Today we are taking a
behind-the-scenes look at the process by which Steep Regressions work so
well for advantage-players.
Effort IN…Profit OUT
If you
don't put the necessary effort INTO calculating your validated
in-casino point-cycle 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
Point-then-7-Out 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 paying-hits.
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 Place-bet the 8 for $12 and regress it to $6 after one hit; then
you’d still have an $8 net-profit 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 in-rack net-profit of $2 (but of
course you now have twice the amount of money still in action).
Likewise, as you spread out to $44-Inside ($12 each on the 6 & 8, and $10
each on the 5 & 9); one $14 paying-hit doesn’t leave ANY net-profit to
work with while you still have all four Inside Numbers covered even if you
regress them down to $22-Inside.
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 Inside-Numbers
wager to $66-Inside, which would still leave you one-buck short in order
to cover the 5, 6, 8, & 9.
In the
alternative, you could start with a steeper ratio $88-Inside for a $28
one-hit payout which generates enough cash-flow to cover a Steep
Regression to the $22-Inside level and still guarantee a $6 net-profit
after all is said and done even if a 7-Out 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 “first-hit” payoff), the higher your
initial wagers (both individually and collectively) have to be in order
for the first hit to pay enough for minimum-bet 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 net-profit…or stated in the alternative; the
fewer advantaged-bets 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 point-cycle SRR in order to extract your rightfully
deserved maximal-revenue 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 betting-method
you are contemplating.
SRR Expectancy-Rate
Calculating your Sevens-to-Rolls Ratio is quite simple. We know for
example that…
The
sevens-expectancy-rate for an SRR-6 random-shooter is 16.67% on any given
roll (6-out-of-36 possible outcomes).
By dividing those six
possible 7’s into the thirty-six possible outcomes, we determine the 7’s
expectancy-rate for a random SRR-6 shooter to be 1-in-6 (16.67%) on any
given roll.
Likewise, we can do
the same for any SRR-rate:
The
sevens-expectancy-rate for an SRR-7 shooter is 14.29% on any given roll
(5.14-out-of-36 possible outcomes).
The
sevens-expectancy-rate for an SRR-8 shooter is 12.50% on any given roll
(4.5-out-of-36 possible outcomes).
The
sevens-expectancy-rate for an SRR-9 shooter is 11.11% on any given roll
(4-out-of-36 possible outcomes).
Even if you have a
fractional Sevens-to-Rolls Ratio of let’s say, 1:6.5, you can use the same
formula to determine that you’ll see an average sevens-expectancy-rate of
15.39% on any given roll (5.54-out-of-36 possible outcomes).
Though your SRR-rate
is NOT the be all and end all of dice-influencing; it is one
of the critical factors that you have to keep in mind whenever you are
structuring your advantage-play bets simply because a roll-ending 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.
Global-Bet
Expectancy-Rates
I refer to multi-number 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
fully-encompassing wagers that cover several numbers at the same time.
In the hands of a random-roller, 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 advantage-play bankroll to
stay in positive-expectation territory.
Conversely, each one of those bets holds their own special place in
the world of dice-influencing. Your task as an advantage-player, 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 expectancy-rate.
For example…
In the random world,
the Across-numbers (4, 5, 6, 8, 9, and 10), account for 24-out-of-36
possible outcomes. That equates to an appearance-rate of 66.67% and an
Across-Numbers-to-7's Ratio of 4.00:1
For the SRR-8 shooter,
the Across-Numbers will account for about 25.20-out-of-36 possible
outcomes and a slightly improved appearance-rate of 70.00%.
Although the 1.2
additional appearances of Across-numbers over random (24 versus 25.2) may
not seem like much; when it is combined with the lower
appearance-rate of the 7 (4.5 for SRR-8 versus 6.0 for random); then all
of a sudden the Across-Numbers-to-7'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 All-Across wager:
SRR-rate |
Appearance-Rate |
Appearance-Percentage |
Across
#'s-to-7's Ratio |
SRR-6 |
24.00-out-of-36 |
66.67% |
4.0:1 |
SRR-7 |
24.69-out-of-36 |
68.58% |
4.8:1 |
SRR-8 |
25.20-out-of-36 |
70.00% |
5.6:1 |
SRR-9 |
25.60-out-of-36 |
71.11% |
6.4:1 |
Now obviously those
respective appearance-rates change as we change the type of bet that we
make. For example, the appearance-rates for a broader bet like the Iron
Cross (Anything-but-7) increases…
SRR-rate |
Appearance-Rate |
Appearance-Percentage |
Iron
Cross
#'s-to-7's Ratio |
SRR-6 |
30.00-out-of-36 |
83.33% |
5:1 |
SRR-7 |
30.86-out-of-36 |
85.72% |
6:1 |
SRR-8 |
31.50-out-of-36 |
87.50% |
7:1 |
SRR-9 |
32.00-out-of-36 |
88.89% |
8:1 |
…while the paying-hits
appearance-rate for a less-encompassing bet like the 4 and 10 Place-bet
drops substantially…
SRR-rate |
Appearance-Rate |
Appearance-Percentage |
4’s
and 10's-to-7's
Ratio |
SRR-6 |
6.00-out-of-36 |
16.67% |
1.0:1 |
SRR-7 |
6.17-out-of-36 |
17.14% |
1.2:1 |
SRR-8 |
6.30-out-of-36 |
17.50% |
1.4:1 |
SRR-9 |
6.40-out-of-36 |
17.78% |
1.6:1 |
The fewer 7’s that a
shooter throws, the more its place will be taken by non-7 outcomes. For
simplicity, I spread those 7-replacement outcomes evenly across all the
other non-7 numbers (favoring none). Your own shooting may produce a
different, less even distribution pattern, so it may be best to calculate
your own expectancy-charts for the bets you are contemplating.
In any event, each SRR-rate
change not only alters the ratio of 7’s-to-non-7’s, but also the
appearance-rate (expected hit-rate) of each bet-type. As a result, the
average payout from each of these global-type bets changes too.
Weighted
Bet Payout
When we look at the potential payout for any multi-number 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
Place-bet 6 and 8 it is easy because both the 6 and 8 appear the same
number of times and they both have the same Place-bet payout-rate of 7:6.
On the other hand, the
Across-wager takes a little more time to figure out because it covers six
different numbers with three different occurrence-rates and three
different payout-rates.
To determine the
weighted (average) bet-payout for a given multi-number wager like the
Across-bet, we calculate the payout and the occurrence-rate for each of
the individual Place-bets within the global-wager itself.
For example with
$32-Across…
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
occurrence-rate 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 per-hit payout by eight to
reflect those two numbers appearance-rate 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 24-ways we multiplied their
respective individual payouts by.
That gives us an
average weighted All-Across 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
house-edge substantially. Therefore, you’ll also want to adjust for that
on the average weighted-payout for your pre-regression large-bet. For
example, the weighted payout for a $160-Across wager is $38.50 (net of
vig).
Here’s a summary of
the basic weighted payouts for each of the global-bets we’ve been
discussing in this series:
Weighted Bet Payout
Per-Hit |
Global-bet |
$22-Inside |
$32-Across |
$20-Outside
|
$22-
Even |
$22-
Iron Cross
|
Weighted-Payout |
$7.00 |
$7.50 |
$7.86 |
$7.75 |
$4.10 |
The weighted-payouts
will be used when calculating how much each winning-hit will pay and
therefore how well each global-bet will stack up against the 7. To do
that, we have to take a detailed look at the expected
roll-duration/bet-survival rate for each SRR and for each of these
global-bets.
Determining Bet-Specific Roll-Duration Decay-Rates
We've long talked
about the critical importance of exploiting the fattest, most frequently
occurring portion of the roll-duration expectancy-curve.
“Roll-duration” simply
means how long, on average, your point-cycle will last, and how likely a
particular bet is to hit before the 7 appears.
For an SRR-8 shooter,
there's a 87.50% chance that he'll get past his first point-cycle 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 p-c roll.
Though that tells us
how likely he is to throw a "non-7", it doesn't help us in terms of
addressing any specific bets that he might make (other than the
Anything-but-7 Iron Cross wager which perfectly mirrors non-7
roll-duration, as it should).
For other methods that are less-encompassing than the Iron Cross, we have
to look at their specific occurrence-rate and figure out the decay-rate as
it pertains to that wager.
Once we know what the per-roll probability of that bet is, we can take the
cumulative roll-duration decay-rate to figure out where and for how long
that bet stays in positive-expectation territory.
Again, the PER-ROLL expectancy of the 7 remains rock-steady for the SRR-8
shooter at 12.5% on any given roll (16.67% for an SRR-6 random-roller,
14.29% for an SRR-7 shooter, and 11.11% for an SRR-9 shooter); however the
cumulative odds of making MORE than one non-7 roll in a row
actually deteriorates quite rapidly...and for some types of bets, that
deterioration is more pronounced due to their low initial appearance-rate.
For example:
The Across-bet starts
off at an expected appearance-rate of 70.00% on the first point-cycle
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 decay-rate of non-7
outcomes in a row as it relates to the Across-bet...or stated in the
alternative; the cumulative-odds of the 7 appearing after two, three, or
four, etc. non-7's in a row.
I have charted the roll-duration hit-probability decay-rate for each of
the bet-types that we’ve covered in this series:
Roll-Duration Hit-Probability Decay-Rate
SRR-7
|
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% |
Roll-Duration Hit-Probability Decay-Rate
SRR-8 |
|
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% |
Roll-Duration Hit-Probability Decay-Rate
SRR-9 |
|
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 roll-duration decay-rate for any given bet-type with
regression-betting, and most importantly, how do we determine the
optimal regression point?
Determining Optimal Regression Trigger-Point
Once we know what the per-roll probability of a bet is, we take the
cumulative roll-duration hit-probability decay-rate (as seen above) to
figure out where and for how long that bet stays in positive-expectation
territory.
Calculating how long
that bet stays in positive-expectation territory and where the Optimal
Trigger-Point is (in which to do the large-to-small 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
"7-exposure" value of the bet. That is the total amount of money
you would lose if a 7 shows up. For $22-Inside it is $22, and for
$160-Across, it is $160.
Each SRR-rate has it's
own per-roll risk associated with it. For a random SRR-6 shooter it
is 16.67%; for SRR-7 it is 14.29%, for SRR-8 it is 12.50% and for a SRR-9
shooter it is 11.11%.
We use those figures
to calculate the proportional-risk threshold that any wager has to
overcome to be in positive-expectation territory.
For example, an SRR-7
shooter who is betting $5 each on the Place-bet 5 and 9 has a minimum
$1.43 proportional-risk threshold to overcome. That number is derived from
the $10.00 7-exposure value of his two $5 Place-bets ($10.00 7-exposure x
14.29% per-roll 7's-expectancy = $1.43 proportional-risk threshold).
We then look at the
SRR-7 point-cycle roll-duration expectancy for this particular wager. In
this case, he has a 22.85% chance of hitting either a 5 or 9 on his first
point-cycle roll. That equates to $1.60 in expected-earnings on a $7
payout. On his second p-c roll, it declines to $1.37 (which is below his
$1.43 proportional-risk threshold), so he is best advised to keep his
large pre-regression 5 and 9 wager out there for only one hit before
regressing it.
On the other hand, an
SRR-8 player only has a $1.25 proportional-risk threshold to overcome on
the same five-dollar 5 and 9 Place-bet, so his expected-earnings are
$1.63, $1.42 and $1.25 on his respective first, second, and third p-c
positive-expectation rolls. In that case, he can afford to take three
winning-hits before optimally regressing his bets.
The reason you'll often see the Optimal ISR Trigger-Point extend beyond
that particular global-bets "7's-to-winning-hits" ratio is due to the
better-than-even-money payout that Place-bets generate (7:6 for 6 and 8;
7:5 for 5 and 9, and 9:5 or 2:1-buy for the 4 and 10).
Let’s take a look at a
typical multi-number bet to see how this optimal regression trigger-point
process works in real life:
The first thing we
have to do is figure out what our per-roll loss-expectancy 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 per-roll expectancy of the 7 for that particular SRR-rate.
For a SRR-8 shooter,
the 7's expectancy is 12.5% on any given roll.
On a simple $32-Across
wager, our 7's exposure risk is $32.
For a SRR-8 shooter
the proportionally expected "cost" per-roll on that $32-Across 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 positive-expectation territory…so any
expected revenue-per-roll below that amount puts it into
negative-expectation territory.
To figure out where that positive-to-negative transition point is during
the point-cycle, we take the weighted payout-per-hit and multiply it by
the roll-duration occurrence-rate.
In this case the first
point-cycle roll carries an Across-bet expectancy-rate of 70.00%. We then
multiply the $32-Across expected per-hit weighted-payout of $7.50 by the
70.00% first point-cycle roll expectancy-rate. That equates to $5.25 in
expected revenue from the first p-c roll which is more than the expected
$4.00 "cost".
This expected revenue
figure also takes NON-Across-number outcomes into consideration too (as is
seen in the disparity between expected weighted-payout, the 7's-expectancy
cost, and non-Across-occurrences); which account for 17.50% of the first
p-c roll outcomes).
The second p-c roll
carries an Across-bet expectancy-rate of 61.25%, which equates to $4.59,
so it is still in positive-expectation territory (above the $4.00 expected
proportional risk cost of this wager).
The third p-c roll
carries an Across-bet expectancy-rate of 53.59%, which equates to $4.02,
and although it is still in positive-expectation territory by 2 cents,
it is clearly right on the positive-to-negative transitional cusp.
As you can see, pre-regression 7-Out losses are accounted for in the
Across-numbers appearance-rate minus the expected 7's appearance-rate, so
losses of pre-regression bets are fully built into the equation.
The fourth p-c roll
carries an Across-bet expectancy-rate of 46.89%, which equates to $3.52
which obviously puts this wager into negative-expectation 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 SRR-8 shooter can generally
take three positive-expectation hits at the large-pre-regression bet-level
before reducing his wagers to the lower post-regression amount when the
roll-duration decay-rate transitions into negative-expectation territory.
I have charted out
exactly where the Optimal Regression Trigger-Point is for each of the bets
and each of the SRR-rates that are covered in this series:
Optimal Regression Trigger-Point
SRR-7 |
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 SRR-7 shooter does
not stay in positive-expectation territory for very long during his
point-cycle roll and should therefore optimally regress his bets after
just one or two hits (depending on which global bet-type he has wagered
on).
As your SRR-rate
improves, so does the flexibility of your betting-methods. In most cases,
an SRR-8 shooter can take two or three winning hits before reducing his
initially large wager.
Optimal Regression Trigger-Point
SRR-8 |
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 SRR-9
shooter has the luxury of having all of his global-type bets stay
in positive-expectation territory for four winning hits before
optimally regressing them.
Optimal Regression Trigger-Point
SRR-9 |
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’s-exposure cost of a multi-number wager, we can also
calculate the cost-per-roll threshold that that particular bet has to
overcome for it to remain in positive-expectation territory for a given
SRR-rate.
Simultaneously, we can also define the expected positive-to-negative
crossover-point for each multi-number wager and for each dice-influencing
skill level.
Essentially, in the pre-regression phase, we'll win some and we'll lose
some, but as long as our overall performance is within our
advantage-based positive-expectancy territory; net-profit 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 net-profit. Rather,
ISR’s produce a profit most of the time, and the times when they don’t,
will be far outstripped by the overall net-profit that the winning ones
generate. |