I am trying to determine the denomination game that is best for me to
play for an upcoming promotion. Typically I use the TSI Rating
calculator to find the best Tom Ski Index for my bankroll. However,
this promotion results in 2% cashback to make games that are less than
100% on their own into 100%+ games. Since the 2% cashback is a
guaranteed return, I am trying to determine how it impacts the overall
variance of the game. I would assume it would be lower, making higher
denomination games more playable for a smaller bankroll. If anyone can
offer some insight on this topic I would be greatly appreciative.
TSI Rating Calculator and impact of cashback on variance
Sounds like either the Dunbar VP software or the Bankroll calculator in VP for winners can
solve this dilemma for you.
.....bl
···
--- In vpFREE@yahoogroups.com, "jclind82" <jclind82@...> wrote:
I am trying to determine the denomination game that is best for me to
play for an upcoming promotion. Typically I use the TSI Rating
calculator to find the best Tom Ski Index for my bankroll. However,
this promotion results in 2% cashback to make games that are less than
100% on their own into 100%+ games. Since the 2% cashback is a
guaranteed return, I am trying to determine how it impacts the overall
variance of the game. I would assume it would be lower, making higher
denomination games more playable for a smaller bankroll. If anyone can
offer some insight on this topic I would be greatly appreciative.
jclind82 wrote:
I am trying to determine the denomination game that is best for me to
play for an upcoming promotion. Typically I use the TSI Rating
calculator to find the best Tom Ski Index for my bankroll. However,
this promotion results in 2% cashback to make games that are less
than 100% on their own into 100%+ games. Since the 2% cashback is a
guaranteed return, I am trying to determine how it impacts the
overall variance of the game. I would assume it would be lower,
making higher denomination games more playable for a smaller
bankroll. If anyone can offer some insight on this topic I would be
greatly appreciative.
If you're asking about variance in its true form, any change in a
fixed return per play (such as cashback) has no impact on variance.
It does, of course, impact your expected win/loss and the probability
that you will suffer a loss on a play.
Variance is an expression of swings in actual payback from a wager
against the expected return. It can be calculated as a function of
all possible payoffs from the bet and their respective probabilities.
Amount wagered isn't a factor in the calculation of variance.
You can think of cashback as either a rebate of a portion of each
wager, or a constant increase in the payback of each possible play
outcome, including what otherwise is a no-win result. In either case,
the impact on variance is a wash.
When you treat it as a wager rebate, it has no impact on variance
since wager isn't a component of variance. If you treat it as an
increment to all game payoffs (including a no-win), the incease is a
constant across all payoffs. This increases the expected return from
the wager by the amount of the cashback per play, and all individual
payoffs by the same amount. Consequently, the swing of results vs
expected return is unchanged.
···
------
Thus, the impact of cashback on your session bankroll is a simple,
linear relationship. In simple terms, if you expect to play through
$25,000, you simple expect your end result (including) cashback to be
improved by $500 ... as a constant across all possible outcomes.
If you bankroll yourself for a loss (prior to factoring in cashback)
of a given amount, the number of plays you expect to survive is
unchanged. If, on the other hand, you factor cashback into the net
loss that you're willing to survive, then you obviously expect to play
longer.
Just how much longer, in that case, is (as discussed by bl) can best
be determined by Dunbar's product or VPW. However, since variance
isn't affected, it's unlikely that a 2% increase in cb will make
doubling your denomination (the typical play increment) approachable
on your bankroll, unless you're running close enough to take a swing
at it on a stretch.
However, from time to time, we see reports here and elsewhere of
players who have jumped denomination because they perceive similar
promotions do extend their bankroll sufficiently -- with the
predictable result of either being bitterly disappointed at the
outcome, when hands run approximately according to expectation or more
poorly and they suffer ruin due to higher denom related variance, or
joyous because the session was unusually lucky.
- Harry
jclind82" <jclind82@...> wrote:
I am trying to determine the denomination game that is best for me to
play for an upcoming promotion. Typically I use the TSI Rating
calculator to find the best Tom Ski Index for my bankroll. However,
this promotion results in 2% cashback to make games that are less
than 100% on their own into 100%+ games. Since the 2% cashback is a
guaranteed return, I am trying to determine how it impacts the
overall variance of the game. I would assume it would be lower,
making higher denomination games more playable for a smaller
bankroll. If anyone can offer some insight on this topic I would be
greatly appreciative.
I directed my reply specifically to your statement "I am trying to
determine how it impacts the overall variance of the game", and the
subsequent question of higher denomination approachability.
However, as it turns out, there's no impact on variance. Still, going
back to your original target, an increase in cashback has a very
definite impact on TSI.
As general background for others, TSI stands for TomSki Index. TomSki
is a venerable programmer who developed one of the first well embraced
vp strategy generators (VP Strategy Master). He offered up TSI as an
attractiveness measure of a game.
In short, it weighs the return of a game against the probability that
you will bust before realizing that return. For two games with
identical ER, the game with the lower variance would have the higher
TSI. With unequal ER's, the higher the difference in ER, the higher
the difference in variance must be to put the games on equal footing.
Skip Hughes has written a webpage describing the TSI concept at length
and a download of the TSI calculator can be found there.
http://www.vid-poker.com/TSI.html
One of the inputs into the TSI calculator is game ER. Cashback is
incorporated into that ER as a simple addition: If ER is 100.2% and
cb is .4%, the ER input is 100.4%.
Because cashback will tend to have a greater impact on survivability
on a low variance game than for a high variance game, increasing
cashback will shift the attractiveness of one game over another. It's
necessary to recalculate TSI's at the higher cashback rate to
determine whether that shift is sufficient to actually reverse
attractiveness.
As a final footnote, it's my recollection that Skip (in the former
Skip Hughes Group) ultimately favored another measure to TSI in
assessing game attractiveness. I may be mistaken. I don't know if
this subject is addressed in the newer VP Insider subscription group.
- Harry
"Harry Porter" wrote:
...Cashback is incorporated into that ER as a simple addition:
If ER is 100.2% and cb is .4%, the ER input is 100.4%. ...
···
==================================================================
Well Harry, that might be simple for you, but I can't come up with
that. 
Jeff, pinch-hitting for jt
Harry Porter wrote:
...Cashback is incorporated into that ER as a simple addition:
If ER is 100.2% and cb is .4%, the ER input is 100.4%. ...Well Harry, that might be simple for you, but I can't come up with
that.
jeffcole2003oct wrote:
Jeff, pinch-hitting for jt
Just a little behind the scenes advisory rake involved. (What do you
expect from restless 2am jottings, anyway?)
(btw, are you suggesting jt couldn't quite cut it? 
- Harry