Today we are taking a
behindthescenes look at the process by which Steep Regressions work so
well for advantageplayers.
Effort IN…Profit OUT
If you
don't put the necessary effort INTO calculating your validated
incasino pointcycle SRR, then it makes it much tougher to extract your
rightfully deserved profit OUT of it.
Steep
Regressions let you take advantage of all but the shortest
Pointthen7Out hands by locking in an early profit on the first paying
hit; yet it also lets you stay “in the game” (with multiple active wagers)
in the event that you do manage to get a couple more, or even many
more payinghits.
You’ll
find that the broader you spread your initial bets, the steeper the
regression has to be to accomplish the same goal. For example, if you
simply Placebet the 8 for $12 and regress it to $6 after one hit; then
you’d still have an $8 netprofit to show for it, even if the 7 shows up
on the very next roll. However, if you make that same bet on both
the 6 and the 8, then you’ll only have an inrack netprofit of $2 (but of
course you now have twice the amount of money still in action).
Likewise, as you spread out to $44Inside ($12 each on the 6 & 8, and $10
each on the 5 & 9); one $14 payinghit doesn’t leave ANY netprofit to
work with while you still have all four Inside Numbers covered even if you
regress them down to $22Inside.
In this
case, you could reduce the breadth of your bets by just wagering on the 6
& 8 for $6 each, or you could increase the initial InsideNumbers
wager to $66Inside, which would still leave you onebuck short in order
to cover the 5, 6, 8, & 9.
In the
alternative, you could start with a steeper ratio $88Inside for a $28
onehit payout which generates enough cashflow to cover a Steep
Regression to the $22Inside level and still guarantee a $6 netprofit
after all is said and done even if a 7Out shows up on the very next roll.
As you
can see, the wider you want to spread your bets (to increase your
prospects of picking up a “firsthit” payoff), the higher your
initial wagers (both individually and collectively) have to be in order
for the first hit to pay enough for minimumbet coverage on just as wide a
range of bets once you regress them.
In other words; the wider the range of bets you want to cover; the
higher the initial large total bet has to be in order to
generate enough revenue to cover the subsequent small wager and
still show an overall netprofit…or stated in the alternative; the
fewer advantagedbets that you spread your money over, the lower
your initial large ISR bet needs to be.
But again, you have to
put the necessary effort INTO calculating
your validated pointcycle SRR in order to extract your rightfully
deserved maximalrevenue OUT of it.
Several readers have
asked about the formulas and calculations that go into the overall ISR
validation process, and I’m happy to oblige. I’ll also quickly note that
you can use the same formulas and methods to validate ANY bettingmethod
you are contemplating.
SRR ExpectancyRate
Calculating your SevenstoRolls Ratio is quite simple. We know for
example that…
The
sevensexpectancyrate for an SRR6 randomshooter is 16.67% on any given
roll (6outof36 possible outcomes).
By dividing those six
possible 7’s into the thirtysix possible outcomes, we determine the 7’s
expectancyrate for a random SRR6 shooter to be 1in6 (16.67%) on any
given roll.
Likewise, we can do
the same for any SRRrate:
The
sevensexpectancyrate for an SRR7 shooter is 14.29% on any given roll
(5.14outof36 possible outcomes).
The
sevensexpectancyrate for an SRR8 shooter is 12.50% on any given roll
(4.5outof36 possible outcomes).
The
sevensexpectancyrate for an SRR9 shooter is 11.11% on any given roll
(4outof36 possible outcomes).
Even if you have a
fractional SevenstoRolls Ratio of let’s say, 1:6.5, you can use the same
formula to determine that you’ll see an average sevensexpectancyrate of
15.39% on any given roll (5.54outof36 possible outcomes).
Though your SRRrate
is NOT the be all and end all of diceinfluencing; it is one
of the critical factors that you have to keep in mind whenever you are
structuring your advantageplay bets simply because a rollending 7 wipes
out all of your active Rightside wagers at the same time.
If you ignore your SRR,
then you ignore the overall risk your bets are subject to.
GlobalBet
ExpectancyRates
I refer to multinumber wagers like Inside (5, 6, 8, and 9),
Across (4, 5, 6, 8, 9, and 10), Outside (4, 5, 9, and 10),
Even (4, 6, 8, and 10), Iron Cross (5, 6, 8, and Field) and
similar, as “global bets”, because they are semi or
fullyencompassing wagers that cover several numbers at the same time.
In the hands of a randomroller, NONE of those bets hold
ANY merit whatsoever, and frankly NONE of your money should be
ventured on ANY of them if you want your advantageplay bankroll to
stay in positiveexpectation territory.
Conversely, each one of those bets holds their own special place in
the world of diceinfluencing. Your task as an advantageplayer, is to
figure out how good your own shooting ability is; and then determine which
bets are best suited to those talents.
Part of that process is to figure out how often you can expect one
of the numbers covered by any of those wagers will show up and then
compare it to your 7’s expectancyrate.
For example…
In the random world,
the Acrossnumbers (4, 5, 6, 8, 9, and 10), account for 24outof36
possible outcomes. That equates to an appearancerate of 66.67% and an
AcrossNumbersto7's Ratio of 4.00:1
For the SRR8 shooter,
the AcrossNumbers will account for about 25.20outof36 possible
outcomes and a slightly improved appearancerate of 70.00%.
Although the 1.2
additional appearances of Acrossnumbers over random (24 versus 25.2) may
not seem like much; when it is combined with the lower
appearancerate of the 7 (4.5 for SRR8 versus 6.0 for random); then all
of a sudden the AcrossNumbersto7's Ratio improves dramatically to 5.6:1
instead of 4:1 for random (a whopping 40% improvement).
Here’s a chart that
shows those rates for the AllAcross wager:
SRRrate 
AppearanceRate 
AppearancePercentage 
Across
#'sto7's Ratio 
SRR6 
24.00outof36 
66.67% 
4.0:1 
SRR7 
24.69outof36 
68.58% 
4.8:1 
SRR8 
25.20outof36 
70.00% 
5.6:1 
SRR9 
25.60outof36 
71.11% 
6.4:1 
Now obviously those
respective appearancerates change as we change the type of bet that we
make. For example, the appearancerates for a broader bet like the Iron
Cross (Anythingbut7) increases…
SRRrate 
AppearanceRate 
AppearancePercentage 
Iron
Cross
#'sto7's Ratio 
SRR6 
30.00outof36 
83.33% 
5:1 
SRR7 
30.86outof36 
85.72% 
6:1 
SRR8 
31.50outof36 
87.50% 
7:1 
SRR9 
32.00outof36 
88.89% 
8:1 
…while the payinghits
appearancerate for a lessencompassing bet like the 4 and 10 Placebet
drops substantially…
SRRrate 
AppearanceRate 
AppearancePercentage 
4’s
and 10'sto7's
Ratio 
SRR6 
6.00outof36 
16.67% 
1.0:1 
SRR7 
6.17outof36 
17.14% 
1.2:1 
SRR8 
6.30outof36 
17.50% 
1.4:1 
SRR9 
6.40outof36 
17.78% 
1.6:1 
The fewer 7’s that a
shooter throws, the more its place will be taken by non7 outcomes. For
simplicity, I spread those 7replacement outcomes evenly across all the
other non7 numbers (favoring none). Your own shooting may produce a
different, less even distribution pattern, so it may be best to calculate
your own expectancycharts for the bets you are contemplating.
In any event, each SRRrate
change not only alters the ratio of 7’stonon7’s, but also the
appearancerate (expected hitrate) of each bettype. As a result, the
average payout from each of these globaltype bets changes too.
Weighted
Bet Payout
When we look at the potential payout for any multinumber wager, we have
to look at how often each number within that wager will pay off relative
to any of the other wagers.
For a bet like the
Placebet 6 and 8 it is easy because both the 6 and 8 appear the same
number of times and they both have the same Placebet payoutrate of 7:6.
On the other hand, the
Acrosswager takes a little more time to figure out because it covers six
different numbers with three different occurrencerates and three
different payoutrates.
To determine the
weighted (average) betpayout for a given multinumber wager like the
Acrossbet, we calculate the payout and the occurrencerate for each of
the individual Placebets within the globalwager itself.
For example with
$32Across…
The wagers are spread
out with $5 each on the 4 and 10, $5 each on the 5 and 9, and $6 each on
the 6 and 8.
To accurately assess
what the average weighted payout will be, we have to multiply the
occurrencerate with its respective payout.
Therefore we multiply
the 4 and 10 payout of $9 by six because there are three ways each to roll
the 4 and 10.
We do the same for the
5 and 9, but in this case we multiply the $7 perhit payout by eight to
reflect those two numbers appearancerate of four times each.
We also do that for
the 6's and 8's $7 payout and then multiply it by ten to reflect the five
ways each that we can make the 6 and the five ways each that we can make
an 8.
All of that equates to
$54 for the 4 and 10, $56 for the 5 and 9, and $70 for the 6 and 8. That
equals $180, which we then divide by the 24ways we multiplied their
respective individual payouts by.
That gives us an
average weighted AllAcross payout of $7.50 per winning hit. When your
wager on the 4 and 10 reaches $20, then it’s a good idea to “buy” it. By
paying a vig (commission) of 5%, you receive a 2:1 payout which lowers the
houseedge substantially. Therefore, you’ll also want to adjust for that
on the average weightedpayout for your preregression largebet. For
example, the weighted payout for a $160Across wager is $38.50 (net of
vig).
Here’s a summary of
the basic weighted payouts for each of the globalbets we’ve been
discussing in this series:
Weighted Bet Payout
PerHit 
Globalbet 
$22Inside 
$32Across 
$20Outside

$22
Even 
$22
Iron Cross

WeightedPayout 
$7.00 
$7.50 
$7.86 
$7.75 
$4.10 
The weightedpayouts
will be used when calculating how much each winninghit will pay and
therefore how well each globalbet will stack up against the 7. To do
that, we have to take a detailed look at the expected
rollduration/betsurvival rate for each SRR and for each of these
globalbets.
Determining BetSpecific RollDuration DecayRates
We've long talked
about the critical importance of exploiting the fattest, most frequently
occurring portion of the rollduration expectancycurve.
“Rollduration” simply
means how long, on average, your pointcycle will last, and how likely a
particular bet is to hit before the 7 appears.
For an SRR8 shooter,
there's a 87.50% chance that he'll get past his first pointcycle roll; a
76.56% chance that he'll get past the second one; a 66.99% chance on the
third; and a 58.62% chance that he'll survive the fourth pc roll.
Though that tells us
how likely he is to throw a "non7", it doesn't help us in terms of
addressing any specific bets that he might make (other than the
Anythingbut7 Iron Cross wager which perfectly mirrors non7
rollduration, as it should).
For other methods that are lessencompassing than the Iron Cross, we have
to look at their specific occurrencerate and figure out the decayrate as
it pertains to that wager.
Once we know what the perroll probability of that bet is, we can take the
cumulative rollduration decayrate to figure out where and for how long
that bet stays in positiveexpectation territory.
Again, the PERROLL expectancy of the 7 remains rocksteady for the SRR8
shooter at 12.5% on any given roll (16.67% for an SRR6 randomroller,
14.29% for an SRR7 shooter, and 11.11% for an SRR9 shooter); however the
cumulative odds of making MORE than one non7 roll in a row
actually deteriorates quite rapidly...and for some types of bets, that
deterioration is more pronounced due to their low initial appearancerate.
For example:
The Acrossbet starts
off at an expected appearancerate of 70.00% on the first pointcycle
roll, but declines to 61.25% on the second one, 53.59% on the third one,
and only 46.89% on the fourth one. That is due to the decayrate of non7
outcomes in a row as it relates to the Acrossbet...or stated in the
alternative; the cumulativeodds of the 7 appearing after two, three, or
four, etc. non7's in a row.
I have charted the rollduration hitprobability decayrate for each of
the bettypes that we’ve covered in this series:
RollDuration HitProbability DecayRate
SRR7

Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
51.19% 
68.58% 
40.00% 
45.72% 
85.72% 
28.57% 
22.85% 
17.14% 
2 
43.87% 
58.78% 
34.28% 
39.19% 
73.47% 
24.49% 
19.59% 
14.69% 
3 
37.61% 
50.38% 
29.38% 
33.59% 
62.97% 
20.99% 
16.79% 
12.59% 
4 
32.23% 
43.18% 
25.19% 
28.79% 
53.97% 
17.99% 
14.39% 
10.79% 
5 
27.63% 
37.01% 
21.59% 
24.67% 
46.26% 
15.42% 
12.34% 
9.25% 
6 
23.68% 
31.72% 
18.50% 
21.15% 
39.65% 
13.22% 
10.57% 
7.93% 
7 
20.29% 
27.19% 
15.86% 
18.13% 
33.98% 
11.33% 
9.06% 
6.80% 
8 
17.39% 
23.30% 
13.59% 
15.53% 
29.13% 
9.71% 
7.77% 
5.82% 
9 
14.91% 
19.97% 
11.65% 
13.32% 
24.97% 
8.32% 
6.66% 
4.99% 
10 
12.78% 
17.12% 
9.98% 
11.41% 
21.40% 
7.13% 
5.71% 
4.28% 
RollDuration HitProbability DecayRate
SRR8 

Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
52.08% 
70.00% 
40.83% 
46.67% 
87.50% 
29.16% 
23.33% 
17.50% 
2 
45.57% 
61.25% 
35.73% 
40.84% 
76.56% 
25.52% 
20.41% 
15.31% 
3 
39.87% 
53.59% 
31.26% 
35.71% 
66.99% 
22.33% 
17.86% 
13.40% 
4 
34.89% 
46.89% 
27.35% 
31.27% 
58.62% 
19.53% 
15.63% 
11.72% 
5 
30.53% 
41.03% 
23.93% 
27.36% 
51.29% 
17.09% 
13.68% 
10.26% 
6 
26.71% 
35.90% 
20.94% 
23.94% 
44.88% 
14.96% 
11.97% 
8.98% 
7 
23.37% 
31.42% 
18.32% 
20.95% 
39.27% 
13.09% 
10.47% 
7.85% 
8 
20.45% 
27.49% 
16.03% 
18.33% 
34.36% 
11.45% 
9.16% 
6.87% 
9 
17.89% 
24.05% 
14.03% 
16.04% 
30.07% 
10.02% 
8.02% 
6.01% 
10 
15.66% 
21.05% 
12.28% 
14.03% 
26.31% 
8.77% 
7.01% 
5.26% 
RollDuration HitProbability DecayRate
SRR9 

Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
52.78% 
71.11% 
41.47% 
47.42% 
88.89% 
29.63% 
23.71% 
17.78% 
2 
46.92% 
63.21% 
36.86% 
42.15% 
79.01% 
26.34% 
21.08% 
15.80% 
3 
41.70% 
56.19% 
32.77% 
37.47% 
70.24% 
23.41% 
18.73% 
14.05% 
4 
37.07% 
49.94% 
29.13% 
33.31% 
62.43% 
20.81% 
16.65% 
12.49% 
5 
32.95% 
44.40% 
25.89% 
29.61% 
55.50% 
18.50% 
14.80% 
11.10% 
6 
29.29% 
39.46% 
23.01% 
26.32% 
49.33% 
16.44% 
13.16% 
9.87% 
7 
26.04% 
35.08% 
20.46% 
23.39% 
43.85% 
14.62% 
11.69% 
8.77% 
8 
23.14% 
31.18% 
18.18% 
20.79% 
38.98% 
12.99% 
10.39% 
7.80% 
9 
20.57% 
27.72% 
16.16% 
18.43% 
34.65% 
11.55% 
9.24% 
6.93% 
10 
18.29%

24.64% 
14.37% 
16.43% 
30.80% 
10.27% 
8.21% 
6.16% 
So how do we reconcile
the rollduration decayrate for any given bettype with
regressionbetting, and most importantly, how do we determine the
optimal regression point?
Determining Optimal Regression TriggerPoint
Once we know what the perroll probability of a bet is, we take the
cumulative rollduration hitprobability decayrate (as seen above) to
figure out where and for how long that bet stays in positiveexpectation
territory.
Calculating how long
that bet stays in positiveexpectation territory and where the Optimal
TriggerPoint is (in which to do the largetosmall regression) for each
particular type of bet is critical in terms of extracting as much profit
from as many hands as possible.
The process is fairly simple:
First we look at the
"7exposure" value of the bet. That is the total amount of money
you would lose if a 7 shows up. For $22Inside it is $22, and for
$160Across, it is $160.
Each SRRrate has it's
own perroll risk associated with it. For a random SRR6 shooter it
is 16.67%; for SRR7 it is 14.29%, for SRR8 it is 12.50% and for a SRR9
shooter it is 11.11%.
We use those figures
to calculate the proportionalrisk threshold that any wager has to
overcome to be in positiveexpectation territory.
For example, an SRR7
shooter who is betting $5 each on the Placebet 5 and 9 has a minimum
$1.43 proportionalrisk threshold to overcome. That number is derived from
the $10.00 7exposure value of his two $5 Placebets ($10.00 7exposure x
14.29% perroll 7'sexpectancy = $1.43 proportionalrisk threshold).
We then look at the
SRR7 pointcycle rollduration expectancy for this particular wager. In
this case, he has a 22.85% chance of hitting either a 5 or 9 on his first
pointcycle roll. That equates to $1.60 in expectedearnings on a $7
payout. On his second pc roll, it declines to $1.37 (which is below his
$1.43 proportionalrisk threshold), so he is best advised to keep his
large preregression 5 and 9 wager out there for only one hit before
regressing it.
On the other hand, an
SRR8 player only has a $1.25 proportionalrisk threshold to overcome on
the same fivedollar 5 and 9 Placebet, so his expectedearnings are
$1.63, $1.42 and $1.25 on his respective first, second, and third pc
positiveexpectation rolls. In that case, he can afford to take three
winninghits before optimally regressing his bets.
The reason you'll often see the Optimal ISR TriggerPoint extend beyond
that particular globalbets "7'stowinninghits" ratio is due to the
betterthanevenmoney payout that Placebets generate (7:6 for 6 and 8;
7:5 for 5 and 9, and 9:5 or 2:1buy for the 4 and 10).
Let’s take a look at a
typical multinumber bet to see how this optimal regression triggerpoint
process works in real life:
The first thing we
have to do is figure out what our perroll lossexpectancy is for a given
set of wagers.
To do that we take the
TOTAL 7's exposure of the bets we are appraising and multiply that
by the perroll expectancy of the 7 for that particular SRRrate.
For a SRR8 shooter,
the 7's expectancy is 12.5% on any given roll.
On a simple $32Across
wager, our 7's exposure risk is $32.
For a SRR8 shooter
the proportionally expected "cost" perroll on that $32Across bet
is $4.00. That is the 7's expectancy hurdle that this bet has to overcome
on each roll for it to remain in positiveexpectation territory…so any
expected revenueperroll below that amount puts it into
negativeexpectation territory.
To figure out where that positivetonegative transition point is during
the pointcycle, we take the weighted payoutperhit and multiply it by
the rollduration occurrencerate.
In this case the first
pointcycle roll carries an Acrossbet expectancyrate of 70.00%. We then
multiply the $32Across expected perhit weightedpayout of $7.50 by the
70.00% first pointcycle roll expectancyrate. That equates to $5.25 in
expected revenue from the first pc roll which is more than the expected
$4.00 "cost".
This expected revenue
figure also takes NONAcrossnumber outcomes into consideration too (as is
seen in the disparity between expected weightedpayout, the 7'sexpectancy
cost, and nonAcrossoccurrences); which account for 17.50% of the first
pc roll outcomes).
The second pc roll
carries an Acrossbet expectancyrate of 61.25%, which equates to $4.59,
so it is still in positiveexpectation territory (above the $4.00 expected
proportional risk cost of this wager).
The third pc roll
carries an Acrossbet expectancyrate of 53.59%, which equates to $4.02,
and although it is still in positiveexpectation territory by 2 cents,
it is clearly right on the positivetonegative transitional cusp.
As you can see, preregression 7Out losses are accounted for in the
Acrossnumbers appearancerate minus the expected 7's appearancerate, so
losses of preregression bets are fully built into the equation.
The fourth pc roll
carries an Acrossbet expectancyrate of 46.89%, which equates to $3.52
which obviously puts this wager into negativeexpectation territory. Now
that does not mean that the 7 is automatically going to show up on the
very next roll. Instead, it means that the SRR8 shooter can generally
take three positiveexpectation hits at the largepreregression betlevel
before reducing his wagers to the lower postregression amount when the
rollduration decayrate transitions into negativeexpectation territory.
I have charted out
exactly where the Optimal Regression TriggerPoint is for each of the bets
and each of the SRRrates that are covered in this series:
Optimal Regression TriggerPoint
SRR7 
H
I
T
S 
Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
X 
X 
X 
X 
X 
X 
X 
X 
2 

X 


X 
X 


The SRR7 shooter does
not stay in positiveexpectation territory for very long during his
pointcycle roll and should therefore optimally regress his bets after
just one or two hits (depending on which global bettype he has wagered
on).
As your SRRrate
improves, so does the flexibility of your bettingmethods. In most cases,
an SRR8 shooter can take two or three winning hits before reducing his
initially large wager.
Optimal Regression TriggerPoint
SRR8 
H
I
T
S 
Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
X 
X 
X 
X 
X 
X 
X 
X 
2 
X 
X 
X 
X 
X 
X 
X 
X 
3 
X 
X 

X 
X 
X 
X 

Likewise, a SRR9
shooter has the luxury of having all of his globaltype bets stay
in positiveexpectation territory for four winning hits before
optimally regressing them.
Optimal Regression TriggerPoint
SRR9 
H
I
T
S 
Inside 
Across 
Outside 
Even 
Iron Cross 
6 and 8 
5 and 9 
4 and 10 
1 
X 
X 
X 
X 
X 
X 
X 
X 
2 
X 
X 
X 
X 
X 
X 
X 
X 
3 
X 
X 
X 
X 
X 
X 
X 
X 
4 
X 
X 
X 
X 
X 
X 
X 
X 
In a
nutshell…
Once
we've defined the 7’sexposure cost of a multinumber wager, we can also
calculate the costperroll threshold that that particular bet has to
overcome for it to remain in positiveexpectation territory for a given
SRRrate.
Simultaneously, we can also define the expected positivetonegative
crossoverpoint for each multinumber wager and for each diceinfluencing
skill level.
Essentially, in the preregression phase, we'll win some and we'll lose
some, but as long as our overall performance is within our
advantagebased positiveexpectancy territory; netprofit will continue to
reliably roll in session after session, day after day, and week after
week.
Even
though every hand won’t be a winner, they don’t have to be for
Steep Regressions to continually produce an overall netprofit. Rather,
ISR’s produce a profit most of the time, and the times when they don’t,
will be far outstripped by the overall netprofit that the winning ones
generate. 