2000 coin roy. I do assume there is a time limit of 24hrs for 2nd roy. Therefore, if I play 24hr straight I only get 12,000 games in toward a roy that would take roughly 80 hours to get. Of course, games play faster now than in the old days, but who can play 24 hr. anyway?

The Wiz did mention time limit but didn't figure it that way. I think we all would agree he is Aces in his field.

Just one guys thought.....Jeep

···

--- In vpFREE@yahoogroups.com, "David" <d_richheimer@...> wrote:

The Wizard of Odds ran an analysis regarding a recent Suncoast promotion with a second royal being paid double. His analysis assumed you got to play until you hit 2 royals rather than real world conditions; nevertheless I can't reconcile my logical and his numerical analysis.

http://wizardofodds.com/askthewizard/249

His analysis indicated that best play was to use one strategy for the average royal value, and his computer's values bear him out. Logically I assume that 2 strategies with differing values of the royals would be employed, since the machine plays no differently after the first RF is attained. I assumed his "error" was undervaluing the first RF since it also leads to an increased expectation for a second RF. Therefore I tried using his #, 1500x, for the value of the first RF and 2000x for the second. To my surprise, the expectation was lower that way. The only explanations I can think of are: (i) his numbers are based on total expectations based on 2 RFs being attained exactly at the cycle # (and perhaps the expectation per hand would be higher if a shorter cycle were applicable for the second royal) or (ii) there is something amiss in the computer generated numbers.

I would kindly appreciate the input of some of the probability aces on this board.

David

#5

Thanks Cogno, Tom and Jeep for responding to my question. Cogno and Tom for presenting the theoretical underpinnings of a type of problem new to me in clear terms which went beyond the problem presented but presented insight into the wider class of problems. My (long ago)college professors in probability and game theory should have provided such lucid explanations.

Jeep thanks for pointing out that the theoretical problem wasn't the answer to the Wizard's original questioner, especially since a complex game like JW2 (which I enjoy) is hard to play accurately rapidly, making the 24 hour real world restriction even more significant.

David