vpFREE2 Forums

About Time For a Quiz Question

#1

The group must be getting bored or something...with all the XVP
stuff. Time for some nerd-like math about a bonus for VP play.

Some of you may be familiar with the River Palms in Laughlin. In a
roped-off section called Winners Wharf a premium has been offered, a
personal card of the day.

Details: Swipe you card at the kiosik and get a random card value.
Hit a Quad at this value and you get a 100 coin bonus. If you happen
to have a face card kicker, it is doubled instead. Good for 24 hours
or until you hit, then get a new Quad value.

The plays have diminished over the two years this promo has run, but
at the quarter level there is 9/6 JB, 8/5 Bonus, 9/6 DDB, 10/7 DB,
and the rare 9/5 White Hot Aces (99.6%).

I have had trouble figuring out how to optimize this promotion.

Take Double Bonus and use WDPWP as the tool.

If the card of the day is Aces, 3/4 of the time the payoff is 900
coins, 1/4 it is 1600 coins, when hitting Aces. This is equivalent
of 1,075 for Aces. Change the paytable, run the analysis and get
101.40% return (var 33.7).

Also 2,3,4 is 100.78% (29.3), 458 coin equivalent.

5-K is 100.65% (28.7), 265 coin equivalent.

It is quite apparent saving a pair of Aces over two pair is the
correct play in the long term, when you have Ace as your card. But
should strategy changes take place in this 24 hour short term? 5,000
hands should result in hitting a set of Aces.

What if you only plan to play 10,000 hands? 1,000 hands or just one
hand?

It is a strong promo no matter what, what's your thoughts?

BS

#2

<<<
5-K is 100.65% (28.7), 265 coin equivalent.

It is quite apparent saving a pair of Aces over two pair is the
correct play in the long term, when you have Ace as your card. But
should strategy changes take place in this 24 hour short term?

  What is going on here? I have been reading a perfectly
sound post about analyzing a promotion. I did not check the math,
but it looks reasonable. Then, out of the blue, I encounter this
question about changing the strategy in the short term. I have
no idea why this concept is getting so many people confused. The
correct strategy is the correct strategy. The number of hands you
happen to play today or this weekend or this year is of no
consequence.

  There was a recent thread about playing 2-2-7s-8s that
made it clear some people hold 2-2 from 2-2-7s-8s. They are
sacrificing ER for increased variance. Now this poster seems
to think it might be wise to sacrifice ER for reduced variance.
The first of these can never be correct. The second could be
correct in some situations involving a significant portion of
your bankroll, but that should never happen in VP.

  It sounds like a lot of people want to somehow improve
upon optimal strategy. There is a reason optimal strategy is
called optimal strategy. It's called optimal because it is
optimal. This idea of a 'short term strategy' is a load of crap.

  QZ

#3

There was a recent thread about playing 2-2-7s-8s that

made it clear some people hold 2-2 from 2-2-7s-8s. <<

What I got from that particular thread (and my contribution to it) was that
it was a suggestion put forward only for discussion, mainly because the
difference in variance was negligable. But that possible hold was not
recommended. I know for a fact that the person who originally mentioned it
is an optimum player, and just wanted to get away from the negative
off-topic stuff that was going on at the time. Very few people responded to
that thread, and of those, only one said that they would do it. So rest
easy, optimum play is safe and sound.

lb

#4

I think this is an excellent question. I believe that Qzilla is off
base in his reply. "Optimum" strategy can depend on time available
in certain circumstances. Progressives and one time bonuses
complicate analysis considerably. Interestingly, if you have a
fairly SHORT time until the bonus expires or you will leave, you
should use the generic "long term" strategy with the bonus treated at
full value.

If you plan to play for a period long enough that there is more than
a modest chance you will hit the Aces, the value of the bonus hand
should be derated. This is justified because the total EV that you
achieve for your session will be diminished after the bonus is hit
and reset to a lower value. Here is an approximate approach: Assume
you have a long enough time available that it is very likely you will
hit the Aces. First you can calculate the total EV (in dollars) of
the opportunity as the EV per hand (using the "long term" strategy)
times the average number of hands required to hit the bonus hand.
Then you calculate the EV (again in dollars) you would achieve
assuming the bonus is hit on your next hand, which may or may not be
on this machine or even this casino, over that same average time
interval. Now subtract the DIFFERENCE in EV from the value of the
bonus hand and reoptimize the strategy. If you are really anal, you
can repeat the process using the new value of EV per hand with the
adjusted strategy. The result is that you might not chase the Aces
quite as aggressively with lots of time remaining.

With a time remaining a small multiple of or a large fraction of the
bonus cycle time, the analysis is much more complex. As time
remaining drops, the EV of the opportunity starts to drop and you
should gradually be more aggressive, eventually using the "long term"
strategy.

In practice, the adjusted EV may result in few if any strategy
changes and the difference in EV may be negligible unless the bonus
is substantial.

AJ

--- In vpFREE@yahoogroups.com, "bluestreak86001 <graytleegray@a...>"
<graytleegray@a...> wrote:

The group must be getting bored or something...with all the XVP
stuff. Time for some nerd-like math about a bonus for VP play.

Some of you may be familiar with the River Palms in Laughlin. In a
roped-off section called Winners Wharf a premium has been offered,

a

personal card of the day.

Details: Swipe you card at the kiosik and get a random card

value.

Hit a Quad at this value and you get a 100 coin bonus. If you

happen

to have a face card kicker, it is doubled instead. Good for 24

hours

or until you hit, then get a new Quad value.

The plays have diminished over the two years this promo has run,

but

at the quarter level there is 9/6 JB, 8/5 Bonus, 9/6 DDB, 10/7 DB,
and the rare 9/5 White Hot Aces (99.6%).

I have had trouble figuring out how to optimize this promotion.

Take Double Bonus and use WDPWP as the tool.

If the card of the day is Aces, 3/4 of the time the payoff is 900
coins, 1/4 it is 1600 coins, when hitting Aces. This is equivalent
of 1,075 for Aces. Change the paytable, run the analysis and get
101.40% return (var 33.7).

Also 2,3,4 is 100.78% (29.3), 458 coin equivalent.

5-K is 100.65% (28.7), 265 coin equivalent.

It is quite apparent saving a pair of Aces over two pair is the
correct play in the long term, when you have Ace as your card. But
should strategy changes take place in this 24 hour short term?

5,000

···

hands should result in hitting a set of Aces.

What if you only plan to play 10,000 hands? 1,000 hands or just one
hand?

It is a strong promo no matter what, what's your thoughts?

BS

#5

AJ - I understand where you're coming from. But I think the reasoning
works in those cases where the bonus is available once and only once.
Once you collect the bonus, the effective paytable is reduced to the
standard one (and as you note, the bonus hand is reduced). In such a
case, for example the quad 7 doubler coupon at the LV Hilton, if you
are playing sufficiently long to have a strong expectation of hitting
the quad (say, 20 hours) then no modification is called for. Play
only 10 hours or less and an aggressive strategy for the bonus quad is
desirable.

However, if I understand bluestreak's post, upon collecting the quad
bonus in the promo he's playing you get another quad bonus to shoot
for. In that case, strategy modification fully reflecting the current
bonus quad is appropriate since there's a bonus available at all times
of play.

One analogy that might offer insight is that this is equivalent to
playing 13 different paytables. Just because at any moment you might
change the paytable doesn't mean that you should play a given paytable
with anything less than fully optimized strategy. In most cases,
strategy modifications called for at any given time are modest.

- Harry

#6

<<<
I think this is an excellent question. I believe that Qzilla is off
base in his reply. "Optimum" strategy can depend on time available
in certain circumstances. Progressives and one time bonuses
complicate analysis considerably.

  You and I both know that I was not talking about unusual
circumstances. Even so, most of them are still covered by optimum play.
This topic was discussed in depth several months ago. Consult the
archives for details.

<<<
If you plan to play for a period long enough that there is more than
a modest chance you will hit the Aces, the value of the bonus hand
should be derated. This is justified because the total EV that you
achieve for your session will be diminished after the bonus is hit
and reset to a lower value.

  The strategy with lots of time remaining will be identical to
optimal strategy for the 'base' game. This assumes the promotion is
a 'one time' deal. If it lasts for a given length of time, but can be
hit multiple times, the correct strategy is found by using the strategy
calculated by inserting the value of the hand with the promotion
included in the payoff.

   On the final hand, it will be the optimal strategy for the game
using the full value of the bonus. A rigourous analysis of the strategy
between these extremes is not worthwhile.

<<<
In practice, the adjusted EV may result in few if any strategy
changes and the difference in EV may be negligible unless the bonus
is substantial.

Right.

  QZ

#7

Harry,

If I understand bluestreak's post, he was talking about playing
double bonus or some other game with a very high payout for aces. If
your bonus card is aces, the reset bonus card is likely to be much
less desirable. The ER of the machine after a reset is the sum of
the ERs of the machine with each possible denomination of new bonus
card divided by 13. The ER/EV loss can be very significant.

AJ

However, if I understand bluestreak's post, upon collecting the quad
bonus in the promo he's playing you get another quad bonus to shoot
for. In that case, strategy modification fully reflecting the

current

bonus quad is appropriate since there's a bonus available at all

times

of play.

One analogy that might offer insight is that this is equivalent to
playing 13 different paytables. Just because at any moment you

might

change the paytable doesn't mean that you should play a given

paytable

···

with anything less than fully optimized strategy. In most cases,
strategy modifications called for at any given time are modest.

- Harry

#8

Excerpts from two recent posts on this topic that I think nail the main
issue:

I was not talking about unusual circumstances. Even so, most of them are

still covered by optimum play. This topic was discussed in depth several
months ago. Consult the archives for details. <<

And this:

>In practice, the adjusted EV may result in few if any strategy

changes and the difference in EV may be negligible unless the bonus
is substantial.

In almost all cases (dating back to threads on doubling-up and multistrike)
optimal strategy theoretically nets the best results over time. But as the
second post correctly points out, often slight strategic differences have
such a negligible effect on EV, given short term fluctuations (I've heard
them called spatter) that there's little if any effect on outcome. But
that's also an argument for just staying with the optimal strategy, isn't
it?

lb

#9

AJ wrote:

Harry,

If I understand bluestreak's post, he was talking about playing
double bonus or some other game with a very high payout for aces. If
your bonus card is aces, the reset bonus card is likely to be much
less desirable. The ER of the machine after a reset is the sum of
the ERs of the machine with each possible denomination of new bonus
card divided by 13. The ER/EV loss can be very significant.

I grasp what you're saying, AJ. Now, let me throw out a hypothetial
that I don't think distorts circumstances for consideration of this
question.

Let's say that if you get the Aces bonus card, then you receive double
(or whatever premium) if you hit before the end of the gaming day
(which I understand as being the details of this promo - you better
stop me here is I'm wrong).

Now, I'm going to modify the promo details: All of the other cards
available read: "Sorry, no bonus for the Aces on this card. But you
can try for it on your next card after hitting quad Sevens" (vary the
sevens if you prefer).

Now my question for you: What's the optimal strategy when you hold
the Aces bonus card?

I'm going to propose a few analogies, all of which I think are
equivalent to this play:

Randomly you're given the opportunity to play a machine on the floor
paying the Aces bonus until you hit the Aces or the end of the gaming
day. After that, you have to wait for your next random opportunity.

Or, if you like, let's simply say you have a peculiar quirky nature
and prefer to play this attractive game only when you feel like it,
stay with it until you hit Aces or the end of your trip, and when you
hit Aces you say "enough for now" and walk away until some unspecified
time later. Of course, the other option of walking away when tired is
available and doesn't change strategy.

In each of these cases, the play when double pay Aces are available is
to treat the various sessions as one lifelong continuous session. In
other words, play with optimal strategy that treats the Aces paytable
as permanent.

Now, you probably know from past experience (certainly QZ does) that I
can be doggedly persistent, but if wrong, I'll eventually catch on and
thank you for your patience. So, I'd appreciate you engaging me in
this one if you think I'm still on the wrong track. It's the only way
I learn, even if it means a certain degree of bashing my head into the
wall until I get it!

- Harry

#10

Harry,

Allow me to digress. Rational behavior is sometimes modelled
as "utility" maximization. Utility is loosely defined as a
quantification of individual happiness. There are an almost infinite
number of contributors, making any precise measurement difficult.
Major contributors could be money, mental and physical health,
healthy relationships, adequate sleep, good food, entertainment,
etc. I recently read an article that reported on a study that
attempted to quantify intangibles in dollar terms. They claimed that
a happy marriage was worth about $100,000.

What's this got to do with VP? Our decisions on what to play and
with what strategy should be governed by utility maximization. Most
of the time, we can simplify our thought process and play for the
maximum EV per hour within our bankroll for the time we choose to
dedicate to VP and not stray far from the maximum. Even this
assumption is little questionable for many people based on comments
from more than a few players such as, "pickem gets boring after a few
hours, so I switched to jacks or better".

To analyze a promotion or progressive mathematically, some
assumptions must be made. Different (reasonable) assumptions will
yield different optimal behavior. There are other unnecessary
assumptions that you can make to simplify the analysis if are willing
to accept some inaccuracy. Depending on the circumstances these
simplifying assumptions can lead to trivial errors, but occasionally
they are significant.

One simplifing assumption that is often made is to
ignore "opportunity cost". My original reply claimed that
opportunity cost can be a factor in determining strategy. To show
that this is not totally esoteric, I will illustrate this with a real
world example. Suppose you are to playing an isolated 10/7DB game
with no other good games in the vicinity. Suppose further that 4
aces is a hand pay that typically takes 30 minutes and you will be
bored and frustrated the whole time. My recollection is that
the "optimal" play when dealt a full house including three aces is to
discard the small pair. However when you assign a fairly small
reduction to the value of 4 aces to compensate for the associated
loss of playing time, tip, etc. that comes with the 4 aces, you will
find that holding the pat full house may be the real "optimal"
play.

Hopefully this is somewhat illuminating. Sorry I don't have the
energy to comment on your specific analogys other than to reiterate
that different (reasonable) assumptions often lead to different
answers.

AJ

--- In vpFREE@yahoogroups.com, "Harry Porter <harry.porter@v...>"
<harry.porter@v...> wrote:

AJ wrote:
> Harry,
>
> If I understand bluestreak's post, he was talking about playing
> double bonus or some other game with a very high payout for

aces. If

> your bonus card is aces, the reset bonus card is likely to be

much

> less desirable. The ER of the machine after a reset is the sum

of

> the ERs of the machine with each possible denomination of new

bonus

> card divided by 13. The ER/EV loss can be very significant.

I grasp what you're saying, AJ. Now, let me throw out a hypothetial
that I don't think distorts circumstances for consideration of this
question.

Let's say that if you get the Aces bonus card, then you receive

double

(or whatever premium) if you hit before the end of the gaming day
(which I understand as being the details of this promo - you better
stop me here is I'm wrong).

Now, I'm going to modify the promo details: All of the other cards
available read: "Sorry, no bonus for the Aces on this card. But

you

can try for it on your next card after hitting quad Sevens" (vary

the

sevens if you prefer).

Now my question for you: What's the optimal strategy when you hold
the Aces bonus card?

I'm going to propose a few analogies, all of which I think are
equivalent to this play:

Randomly you're given the opportunity to play a machine on the floor
paying the Aces bonus until you hit the Aces or the end of the

gaming

day. After that, you have to wait for your next random opportunity.

Or, if you like, let's simply say you have a peculiar quirky nature
and prefer to play this attractive game only when you feel like it,
stay with it until you hit Aces or the end of your trip, and when

you

hit Aces you say "enough for now" and walk away until some

unspecified

time later. Of course, the other option of walking away when tired

is

available and doesn't change strategy.

In each of these cases, the play when double pay Aces are available

is

to treat the various sessions as one lifelong continuous session.

In

other words, play with optimal strategy that treats the Aces

paytable

as permanent.

Now, you probably know from past experience (certainly QZ does)

that I

can be doggedly persistent, but if wrong, I'll eventually catch on

and

thank you for your patience. So, I'd appreciate you engaging me in
this one if you think I'm still on the wrong track. It's the only

way

I learn, even if it means a certain degree of bashing my head into

the

···

wall until I get it!

- Harry