Physics and math of roulette

[Guest purpled]

Hi all,

 

I am after some help regarding equations that i have dug up. If anyone wants to take a look and can let me know if it is valid work please reply and i will post a sample.

 

The equations relate to the prediction of roulette by measuring the forces acting on the ball and rotor. Prediction of roulette using various computer methods is possible as shown by Edward O Thorpe, Norman Packard, Doyne Farmer and many more since. It is also possible by using timings and / or visual clocking (a rare skill - two exponents are Laurance Scott and Pierre Basieux), If you don't believe it can be done do a quick search for any of them on google (obviously a massive majority of info. in this area is rubbish)

 

The work i need looking over is not my own and i am not capable of judging if the particular stuff i have is real or nonsense.

 

Haven't posted it straight away in case you all told me to bog off!

 

Thanks in advance

[Guest purpled]

Hi,

Ok a bit more info if it helps.

Apologies about the formatting of the equations, they are not mine and I pasted from an old manual.

 

I am researching for a book on this subject. If you think it is impossible please do a search on Norman Packard, Doyne farmer or Edward O Thorpe before you read on as I’ve only skimmer over it here.

 

Roulette prediction is possible in 4 ways:

 

Bias tracking - physical conditions of a wheel (normally either tilted very slightly, or wear and tear) cause some sections to have winning numbers more frequent that a random distribution. These days’ wheels are checked, adjusted and moved often; so bias tracking is very unlikely now.

 

Dealer signature - It is believed that a skilled croupier can place a roulette ball close to a number they are aiming for. Or during a long shift they get into an unconscious rhythm through "muscle memory", this again leads to hitting one area of a wheel more often than random.

 

Visual tracking - This is where a very skilled player can judge the speed of the ball and the position and speed of the wheel, coupling this with a low scatter (from the obstacles on the track) they can estimate the area a the ball will come to rest, usually about 3 or 4 revolutions before the ball drops from the track onto the rotor. Again if you don't believe this is possible search for Laurance Scott or Pierre Basieux.

 

Computer prediction - either using simple timings to estimate where and when the ball and wheel is at the time the ball loses critical momentum and drops from the track. Or by using Newtonian Physics but only if all parameters have been entered into the equations, which is impractical. There are various other ways that have been tried including neural networks and look up tables.

 

While all of this is incredibly hard to do, it can and has been done. The house edge in European roulette is 2.7%. If you could only predict a section of 4 pockets out of 37 where the ball is unlikely to fall into you have already swung the odds in you favour.

 

 

I have met with modern day protagonists using these methods during my research and these equations are from one in particular. I need to confirm if they are mathematically correct before I can do any more on that section of the book.

 

If interested in this work check out "The Eudaemonic Pie" by Thomas A Bass (called Newtonian casino in the UK).

 

I hope that helps explain why I posted the equations below, are they mathematically correct??:

 

 

The following mathematics deals with the X,Y and Z axis within the confines of a Roulette Wheel enviroment.

 

Y axis¦N1¦*COS(a)-(mg)*COS(a)=0

 

X axis¦N2¦+¦N1¦*SIN(a)+¦mg¦*sin(@)*COS(Y)=m*¦@ centre)=m*V^2/R=m*[Y')^2]*R

 

V=Linear Velocity

R=Ball Track Radius

@=Centripedal acceleration

 

Z axis¦Ffr¦+¦Air Drag¦=m*¦@tan¦=m*Y''*R

 

Friction Force a This is negative as it is opposing the Z axis

 

Air Drag is the force that is equal too:

 

¦Air Drag¦= - 0.5*CD*P*TT*r^2*V^2 (TT is pie) this is also a minus value!

 

CD is Drag Coefficiaent

P is AIr density

r is the balls Radius

 

Z axis is always tangentially directed.

 

------------------------------------------

 

After some very simple Algerbraic Transformation and incorporating the above formulas we get the next differential equation:

 

Y''=(a+air*R)*(Y')^2=b*SIN(Y)+c*COS(Y)+d (*)

 

Where

 

a is the determining friction factor(Ie 0.004)

 

Air =-[0.5*CD*P*TT*r^2*V^2]/m

 

b=a*g*SIN(@)/R

 

c=b/a

 

d=a.g.COS(@)SIN(a)+1)/(R.COS(@)

 

The ball movement sters to this equation only till the moment when it loses the contact with the vertical side of the ball track or:

 

[N2]=0

 

So the Drop off condition is:

 

[(Y')^2]*R+g*COS(@)*tg(a)-g*SIN(@)*COS(Y)=0 (**)

 

Now lets introduce some real values into the equations and see the predicted results:

 

TT=3.14

g=9.807

R=0.4

a=16.7.TT/180 inner slope of stator

CD=0.47

r=0.5.21.10^-3 Radius of ball

P=1.22

m=9.10^-3 Mass of Ball

(a)= 0.004 Friction factor for rolling between the ball and the track

@=0.8 grad Tilt Angle

 

t0= 0 sec

t1=30 seconds

 

These values determin the time interval of 30 sec since the start of spinning!

 

I also calcualted the time the ball loses contact with the vertical wall of the ball track, this is when(**) becomes true!

 

Time till drop off is 17.04 seconds

 

By this time the ball passes 4935 Grad or 13.7 revolutions from start point!

 

At this moment the ball has a velocity of 2.7 Rads/Sec or 0.43 Revs per/Sec!

 

 

 

Any and all help appreciated

Cheers

[CrimsonEnvy]

I was just wondering, does this equation have anything to do with statistical mechanics?