I noticed the original post was missing and so nobody would really have the foggiest what it was all about.

Here is the 'wayback' link so anybody can read what was originally said in the opening post.

Here is the missing first post of the thread...

This analysis is based on a single-zero wheel flat betting on the even chances.

Suppose you were able to reduce the length of your losing runs - how would your edge vary depending on the longest losing run? To put it another way, what should the length of the longest losing run be to ensure that you would make profit flat-betting?

The analysis assumes that there is no limit to the length of the winning runs. I wrote a program which generated even-chance outcomes and varied the length of the longest losing run from 10 to 1, and for each value I calculated the player's edge.

Here's the code:

Code: [Select]

program advantage;

var

i: integer;

procedure get_advantage(maxL: integer);

const

n = 100000000;

var

i, Lrun, w, l: longint;

Pw: real;

begin

w:= 0; l:= 0;

Lrun:= 0;

randomize;

for i:= 1 to n do begin

if random(36) > 18 then begin

Lrun:= 0;

inc(w)

end

else begin

inc(Lrun);

if Lrun <= maxL then

inc(l);

end

end;

Pw:= w/(w + l);

write('Max losing run = ', maxL);

writeln(', HA = ', (Pw*100 - 50):4:3)

end;

// main

begin

for i:= 1 to 10 do

get_advantage(i);

readln

end.

and here are the results:

Max losing run = 1, PA = 15.451

Max losing run = 2, PA = 5.357

Max losing run = 3, PA = 1.194

Max losing run = 4, PA = -0.764

Max losing run = 5, PA = -1.723

Max losing run = 6, PA = -2.229

Max losing run = 7, PA = -2.493

Max losing run = 8, PA = -2.627

Max losing run = 9, PA = -2.704

Max losing run = 10, PA = -2.736

For losing runs of length 10 (or more), the expected PA (player advantage) of approximately -2.7% applies. As you shorten the longest losing run, the PA increases, but it's not until you get to a max losing run of 3 that it becomes positive!

So, if you can find a way to get your maximum losing run down to 3, you will have an advantage of about 1.2%. Alternatively, you could try to recover all losing runs above 3 by some sort of progression (good luck with that).

It's quite surprising how many losses you need to eliminate in order to get an advantage.