Does anyone know how to calculate the EV on a loss rebate play. To
make a long story short, a casino I'm playing at has agreed to rebate
8% of my loss on this trip. They have $5 & $10 9/6 JoB and 8/5
Bonus. The cash back is about .25%. How do you calculate the EV of
such a play? When should I quit (hitting a royal of course)? What's
the better play - 9/6 Jacks or 8/5 Bonus? A friend told me that the
max EV is when you loose half a royal, but I'd like to know for sure.
Loss Rebate
David wrote:
Does anyone know how to calculate the EV on a loss rebate play. To
make a long story short, a casino I'm playing at has agreed to rebate
8% of my loss on this trip. They have $5 & $10 9/6 JoB and 8/5
Bonus. The cash back is about .25%. How do you calculate the EV of
such a play? When should I quit (hitting a royal of course)? What's
the better play - 9/6 Jacks or 8/5 Bonus? A friend told me that the
max EV is when you loose half a royal, but I'd like to know for sure.
Loss rebates present one of the most challenging EV calculations of
any promotion (possibly the most). There are aspects of a loss rebate
that gives rise to an analysis that is comparable to the analysis of
options in the securities market.
The best means I've arrived at by which to perform a loss rebate
analysis is to program an iterative simulation in which you specify
win/loss quit thresholds and then run through a great number of trials
to determine the expected mean outcome.
Of course, that's largely a theoretical exercise on my part. I once
began developing such a program for a friend who had an attractive
opportunity. However, like many such endeavors that don't benefit me
personally, other priorities constantly stood in the way of
completion. (Believe it or not, altruism isn't a particularly strong
virtue of mine 
Still, preliminary efforts yielded results that
might be contrary to some people's inclination.
Variance is a clear friend to this type of promotion. That can take
the form of traditional game variance as well as escalation to higher
denominations. Just how high you might take the denomination depends
upon any limit placed on the rebate as well as bankroll constraints.
For this reason, 8/5 BP would be a more desirable play than 9/6 JB.
However, depending upon specifics, a higher variance, subpar return
alernative might be better yet.
My friend suggested, and my program confirmed, that doubling could be
employed as another means to increase play variance. However, my
preliminary explorations suggested that there were clear limits on the
extent to which redoubling is beneficial -- definitely there's a point
where it would reduce your EV.
Your friend's "half royal pivot" for optimum EV is a decent guestimate
at best. The loss threshold yielding the best EV will be considerably
larger for a high variance game than low variance since you have a
smaller expectation of making a comeback into positive turf from a low
variance game such as Jacks.
Play DDB and I wouldn't be surprised if an optimum loss threshold
might be as high as 2/3 of a royal, or more.
···
------
In absence of stringent quantitative methods on your part to arrive at
a solution (or perhaps I shouldn't underestimate your programming
prowess), I might suggest an empirical approach instead (i.e. "trial
and error"). This wouldn't give you an EV, but it might provide
insight on the most favorable win/loss thresholds.
This involves running trials to see how high you might set your loss
threshold with a respectable chance of a reveral into a profit
position that warrants walking with your gains. Likewise, you'd see
at what gain position you're most likely to maximize your expectation
of what you take away by quitting when it's hit.
The tool that I'd recommend as being the most practical for this
exercise is Frugal Video Poker. You can run a simulation of a large
number of hands and graphically view, over time, that nature of the
play swings. I can't think of any better alternative by which to get
a handle on this in a single glance.
- Harry
David wrote:
Does anyone know how to calculate the EV on a loss rebate play. To
make a long story short, a casino I'm playing at has agreed to rebate
8% of my loss on this trip. They have $5 & $10 9/6 JoB and 8/5
Bonus. The cash back is about .25%. How do you calculate the EV of
such a play? When should I quit (hitting a royal of course)? What's
the better play - 9/6 Jacks or 8/5 Bonus? A friend told me that the
max EV is when you loose half a royal, but I'd like to know for sure.
As you might have noticed from the timestamp, my reply was made in the
middle of the night. As is often the case, I got out of bed for a
couple of hours. So it is that I overlooked the specific of the 8%
rebate. My reply was most applicable to a 100% or 50% rebate situation.
An 8% rebate presents a twist because a much smaller loss rebate is
involved. I began to twist my head around this a bit. In a "winning"
game, the loss rebate has a variable value at any time depending upon
your actual win/loss position.
However, what you describe is a "losing" game. That is, when you're
winning the underlying EV is negative. With the stronger of the two
games, Jacks, the game ER plus cb yields a value less than 100%.
In that scenario, there's no incentive to play, although if you're
going to play nonetheless (recreationally), the loss rebate certainly
makes the play more favorable.
There's little change in the downside at which you would desire to
quit as a consequence of the rebate. If you're comfortable with a
$1000 loss limit when playing without the rebate, presumably you'd be
comfortable with playing to about a $1090 session loss. On the
upside, there's no practical change in your quit point.
It goes without saying that this isn't an "advantage" play. I
apologize for the misguided focus of my original reply. However, I
hope it shed a little light on rebate program considerations in general.
- Harry
Were it possible to pull my last two posts in this thread, I would
certainly do so, since I'm clearly piecing my thoughts together this
morning like a patchwork quilt.
My last abbreviated post is inaccurate and should indeed be retracted.
Elements of my first post very much apply to this situation.
A basic perspective on this problem is to divide expected session
results into wins and losses. The wins are unaffected by this
promotion. The loss economics are improved.
I'm not prepared to delve into the specifics right now, breakfast is
calling, and I won't have another opportunity to take the time today.
I will say that it's not appropriate to risk much of a winning
position on further play, so a win threshold is likely relatively low.
You do hope for a big hit, such as a royal, in crossing that
threshold,of course.
On the loss side, each bet has not only it's immediately EV to take
into consideration, but there's added value from the opportunity for a
big hit that would take you across your winning threshold in a single
win.
Ultimately, one approach might be the type of empirical method earlier
suggested. What you would ideally like to arrive at is the
probability of a losing session under any given stated loss threshold,
combined with the the average expected win when a win resulted. From
this information, with the loss rebate added into the equation, an EV
could be determined for a given loss/win threshold.
But, once again, I'm not stating anything particularly revelationary
there. It's simply that the best way to arriving at the values would
be a series of simulations. In this case, a computer program would
best serve you, but Frugal would provide some rough measurements.
On what I can put together on the fly, I can say which of the two
games discussed (JB/BP) would be a stronger game. I'm inclined toward
BP since quad Aces might yield a decent net win position at which to
quit. But in that case, were 98.9% DDB available, I certainly would
favor that even more.
Again, I offer my regret for this series of posts.
- Harry
Hi David,
If I were faced with something like this, I would open my copy of
Dunbar's Risk Analyzer for Video Poker. Then...
1. I would fill in all of the relevant information for my play
(coin-size, tip info, hourly cost of errors, cashback (set to 0% since
we are calculating the rebate), bankroll -- what I am willing to lose
on this trip, hours and hands/hour of play -- set a maximum expected
amount, tax information.
2. I would set the number of trials to a large number (10K or more;
the more the better but also the longer it will take!) and let the
short-term RoR calculation go for a while.
3. Take the results table and calculate an average win/loss for each
row. This is easy for all except the "double or more" category.
Luckily, all of the winning categories will cancel themselves out
later, so we can set this as just a double and it will not hurt us!
4. Multiply the average for the "bin" by the percentage of the time
your result ended up in that bin.
5. Add the numbers in step 4 to get your non-rebated expected result
6. Multiply all losing values in step 4 by 0.92 to account for the
loss rebate.
7. Add the numbers in step 5 to get your rebated expected result
8. Subtract 7 from 5 to get your average rebate.
9. Divide your average rebate by your average coin-in (you need to see
the calculation for the average number of hands played to get this
number). Convert this to a percentage.
The percentage from step 9 is the added EV of the loss rebate. To get
the overall EV of the play:
Total EV = Base EV + Cashback + Rebate EV
In the case of 9/6 JoB playing at the $5 level with a $10K session
bankroll for 4 hours at 750 hands/hr, the rebate adds slightly more
than 0.21%. Given a 0.25% cashback rate, this gives an overall value of:
Total EV = 99.54% + 0.25% + 0.21% = 100%.
Of course, you have to play perfectly to get this result. And
changing any of the assumptions changes the value of the rebate. (For
example, increasing the bankroll to $20,000 drops the rebate to a bit
more than 0.17%.)
Hope this helps...
Ken
···
--- In vpFREE@yahoogroups.com, "David" <virtue21@...> wrote:
Does anyone know how to calculate the EV on a loss rebate play. To
make a long story short, a casino I'm playing at has agreed to rebate
8% of my loss on this trip. They have $5 & $10 9/6 JoB and 8/5
Bonus. The cash back is about .25%. How do you calculate the EV of
such a play? When should I quit (hitting a royal of course)? What's
the better play - 9/6 Jacks or 8/5 Bonus? A friend told me that the
max EV is when you loose half a royal, but I'd like to know for sure.
kkirschner wrote:
If I were faced with something like this, I would open my copy of
Dunbar's Risk Analyzer for Video Poker. Then...
Not a bad initial approach to get one's hand around the problem.
However, the Dunbar spreadsheet program doesn't provide the option to
specify stop loss/win thresholds. This likely would have the effect
of undervaluing the promotion when the underlying game is negative.
If I have my mind around your proposition correctly (which may be
dubious, given my record this morning ;), it's not really possible to
get a good measure of the added value by variance to the promotion.
- Harry
Harry,
You are correct. The method I used will provide a low-end value for
the rebate because of the lack of a stop-win. There is a stop-loss --
whatever bankroll you provide the program!
You can run the tests iteratively to determine what bankroll provides
the desired expected return. But since I suspect the rebate is being
based on some anticipated level of play, you have to weigh potential
future offers as well.
If someone is receiving a loss rebate, they are almost certainly on
RFB...and maybe even better. This might have value that needs to be
considered -- burn them once to get out with a quick win in a
loss-rebate situation and you might never get an offer again.
Ken
···
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:
kkirschner wrote:
> If I were faced with something like this, I would open my copy of
> Dunbar's Risk Analyzer for Video Poker. Then...Not a bad initial approach to get one's hand around the problem.
However, the Dunbar spreadsheet program doesn't provide the option to
specify stop loss/win thresholds. This likely would have the effect
of undervaluing the promotion when the underlying game is negative.If I have my mind around your proposition correctly (which may be
dubious, given my record this morning ;), it's not really possible to
get a good measure of the added value by variance to the promotion.- Harry
If I remember correctly, Peter Griffin's book "*Extra Stuff: Gambling
Ramblings" *has a chapter on figuring this out precisely.
Sadly, I don't have the time to go dig up the book.
[Non-text portions of this message have been removed]
retracted.
Just go to your post and hit delete down at he bottom
···
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:
Were it possible to pull my last two posts in this thread, I would
certainly do so, since I'm clearly piecing my thoughts together this
morning like a patchwork quilt.My last abbreviated post is inaccurate and should indeed be