## Tuesday, July 18, 2000

### Winning at Roulette

Contents:
Initial Rant / Introduction
Essential Overview
The Data
The Programs used on My HP48gx; as Crude Flowcharts
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Initial Rant / Introduction
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i found a book the other day that reminded me of a 'theory' involving statistical manipulation that i'd been thinking about for a long time, and this brief article in:
The Pig that Wants to be Eaten /
100 [ Thought ( Gedankenversuch ) ] Experiments for The Armchair Philosopher
Assembled by Julian Baggini © 2005

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...discussed it without a deeper search for it's possible implications...
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So i began to consider them...
The essential idea was that if you're standing beside a roulette wheel and you become aware that there has been an unusual sequence of 'Reds' that have come up...
A Black should be long overdue, and that statistically,
it would be prudent to bet a large sum on Black. ( ??? )
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The article insisted however that each spin entails it's own probability factor,
which for a Roulette Wheel, the chances of Red or Black coming up, on any given spin, would be about 9 in 19, or not quite half...
Because-- of the two green slots, Zero and ZeroZero.
As much as you think Black is 'Overdue' for any given sequence of spins...
And It might well be overdue... Each spin must be considered on its own merits...
---
So i wrote a program on my HP48gx Programable Calculator to check this out...
And sure enough, there was no perceivable advantage to betting a constant amount on the under-represented colour.
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Are you surprised by this?
i was surprised by this...
But i also got to thinking...
Just which spins are you considering...???
That is; Are you considering the last 6 spins, or the last 60, 600
or 6000...???
Each spin on a roulette wheel takes about 2 minutes to complete it's cycle
from taking in all the bets,
to determining the winner,
to paying off everyone,
or collecting their loses,
to starting over again...
So there is this 'Time Constraint' to how many spins you can consider...
Plus -- The Casino's generally don't like people that are playing a 'System'...
So that they may scowl and grunt when you begin taking notes or entering data into a lap top computer...
So-- If there is a System that can exploit some statistical weakness in the operation of the Roulette Wheel; We're going to have to keep in simple, Simple enough so that you can work it in your head.
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Is there such a System?
i think that there is...
But i haven't quite worked it out -Completely- yet... !!! ???
What i do have; Are several pages of VERY promising data, and some numbers that seem to suggest that,
given my present betting suggestions,
You can CONSISTENTLY WIN...
a very small amount per spin.
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How small...?
About per spin, when betting with a 'Base Unit' of 1\$...???
If your base unit was \$1000, then you'd consistently win \$60 per spin.
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It's VERY IMPORTANT to remember though...
That this is Gambling...
You can not control ( by this method ) the outcome of individual spins,
So that there is ALSO The Possibility that you could lose your Alpha Kitty...!!!
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The Alpha Kitty is the amount that you start out with.
For all my Analytic Runs,
that consisted of a very unrealistic number of spins,
in the thousands...
i started each with \$300, and usually... Usually won another \$300, consistently...
UNLESS--
And this is the curious part...
If the number of Reds or Blacks suddenly flew off in some VERY Anomolous direction,
Then the System faltered...!!!
It Crashed.
The Kitty was lost.
---

BUT --
If the Reds & Blacks behaved themselves, and stuck within their statistical range of normalacies...
Then i would consistently win.
Consistently.
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It would be a Roller Coaster.
I'm not saying it's NOT a Roller Coaster...!!!
You win some, you lose some...
But you win more often than you lose...!
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That is...
Let me tell you the secret.
You don't actually win more often than you lose...
The system predicts whether a Black or Red will come up next,
But it's Not any better than Chance at this...!!!
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But this is THE CRAZIEST PART...
When i set up Two Players,
The Dumb Player picks randomly and bets randomly,
It Consistently Loses...
But The Smart Player; Using this System, predicts which Colour will come up,
and bets ACCORDINGLY-- It Consistently Wins...!!!
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The SECRET is the BETTING.
The Sledge Hammer approach to this is that;
The greater the SUPPOSED CHANCE of either Black or Red will come up,
You BET More...
So if for a given stretch of spins:
Red has come up 8 times,
and Black has come up 4 times...
You would bet a comparitively Larger Amount on Black,
Than if Black had come up 6 times...
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That should seem simple and obvious.
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But how much should you bet...???
This gave me alot of trouble.
As i mentioned before, It would depend, statistically on how many spins you were considering-
If you're only considering the last 12 spins, Red might seem highly OverRepresented, but if you're considering 6000 spins, Red might be sorely UnderRepresented...!!!
???
Allowing for this; The thoughtful person would conclude that the system couldn't possibly work...!!!
But the data i've accumulated seems to unequivocally suggest that it DOES Work...!!!
And -- i also suspect that if i could refine The Betting Scale,
i could win more consistently, with greater results...
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What do i have so far?
i started out with a straight coin flip, and consistently got results like:
Smart player 1524 -vs- Dumb player 109
Smart player 1788 -vs- Dumb player 892
Dumb did occasionally win on these early trials...
But not by the amounts that Smart was winning, when Smart won...
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One thing i noticed, was the variance of Maximum to Minimum Wins for Dumb when i played with 500 flips. Dumb's range was consistently around 600...
So that if it's best number of wins during a given trail of 500 flips was 142, it's loses would be around -533.
Smart; on the other foot, was all over the place...!
If it won 2486, it's Max' would be 2806 and it's Min' would be .5.
If it won 30,258, it's Max' winning would be 33,014 with a lowest point of 0.
In other words; The Dumb Player, picking Heads or Tails and Betting Randomly,
Won and Lost Randomly, adhereing to Statistical Probabilities...
While The Smart Player Bucked the Statistical Probibilities...!!!
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Another point that i was considering, and i still don't have a good answer for this...
Is that -Although- The System allows you to Win Consistently, you still are permitted the possibility of losing.
Losing Everything!
So that-- If you are winning, when should you bail out?
One suggestion is that, if you double your money, you take you winnings, put them in a pocket, and continue to play with your original alpha kitty amount... So that your winnings are protected. If you lose the kitty at some point after that. You're done.
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Another idea is that the winning 'Curve' or 'Slope' will tell you if you're above or below what you 'should be' winning at any given point in your run.
If you're below the slope, you keep playing,
If you're above the slope, and it is honorable to bail out.
But to bail out when you losing a little, as the system has warned you, repeatedly, may happen...
Makes you a Chicken Shit.
If you're going to ride this Roller Coaster, you have to have the nerve to stay on for the whole ride,
Jumping out before you get to the top will only cause traumatic injuries.
The trouble is though... Where is the top...???
Some trials have shown VERY high winnings,
Others have shown modest winnings,
and some have taken all my money.
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After a few days,
i looked up the equation for
Pascal's Triangle,
which is used to determine statistcal probabilities...
The equation is:
((n+1)!)/(k!((n+1)-k)!)
n is the number of coin flips
k is the number of heads
The result is the statistical chances of the k number of heads coming up for n coin flips.
---
Given this; and more tinkering...
My last version ( of many ) allowed that if:
There was a Zero difference between Reds & Blacks
i would bet 1 Monetary Unit.
( i've been told that for the Casino's around Spokane Washington, you have to place a minimum bet of 3\$-- So Either 3\$ would replace this minimum amount, or 3\$ would become your Basic Monetary Unit... Which would mean that i would suggest that your alpha kitty expand to \$900, instead of \$300...??? )
If there is a Difference of Two, then you bet 3 Units.
Also; For this system, i was considering a Set of 12 Spins, that were ongoing...
So that each last spin is added to The Set, and the 13th previous spin is deleted...
Which means that ( work this out for youself ) there is never the case of 1 too many Reds or Blacks...!
( Or any odd number, for that matter...!!! )
This also means that when you're considering the next spin resulting set...???...
That set of 12 spins may either be with the same number of Reds & Blacks,
or Two more of The Desired Red or Black
or the Undesired Reds or Blacks...
and this comes into how many good sets may be considered when you're determining how much to bet... !
This is one of the mysterious parts that still needs considerable work...!!! )
A Difference of 4 means that you bet 3 Units, ( same as 2 ! )
A Difference of 6, means that you bet 7 Units.
A Difference of 8, means that you bet 20 Units.
A Difference of 10, means that you bet 101 Units.
A Difference of 12, means that you bet 85 Units...!!!
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You would think,
And i mentioned this earlier,
That if there was a String of Reds, say 12 Reds for our set of 12 Considered Spins...
You would Bet ALOT on Black...
But you have to ALSO remember that EACH INDIVIDUAL SPIN is not concerned with the Set...!!!
It could be Red, It could be Black, It could be Green, The ball may fly off the wheel.
The System breaks down when Statistical Probabilities become too improbable...!!!
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The System somehow beats the Odds by Ignoring the Individual Spins,
and taking advantage of an artifical,
and entirely arbitrarily chosen number of spins within a given set.
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If you win any money using this system, be sure and leave a comment.

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Essential Idea
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The Initial Idea for this Scheme was that;
If you’re gambling at a Roulette Wheel and you notice that there has been an unusual number of Reds coming up,
Then—Statistically; there should be a greater chance of Blacks as the next ‘Number’ that comes up.
The ‘Book’ [ Common -Educated- Wisdom ] Says tha;
‘No’- Each Spin is governed by it’s own unique Statistical Probabilities...
Essentially 9 in 19 for either Red or Black, for any given Spin.
Note: Because an American Roulette Wheel has The Zero & ZeroZero Slots,
The Chances of a Red or Black coming up, is not precisely One Half.
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As it turns out, Computer simulations of these phenomena, and the ability to predict the colour of an up-coming ‘Number’ are within the constraints of chance.
That is: You can not reliably predict the colour of an up-coming ‘Number’.
This defies reason; or the common sense of simple minds, But it seems to be so.
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Curiously; When you place wagers of A Constant Value, based on this premise, you will do no better than the fool standing next to you.
BUT- If you Vary the Amount of your Wagers, Depending upon The Perceived Likelihood of a Colour coming up...
i.e.; If there has been way too many Reds during the most recent sequence of Spins, Then you would expect a Black to appear ‘Next’- And so you would base the Amount of your Wager on How Many Reds, Disproportionate to Blacks, have Appeared.
The Greater the Disproportionality, The greater your Wager.
Simple enough.
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THE DATA

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When i first started playing around with this;
i created a series of programs, continuously being ‘refined’ that began with a simple coin flip,
and a program that would determine The Disproportionality of Heads to Tails and Then Wager Varying Amounts.
Thousands of Trials were run and the results are as follows:
Note: The exact amount and ‘Theory’ behind how much The Smart Player was Wagering varied considerably, as in the early explorations, i had no idea what this formulation should be- The only consistent element was that The Dumb Player; Picked Head or Tails Randomly and Wagered Randomly,
within the same range as The Smart Player.

Run A:
The first trial i recorded shows that The Dumb Player,
after 10,003 Flips
Won by 46 Wagering Haematids...!!!
Smart = 5027 : Dumb = 5073
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Run B:
Dumb bets 1 per Flip.
Smart bets .25 x ABS(H-T)
Number of Heads 5022 : Tails 4978
Smart wins with an accumulated sum of 1492
Dumb loses with –48
Let me remind you that these numbers do not reflect the number times Smart or Dumb chose the ‘Correct’ Side of the Coin, But are the amounts ( in Dollars/Haematids ) that each has won by placing Strategic Bets.
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Run C:
Dumb bets 1 per Flip
Smart bets ABS(H-T)
Added or Subtracted depending upon whether Smart or Dumb Picks the House’s Flip.
Number of Heads 5074 : Tails 4926
Smart wins with 15,952 ( !!! )
Dumb loses with –96
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Run D:
Dumb bets a Randomly Selected Amount: 1 to 3 per Flip
Smart bets ABS(H-T) x 3
Number of Heads 5074 : Tails 4926
Smart wins with 30,606
Dumb loses with 17,030
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Run E:
Dumb bets a Randomly Selected Amount: 1 or 2 per Flip
Smart bets ABS(H-T) x 2
Number of Heads 245 : Tails 255
( Reduced to 500 Flips )
Dumb wins with 731!
Smart Loses with 600...
Curiously: The highest Dumb got was 731, rising sharply towards the end of the run,
While Smart got all the way up to 1,202, then slowly lost ground to 600...???

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Run Eb:
Number of Heads 266 : Tails 234
Smart wins with 1,524
Dumb loses with 109
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Run Ec:
Number of Heads 239 : Tails 261
Dumb wins with 1,023 – Highest Amount 1,088 / Lowest –63
Smart loses with 984 – Highest Amount 1,500 / Lowest 2
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Run F:
Smart only bets if ABS(H-T) > 4
Number of Heads 232 : Tails 268
Smart wins with 1,788 : Highest 2,324 Lowest 0
Dumb loses with 892 : Highest 1,147 Lowest –64
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At this point i thought that i’d try actually flipping a coin and using my scheme to predict the outcomes, and betting accordingly...
Because of my general impatience in these matters, and limited to the length of the paper in my notebook, i only tried 29 Flips.
The final result was Zero Dollars acquired, from a starting amount of Zero.
The most intermediate amount accumulated was 20, the lowest –8.
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Run G:
( Return to Calculator Simulations )
Here i tried to fine tune the amount wagered by taking

the ABS(H-T) x (ABS(H-T)/2) and betting that amount...
Number of Heads 221 : Tails 279 -
Note The High Anomalous Difference of 58...?
Smart wins with 39,744 : Maximum 42,587 Minimum .5
Dumb loses with 2,294 : Maximum 2,294 Minimum –241
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Run Gb:
Number of Heads 258 : Tails 242 – NonAnomalous Difference
Smart wins with 2,486 : Maximum 2,806 Minimum .5
Dumb loses with –489 : Maximum 142 Minimum –533
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Run Gc:
Number of Heads 255 : Tails 245 – NonAnomalous Difference
Smart wins with 2,595 : Maximum 2,862 Minimum .5
Dumb loses with 315 : Maximum 448 Minimum –281
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Run Gd:
Number of Heads 251 : Tails 249 – NonAnomalous Difference
Smart wins with 2,112 : Maximum 3,619 Minimum .5
Dumb loses with 288 : Maximum 366 Minimum –291
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Run Ge:
Number of Heads 276 : Tails 224 –Anomalous Difference of 52
Smart wins with 30,258 : Maximum 33,015 Minimum .5
Dumb loses with 1,138 : Maximum 1,196 Minimum –289
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Run Gf:
Number of Heads 257 : Tails 243 – NonAnomalous Difference
Smart wins with 1,643 : Maximum 1,643 Minimum .5
Dumb loses with -28 : Maximum 423 Minimum -60
Something kind of quirky occurred in these last five trials;
The Range of Dumb’s winnings & loses was around ‘600’ for each...???
And Smart never lost money on any of them...!!!

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Roulette Simulations:
-
Here i switched from a Coin Flip to a more Accurate Roulette Simulator.
The Generator that i used;

Simply made a Random number from 1 to 38
Then subtracted 2,
Leaving 1 to 36 ( MOD 2 ) for Red’s & Black’s
And –1 and 0 for Zero & ZeroZero
The Expected Results for a Series of 380 Spins,
should have been 180 Red’s : 180 Blacks : 20 Green’s.
The Program Generated:
189 Red’s : 163 Blacks : 28 Green’s
181 Red’s : 176 Blacks : 23 Green’s
This was determined by a panel of judges to be acceptable.
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Run H:
Number of Red’s 234 : Blacks 238
Smart wins with 539 / Maximum 2,601 Minimum .5
Dumb loses with –520 / Maximum 42 Minimum -1032
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Run I:
Number of Red’s 221 : Blacks 252
Smart wins with 4,055 / Maximum 5,047 Minimum 0
Dumb loses with –910 / Maximum 13 Minimum -910
-

Run J:
Number of Red’s 233 : Blacks 242
Smart wins with 1,324 / Maximum 3,004 Minimum .5
Dumb loses with –1,288 / Maximum 3 Minimum –1,477
-

Run K:
Number of Red’s 237 : Blacks 241
Smart wins with 772 / Maximum 1,779 Minimum 0
Dumb loses with –619 / Maximum 44 Minimum -672
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Run L:
Number of Red’s 238 : Blacks 230
Dumb wins with -32 / Maximum 0 Minimum -36
Smart loses with –679 / Maximum 2,451 Minimum –789
This was a Very Quirky Run...

Smart is all over the place...???
Should it be ignored,

or is it the exception that (dis(proves)) the rule...???
-

Run M:
Number of Red’s 231 : Blacks 241
Smart wins with 1,001 / Maximum 1,093 Minimum .5
Dumb loses with –50 / Maximum 9 Minimum -50
-

Run N:
Number of Red’s 239 : Blacks 237
Smart wins with 753 / Maximum 1,060 Minimum .5
Dumb loses with –40 / Maximum 5 Minimum -44
---
Up to here; Smart and Dumb started wagering with Zero in their Personal Accounts,
Hereafter;
Smart starts with \$100
Also:
Dumb is no longer playing. Smart is playing against The House.
Smart Wagers ABS(R-B)/VarianceFactor x ABS(R-B)
The VarianceFactor is an arbitrary amount that i was fooling around with to find something that 'Worked Best'...???
Difference: is the Difference between Red & Black at the end of the Trial.
Kitty: is the Amount in ( \$ ) that was won at the end of the Trial.
Max and Min are the Amounts at those extremeums during the trial.

---
Red : Difference : Black : Kitty : VF : Maximum : Minimum
131 Spins per Trial.

66 : (1) : 65 : \$205 : 5 : 205 : 60
85 : (39!) : 46 : \$-3338!!! : 5 : 109 : -3354
59 : (13) : 72 : \$249 : 5 : 349 : -291
63 : (5) : 68 : \$227 : 5 : 231 : 77

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From here: Difference refers to The Maximum Difference

-
70 : (14) : 61 : \$196 : 5 : 229 : 1
70 : (16) : 61 : \$215 : 5 : 215 : -45
75 : (23) : 56 : \$69 : 5 : 165 : -551
Even after dropping to -551, it recovers to lose only 31\$
-
70 : (12) : 61 : \$202 : 4 : 240 : 63
69 : (10) : 62 : \$197 : 4 : 197 : 76
60 : (8) : 63 : \$207 : 4 : 207 : 86
67 : (11) : 64 : \$217 : 4 : 218 : 34
68 : (7) : 63 : \$172 : 4 : 180 : 93

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70 : (16) : 61 : \$403! : 3 : 403 : -130
64 : (7) : 63 : \$238 : 3 : 238 : 91
72 : (13) : 59 : \$40! : 3 : 179 : 13
66 : (9) : 65 : \$274 : 3 : 274 : 49
-
500 Spins per Trial.
253 : (20) : 247 : \$1,445 : 3 : 1,460 : 21
262 : (33) : 238 : \$924 : 3 : 1084 : -2062!!!
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Safety Valve Installed to prevent Cascade Failures
during Highly Anomalous Series of Reds or Blacks...???

-
234 : (33) : 266 : \$1,259! : 3 : 1,367 : -13
245 : (22) : 255 : \$-397! : 3 : 529 : -397
257 : (38) : 243 : \$613 : 3 : 613 : -1418!!!
-
Removed Safety Valve...!!!
Around here i was also playing around with a Limit of how much The Wager could be,

as a % of what was in The Kitty,
Such that if The Wager was more than 80% of The Kitty,
You could only Bet 80%.
This amount varied from 25% to 80% with unspecified results...???
-
255 : (22) : 245 : \$125 : 2 : 130 : 39
242 : (22) : 258 : \$0! : 2 : 197 : 0
239 : (26) : 261 : \$539! : 2 : 584 : 57
249 : (12) : 251 : \$672! : 5 : 672 : -130
70 : (16) : 61 : \$403! : 4 : 403 : 100
---
At this point i was also beginning to wonder about things like;
After 'x' number of spins, how much should i have won...???
Is there a Curve or a Slope that would predict this amount...???
When would it be wise or prudent to quit...???
-
New System considers only The Last 12 Spins
Alpha Kitty = \$100
Betting Factor is 2, which doesn't seem to make any difference as to what it is...???
-

Kitty at End : Max : Min : MaxProfit/MaxLoss
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Zeroed Out - Max was 134
\$208
: 218 : 56 : 118/44
\$99 : 138 : 56 : 118/44
\$100 : 166 : 48 : 66/52
\$116 : 162 : 82 : 62/18
\$214 : 250 : 96 : 150/4
\$133 : 210 : 64 : 110/46
\$202 : 202 : 98 : 102/2
Zeroed Out @ 38 Spins : Max 124 : 24/100
Zeroed Out @ 74 Spins : Max 126 : 26/100
\$111 : 134 : 18 : 34/82
\$69 : 104 : 48 : 4/52
-
This set of trials went pretty badly,
Even assuming that the player were able to jump out at The Most Opportune Time,
The amount of profit is pretty dismal.
For my 2 Cents worth, if i'm going to stand at a Roulette Wheel all evening, i would want to wipe The House's ass with sandpaper, and this technique doesn't seem to be owning up to this desired potential.
-
Examining the Odds with Pascal's Triangle...

-
This latest incarnation of The System only considers The Last 12 Spins,
Such that any probabilities considered would fall within this range...
-
There is a 1 in 4096 of 12 Red's showing up...
There is a 1 in 341 of 11 Red's showing up...
There is a 1 in 62 of 10 Red's showing up...
There is a 1 in 19 of 9 Red's showing up...
There is a 1 in 8 of 8 Red's showing up...
There is a 1 in 5 of 7 Red's showing up...
There is a 1 in 4 of 6 Red's showing up...
There is a 1 in 5 of 5 Red's showing up...
There is a 1 in 8 of 4 Red's showing up...
There is a 1 in 19 of 3 Red's showing up...
There is a 1 in 62 of 2 Red's showing up...
There is a 1 in 341 of 1 Red showing up...

-
The Formula for this is:
! means: somenumber multipled by all the numbers less than it, to 1
e.g.,
6! = 6 x 5 x 4 x 3 x 2 x 1
( NumberOfMarbles + 1 )!
Divided by:
TheNumberOfRedMarbles!

times
((NumberOfMarbles + 1)
minus
TheNumberOfRedMarbles)!
-
Or:
(m+1)! / (r!*((m+1)-r)!
The result is the probability of That number of Red Marbles ( r )

Occurring in a group of Randomly selected Marbles
Of a predetermined quantity ( m ).
-
The Probability of a Red or Black coming up on a Roulette Wheel is 9 in 19
Slightly less than '50/50'
Because of the two Green Slots:
The Probability of a Green coming up is 1 in 19.
The Probability of The Ball flying off The Wheel is...
( i don't think you can bet on that, so why worry about it...? )
-
My notes become very confusing here...
But i seem to recall that i was thinking that if there were an abundance of Reds,
i would consider not just the probability of a Black coming up,

But The Set of 12 Spins showing 1 new Black or 1 old Black coming up...???
As The 13th Spin would be discarded,
The next Spin could Equalize or Destabilize the Number of Red's to Blacks...???
-
It made sense to me then.
-
So the numbers i cam up with were:
Because of the way The Set of 12 Discards and Adds Spins,
You can only have Differential Quantities of 2 MOD = 1
???
ABS (Red - Black) = 0; then Bet 1
If it's 2; then Bet 3
If it's 4; then Bet 3
If it's 6; then Bet 7
If it's 8; then Bet 20
If it's 10; then Bet 101
If it's 12; then Bet 85
( !!! ??? )
-
Trials:

-
Alpha Kitty = \$300
Number of Spins = 5000
Kitty = Amount at end of the Trial
Max = Maximum Amount won during Trail
Min = Minimum Amount during Trial
Gain as Fraction = Actual Winnings / Actual Losses
Gain per Spin ( Max =

Amount expected to win; Per Spin; if you baled out at Zenith
Gain per Spin ( End =

Amount expected to win, Per Spin; if you hung on to the End
Hitz = Number of Correct Colour Guess' :

...Smart vs The House as a Fraction
Pure chance of Hitz is .4737 and it doesn't seem to significantly deviate from this...
Although- It is always above it...???

-
Kitty : Max : Min : GaF : GpS(Max) : GpS(End) : Hitz
-
\$571 : 766 : 158 : 3.28 : .09c : .05c : .4832
Zeroed Out @ 2155 Spins
\$0 : 680 : -19 : -- : .18c : .00c : .4863
\$700 : 706 : 121 : 2.268 : .08c : .08c : .4772
Zeroed @ 979 Spins
\$0 : 483 : -3 : 26.143!!! : .19c : .00c : .4863
This is apparently a classic case of Catastrophic Cascade Failure due to a Very Anomalous Chromatic Distribution...!!!

A plot of this Trial shows that fell VERY Quickly after hitting a local peak of 293...
So ignoring the Catastrophic Element-

The Gain as a Fraction would be about 26.143
Which is absurdly high.
\$654 : 727 : 170 : 3.285 : .08c : .07c : .4944

After 25,000 Spins for these latest Trials,
It would seem that;
Using this System;

The Smart Player should expect a solid return of 6 to 7 Cents for every Dollar Wagered.
( That would mean \$1.06 to \$1.07 per Spin, before deducting the Wagered Amount )
Obviously then;

Betting \$1000 as a 'Unit' Wager, you could expect to Win \$60 to \$70 per Spin.
-
The Programs

as Crude Flow Charts
---
[SmartPlayer]
Calculate Red-Black; Absolute ( Make Positive ) for any given Spin.
These Quantities; Red & Black are Tallied within The Set of 12 which is also ongoing.
For each Spin that The House Makes; The Oldest Spin ( #13 ) is Discarded, and the New Spin is added to the Set. Then The Red & Black Quantities are reassessed.
If this Difference between Red & Black is 0; Then a Bet of 1 is made.
If the difference is 2; The Bet is 3.
4 is 3, 6 is 7, 8 is 20, 10 is 101 and 12 is 85.
If there are too many Reds, Bet on Black.
And Vice Versa.
You may also want to build in a safety feature that doesn't allow you to bet more than is in your Kitty, or a substantial fraction/percentage thereof.
This threshold is something that you, yourself, must agonize over.
-
[HouseRouletterSpinner]
Randomly Generate a Number between 1 & 38
Subtract 2
If the result is -1 or 0, then it's presumed to be either Zero or ZeroZero on The Roulette Wheel. It is discarded and no number's are added to The Set of 12.
Otherwise The Number is Sieved through a Modulus Two Function which will make it a 1 for Red or a 0 for Black.
This result is attached to a prearranged list of 1's and 0's
{ 1 0 1 0 1 0 1 0 1 0 1 0 } ( The Set of 12 at the Beginning )
The oldest is Discarded from one end, While the new Red or Black, 1 or 0 is attached to the other end.
The 1's are counted and assigned to The Variable 'Red'.
The 0's are counted and assigned to The Variable 'Black'.

[TheLoopOfSpins]
Determine How Many Spins you would Like...
Store The Alpha Kitty with The Desired Amount.
Store The Initial :
The Set of 12
Store Zero in Hitz If you're Interested in that Variable.
Store/Initialize all The Other Variables that you'd like to Track.
Generate The Smart Player's Prediction and Wager
Generate The House's Spin Colour
Did The Smart Player Guess Correctly?
If so; Add The Wager to The Kitty.
Otherwise; Subtract The Wager from The Kitty.
Post all Variables that you'd like to view during The Trial.
If Kitty equals Zero =
Abort!
Otherwise; Repeat until All Spins are completed.
-
That's all i have...
There's more in the Directory; But it's just a load of crap.
-
Does this System really work?
Does it...???
No-
Really, i'm asking you...
Do you think it actually returns a small,

but consistent profit margin...???
eh?
--- --- ---
Supplement / APPENDIX Ω

After receiving and analyzing a significant amout of critical exposition;
[ see:
HP48 NewsGroup: Can You Win @ Roulette...??? ( part a )
&
HP48 NewsGroup: Can You Win @ Roulette...??? ( part b ) ]
---
i have decided that The Key Ingredient for Winning at Roulette is not The Guessing of Which Colour will come up at all...
That may be Completely RANDOMIZED--
---
The Key--
If there is one;
Is in The Betting;
And The Scheme here that i've rediscovered, ( Sort of Vaguely )

Is known, i think, as "Doubling Up".
Also called:
The Martingale System or The O'Hare Straddle
---
This latest round of Simulations that i've done;
Tried several new 'Dumb' Attacks:
Just to make sure that the Simulator was still working, i retried The Smart Emulator...
Each Run consisted of 500 Roulette Spins,

And each Trial consisted of 5 of these Runs,
So that Each Smart or Dumb Emulator got to play with 2,500 Roulette Spins.
---
Smart Zeroed Out on two of the Trials,

And for the other 3, Won \$20, \$105 & \$214.
It continued to look, both; Somewhat Inconsistent--

Yet Optimistically Promising.
Just to remind you;
This Approach consists of Betting on the Deficient Colour; Proportional to it's Deficiency,
In Increments of { 1 3 3 7 20 101 85 }
---
Dumb a) Bet on the Excessive Colour; Proportional to it's Deficiency.
It Won/Lost \$-13, \$+52, \$-141, \$-74 & \$-161
It never Zeroed Out, But it only Won Meagerly...???
Is there something to Betting on The Deficient Colour...???
Probably not...
The Maximum Zenith's for Smart was 387.4,
While Max Zenith's for Dumb a) was 366.7...
Not terribly different...???
---
Dumb b) Bet on The Excessive Colour; Anti Proportionally!
Disaster! It Zeroed out every time...!
BUT...!!! Before Zeroing out--
It's Average Maximum Zenith's were \$1,144.2...!
All Maximum Zenith's were above The Alpha Kitty of \$300.
Way better than Smart or Dumb a)'s...???
---
Dumb c) Bet on The Deficient Colour; Anti Proportionally...
Again-- It Zeroed Out for Every Trial...

With a Maximum Zenith of Minus \$8...!!!
It's difficult to make any conclusive denouement's when the data isn't being the least consistent or even 'Trying' to form a pattern of some kind...!!!
---

Dumb d) Bet Randomly on Red or B-; Proportionally to The Deficient Ratios...
Proportional Wagering Pays off...
\$47, \$141, \$445, \$51 with one loss of \$-33.
These are Winnings Over The Alpha Kitty...
( More than what The Player brought in )
---
Dumb e) Bet Randomly; Anti Proportionally.
Zeroed Out Every time, But with a Maximum Zenith Average of \$93.
---
Dumb f) Bet Randomly; Randomly from Proportional List
The Wild Card
Zero's Out for 4 of the Trials,
But Wins one Trial with \$1,391...!!!
On One of the Zeroed Trials, it got up to \$842 ( Winnings )
The Average Maximum Zenith was \$482.6
---
Dumb g) Bet Randomly; Wagering Cyclically...
Wagering Forward & Backwards { 2 4 6 8 10 12 }
Wins \$32
Wagering only Forward; 2 to 12, 2 to 12...
Wins \$18
---
Dumb h) Bet Randomly: Wagering Modulus Mirror Clock
What i mean by Modulus Mirror Clock is that the Wagers are arranged around a illusive Clock:
{ 2 4 8 16 32 64 128 64 32 16 8 4 }
The Net Effect is that while an incremental amount is advanced, or decremented, in units of '1', the amount, taken from The Clock's Face Values, changes by only 'One Step' per Spin.
Since this Set contains 7 unique elements, The Modulus Set Limit would be "7".
---
The Program that i used to accomplish this is:
[ Mod~ ]
Incremental Number = 'n' Store
Modulus Set Limit = 'm' Store
IF m <>
THEN ABS(m) + 2 = 'm' Store
END
( m * 2 ) - 1 = 'i' Store ( Integer Modulus )
MOD(n-1,i) + 1 = 'r' Store
IF r > m
THEN ( m * 2 ) - r = 'r' Store
END
r is The Answer
---
This overly complicated approach resulted in One Trial that Won \$1,536,
While the other 4 trials Zeroed Out with Maximum Zenith's of; \$102, \$1,348; \$358 & \$132.
---
What does this all mean...???
Is there some Crazy Variation on 'Doubling Up' that actually works...???
---
Future Examiners...
Good Luck!
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