Regression Avoids Depression
Part 20
Today we are going to dive into the whole
how-much-money-do-I-REALLY-need-to-properly-exploit-my-edge question
in extraordinary detail.
Having An Edge Does Not
Guarantee a Profit
Even if you play with a substantial advantage
over the casino, it does not guarantee that you will always emerge with a
profit.
Edge is one thing, but the win-some,
lose-some volatility on the bets that you make, is something
completely different.
To my mind, volatility has to be
chief amongst the considerations when a player is seeking to exploit his edge
over the casino on any given bet.
Without a doubt, knowing what your "EV edge" (expected-value
advantage) over the house is, is always important; but knowing how volatile
that edge is, is something that also has to be considered.
For example, a 1% edge over your flat Passline
wager is much less volatile than a 1% edge over the prop-bet 12-Midnight. So
even though your edge over both of those bets is the same; you’ll
likely experience much wider volatility swings with one than the
other.
When the same value of wagers are made, the
12-Midnight bettor will require a much larger bankroll than the Passline-bettor
does. That is because the Prop-bettor with the same edge as the PL-only
bettor, will endure much more bankroll volatility on his way to deriving
the same overall 1% edge-derived-profit as the PL-bettor does.
Consider this…
Ø
An advantage-player has to
overcome a hefty house-edge of 13.89% on the 12-Midnight, but only has to
surmount a miniscule 1.41% house-edge on a flat Pass-line wager.
Ø
The 12-Midnight has a less
recurrent win-frequency (due to it’s lower appearance-rate), but a
much higher 30:1 payout-to-bet ratio.
Ø
The Passline enjoys a more
recurrent win-frequency (due to it’s higher win-rate), but a lower,
even-money (1:1) payout-ratio.
As a result, a 1% player-edge (or any
positive-expectation edge for that matter) on a particular bet cannot be
viewed in isolation. Rather, each wager has to be viewed in relation to the
occurrence-rate (the expected frequency) of its appearance, as well as the
payout-ratio (x:1) of what that particular bet pays when it does show up.
To get a handle on bet-volatility (and
therefore the volatility you'll experience over your entire gaming
bankroll if you look at all of your wagers from this same perspective);
you have to determine how frequently a given advantage-play bet will occur
during an average hand. That way, if we know how often it will usually
show up, we start to get a handle on how volatile each of our
positive-expectation bets will be; and therefore we get an excellent grasp of
how large our bankroll draw-downs will likely be.
Ø
If we know that there will be
naturally occurring gaps in between winning payouts, then we’ll be less likely
to let that formerly annoying pause between paying-hits affect our shooting.
Ø
If we understand how volatility
works within the parameters of our current advantage-play dice-influencing
skills; then there’s less of a chance, as Heavy would say, that “the crap
between our ears” will conspire to diminish the effectiveness of our actual
throws.
For example, in random play, the Inside-bet accounts for 50% of all outcomes,
and provides an Inside-numbers-to-7's ratio of 3:1. In the hands of an SRR-7
shooter, Inside-numbers will generally account for about 51.19% of all outcomes.
Now on the face of it, a slight increase of 1.19% in frequency-occurrence
doesn't seem like much; however that's not the whole picture because the
now-reconfigured Inside-numbers-to-7's ratio suddenly jumps to around 3.6:1,
which is a 20% increase in the all-important hits-per-7-Out ratio. To my mind,
that is where the "advantage" in advantage-play really comes from.
When the dice are in your hand, it’s obviously
quite difficult to tell the difference between a random Inside-Number
appearance-rate of 50% and an SRR-7 appearance-rate of
51.19%; but the difference is there nonetheless, and it
is in that difference where your D-I
skills bear the most profitable fruit.
If there’s a better reason to use roll-tracking
software to track, analyze, and confirm your actual edge against each and every
bet on the layout…I can’t think of one.
I’m not egotistical enough to think that I can
intuitively tell the difference between a randomly-expected Inside-Number
appearance-rate of 50% and a heavily advantaged rate of 51.19% without the aid
of tracking software or at least some serious paper-and-pencil ciphering
time…and that goes a long way to explaining why most dice-influencers miss
out on the majority of the money-making opportunities that their current skills
are offering.
Admittedly, most players prefer to use an
in-the-moment, seat-of-the-pants kind of “intuitive betting” that in most cases
is either one or two rolls too late, or is anticipatorily outsized (over-bet)
for their current skills…which in either case, ends up bruising their ego and
leaves them questioning whether or not they really have any exploitable
D-I talent whatsoever…even though the easy-to-attain but mostly ignored
profit-opportunities are right there in front of them.
Ø
Combining your better-than-random
expected hit-rate with the return-on-investment offered by your positive EV-edge,
provides an easy and straight-forward way to measure: bet-volatility, likely
draw-down levels, and ultimately answers the
how-much-bankroll-is-required-to-properly-finance-this-wager question.
The smart dice-influencer takes a long and
honest look at his current talents to determine where his chief opportunities
are, and then puts a reasonable amount of his betting-weight on only his
strongest, most-compelling wagers in order to derive a consistently extractable
profit.
Though this common sense
approach is not as impetuous or spontaneous as the seat-of-the-pants impulse
betting preferred by most players; it sure produces a lot more profit.
When
To Invest, and How Much To Invest
Looking at the number of decisions you are
likely to produce on any given A-P bet before the 7-Out occurs, let's you
“invest” (wager) the correct
proportionally-adjusted-for-volatility-and-risk amount of money on this
particular advantage-play opportunity.
Investing the proper amount of
adjusted-for-volatility money on each advantage-play opportunity helps you
determine whether that wager will produce the profit (both R.O.I.-percentage and
total dollars-won) that you want or need, and it will also show how much of a
bankroll-swing you are likely to encounter along the way. That in turn let's you
make informed, honest, rational decisions about whether or not you are properly
financed in order to avoid risk of
I-will-give-up-craps-if-I-lose-this-amount-of-money ruin.
When all of your A-P bets are measured in this fashion, you can then determine
how much of a total gaming bankroll you'll need in order to adequately fund the
type and level of all the bets you are considering; so that’s what we are
going to look at today.
As I explained in Part 19
of this series, the following chart shows what your edge-per-roll will likely be
based upon regressing your large initial bet down to a smaller one at the
optimal trigger-point during your point-cycle.
Edge-per-Roll
using Optimized Regression |
Type of Bet
|
SSR-7 |
SSR-8 |
SSR-9 |
Inside
Edge-per-Roll
|
0.48% |
1.25% |
2.13% |
Across
Edge-per-Roll
|
0.42% |
1.17% |
2.06% |
Outside
Edge-per-Roll
|
0.33% |
1.02% |
1.85% |
Even
Edge-per-Roll
|
0.43% |
1.17% |
2.08% |
Iron Cross
Edge-per-Roll
|
0.40% |
1.12% |
2.01% |
6 and 8
Edge-per-Roll
|
0.58% |
1.48% |
2.55% |
5 and 9
Edge-per-Roll
|
0.40% |
1.12% |
2.02% |
4 and 10
Edge-per-Roll
|
0.26% |
0.92% |
1.67% |
We can use these edge-per-roll figures to
answer the whole
how-much-money-do-I-REALLY-need-to-properly-exploit-my-edge question in
extraordinary detail.
Let’s take a look at the
Inside-bet to see how much of a bankroll we should reasonably have in our total
I-will-give-up-craps-if-I-lose-this-amount-of-money gaming
bankroll for this particular wager.
Inside Bet`
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($44
to $22) |
3:1
($66
to $22) |
4:1
($88
to $22) |
5:1
($110
to $22) |
10:1
($220
to $22) |
SRR-7
Edge-per-Roll
0.48% |
$9167 |
$13,750 |
$18,334 |
$22,917
|
$45,833 |
SRR-8
Edge-per-Roll
1.25% |
$3520 |
$5280 |
$7040 |
$8800 |
$17,600 |
SRR-9
Edge-per-Roll
2.13% |
$2065 |
$3098 |
$4131 |
$5164 |
$10,329 |
Now on the face of it, a recommended total
I-will-give-up-craps-if-I-lose-this-amount-of-money bankroll of at least $9000
for an SRR-7 shooter using a 2:1 Steepness ratio ($44 regressed to $22) seems
rather excessive, but that is the amount we need to ensure that we’ll never
reach that “I’m-giving-up-this-damn-game” point in our advantage-play
efforts.
What’s even more illustrative about this chart
is the fact that as your skill-level improves, you can afford to play with a
much smaller bankroll for the exact same multi-number global wager. For
example, an SRR-8 shooter making that same 2:1 regression only needs a total
bankroll of $3500, while the SRR-9 precision-shooter can have a dedicated total
bankroll of only $2000 for this particular wager to attain the same profit
objectives.
Take a look at how that
holds true for the All-Across wager too…
Across Bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($64
to $32) |
3:1
($96
to $32) |
4:1
($128
to $32) |
5:1
($160
to $32) |
10:1
($320
to $32) |
SRR-7
Edge-per-Roll
0.42% |
$15,238 |
$22,857 |
$30,476 |
$38,095 |
$76,190 |
SRR-8
Edge-per-Roll
1.17% |
$5470 |
$8421 |
$10,940 |
$13,675 |
$27,350 |
SRR-9
Edge-per-Roll
2.06% |
$3106 |
$4660 |
$6213 |
$7767 |
$15,534 |
The next thing that becomes
patently clear when you review these charts, is that the more numbers
you spread your wagers across and the more money you have on the
table at any given time to cover these multi-number wagers; the more
of a total bankroll you will need in order to safely stake-horse and
properly finance these bets.
Outside Bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($40
to $20) |
3:1
($60
to $20) |
4:1
($80
to $20) |
5:1
($100
to $20) |
10:1
($200
to $20) |
SRR-7
Edge-per-Roll
0.33% |
$12,121 |
$18,182 |
$24,242 |
$30,303 |
$60,606 |
SRR-8
Edge-per-Roll
1.02% |
$3922 |
$5882 |
$7843 |
$9804 |
$19,608 |
SRR-9
Edge-per-Roll
1.85% |
$2162 |
$3243 |
$4324 |
$5405 |
$10,810 |
By now I’m sure a lot of you will be asking
yourself, “Am I prepared to dedicate this much
money to that particular bet?”
If the answer is “No”;
then you should either reduce your current betting-level on these
wagers…or select a betting-method that covers fewer wagers…or improve
your shooting…or a combination of all of them.
Even-number Bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($44
to $22) |
3:1
($66
to $22) |
4:1
($88
to $22) |
5:1
($110
to $22) |
10:1
($220
to $22) |
SRR-7
Edge-per-Roll
0.43% |
$10,232 |
$15,349 |
$20,465 |
$25,581 |
$51,162 |
SRR-8
Edge-per-Roll
1.17% |
$3760 |
$5641 |
$7521 |
$9401 |
$18,803 |
SRR-9
Edge-per-Roll
2.08% |
$2115 |
$3173 |
$4230 |
$5288 |
$10,577 |
Iron-Cross Bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($44
to $22) |
3:1
($66
to $22) |
4:1
($88
to $22) |
5:1
($110
to $22) |
10:1
($220
to $22) |
SRR-7
Edge-per-Roll
0.40% |
$11,000 |
$16,500 |
$22,000 |
$27,500 |
$55,000 |
SRR-8
Edge-per-Roll
1.12% |
$3928 |
$5893 |
$7857 |
$9821 |
$19,643 |
SRR-9
Edge-per-Roll
2.01% |
$2189 |
$3283 |
$4378 |
$5473 |
$10,945 |
Invest on Strength and
Purge on Weakness
This is where we start to get into some
situations that illuminate the whole idea of focusing your positive-expectation
investments on the strongest wagers in your advantage-play arsenal while
simultaneously avoiding or purging all the weaker or negative-edge bets
from your wagering regimen.
Take a look at the following chart to see how
much (well, actually, how little) of a total gambling budget is needed to
properly and safely exploit a basic 6 and 8 Place-bet when you are using an
Initial Regression style of betting.
6 and 8 Place-bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($24
to $12) |
3:1
($36
to $12) |
4:1
($48
to $12) |
5:1
($60
to $12) |
10:1
($120
to $12) |
SRR-7
Edge-per-Roll
0.58% |
$4138 |
$6207 |
$8276 |
$10,345 |
$20,690 |
SRR-8
Edge-per-Roll
1.48% |
$1621 |
$2432 |
$3243 |
$4054 |
$8108 |
SRR-9
Edge-per-Roll
2.55% |
$941 |
$1412 |
$1882 |
$2353 |
$4706 |
Since the 6 and 8 Place-bet is a fairly
low-volatility wager to begin with, a dice-influencer doesn’t need as much money
to take properly advantage of it. That is because your bankroll will endure
much less whipsaw back-and-forth win-some/lose-some volatility, and therefore
you don’t need as big of a safety-net to comfortably take advantage of your
positive-expectation skills.
The same bankroll-requirement
characteristics that you have for the regressed Place-bet 6 & 8 holds true for
the regressed-at-the-optimal-time Place-bet 5 & 9 too.
Take a look…
5 and 9 Place-bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($20
to $10) |
3:1
($30
to $10) |
4:1
($40
to $10) |
5:1
($50
to $10) |
10:1
($100
to $10) |
SRR-7
Edge-per-Roll
0.40% |
$5000 |
$7500 |
$10,000 |
$12,500 |
$25,000 |
SRR-8
Edge-per-Roll
1.12% |
$1786 |
$2679 |
$3571 |
$4464 |
$8928 |
SRR-9
Edge-per-Roll
2.02% |
$990 |
$1485 |
$1980 |
$2475 |
$4950 |
4 and 10 Place-bet
Optimal Total Bankroll
for this wager
(based on skill-level and
ISR Steepness Ratio) |
ISR
Steepness
Ratio
|
2:1
($20
to $10) |
3:1
($30
to $10) |
4:1
($40
to $10) |
5:1
($50
to $10) |
10:1
($100
to $10) |
SRR-7
Edge-per-Roll
0.26% |
$7692 |
$11,538 |
$15,385 |
$19,230 |
$38,461 |
SRR-8
Edge-per-Roll
0.92% |
$2174 |
$3261 |
$4348 |
$5435 |
$10,870 |
SRR-9
Edge-per-Roll
1.67% |
$1198 |
$1796 |
$2395 |
$2994 |
$5988 |
If You Don’t Know This By Now…
If it isn’t clear by now that you have to be
sufficiently bankrolled in order to take proper advantage of your
dice-influencing, then the lesson has not only been lost; but more importantly,
there is very little chance that you’ll be able to turn your current
dice-influencing skills into sustainable profit…not because you can’t,
but simply because you choose not to.
Coming Up
“Okay Mad Professor, so I’ve
got a proper-sized bankroll and I know which bets I have the biggest edge over,
and I know when to regress them at the optimal trigger-point; now HOW MUCH MONEY
can I expect to make on a per-hand, per-session, per-day, per-week, per-month
and per-year basis?”
In Part 21 of this series, we are going
to dive into the whole
HOW-MUCH-money-can-I-expect-to-make-off-of-these-bets-and-HOW-LONG-before-I-double-my-bankroll
question in extraordinary detail. I hope you’ll join me for that.
Until then,
Good
Luck & Good Skill at the Tables…and in Life.
Sincerely,
The
Mad Professor
Copyright © 2006
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