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:




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.

 All you have to know is that the wins have to overcome the attempts, simple as that.
So if i use a benchmark with three attempts to get +1...... then +1 has to overcome that attempts doing so.

Example.
+1 a winning session.
-3 a losing session.
X no play

[reveal= Ecart Results]920108 Ecart 3.44 +1
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920302 Ecart 3.64 +1
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920406 Ecart 3.00 +1
920428 Ecart 3.00 +1
920519 Ecart 3.54 -3
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920612 Ecart 3.15 .X
920613 Ecart 3.00 +1
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921022 Ecart 3.50 .X
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[/reveal]

Quote from: Sputnik on November 09, 2013, 01:47:40 PM
All you have to know is that the wins have to overcome the attempts, simple as that.

Yes, but how? waiting for losses, which is what I think you're doing here, doesn't work.


Using the above method, you don't wait for losses, you take them. The analysis shows that you will have a positive long-term expectation by eliminating all streaks of losses higher than 3. Anything up to and including 3 is ok. This means that you don't necessarily win in a session because you might have more losses than wins but still no losing runs greater than 3. It doesn't matter because in the long run you will win IF (and granted, it's a big IF) you can neutralize all losses beyond 3.


At the very least this shows that you don't need to start using a martingale until you have 3 losses in a row. Just take all losses <= 3 and start your marty on the 4th consecutive loss (starting with 1 unit).


You could do a similar analysis for longer odds bets, and it could be that there is a less dangerous progression.

Mike


Example:


BB R BB R BB R BB R BB R BB R BB R BB R BB R BB R BB R  always betting on R and not hitting a bad streak longer than 2 ... I would come out ahead.. Interesting... would you care to prove it for us ?




B

Buffster,


No, that's a losing streak longer than THREE, not TWO. Your example spins are a case of what I referred to in my previous post; remember this is flat betting (apart from the recovery stage which only kicks in when you have a losing streak > 3) so with your example obviously you would lose over that sequence if betting red, because you are flat betting and there are twice as many blacks as reds. But in the long term the winning streaks will more than make up for the losses PROVIDED THAT you can cancel out the losing streaks > 3. The edge is only 1.2%, but it's enough. Or you could start your recovery if you hit a 3rd loss in which case your edge would jump to over 5% (as shown in the table in my first post).


The proof is in the computer simulation. In the long run you will get the same number of runs of wins and losses, plus the extra losses from the zero.  So for example if you could limit your losing run to say 10, meaning 10 consecutive losses, then after the 3rd loss you could start a 7 step progression like this:


1,1,2,4,8,16,32


Notice that it isn't a standard marty of 1,2,4... because you don't need to make a profit, only break even. IF you can win at any point in this progression then in the long run you will have a 1.2% advantage.


W  +1
W  +2
L   take the loss +1
L   take the loss    0
W                      +1
L   take the loss    0
W                      +1 
W                      +2
L   take the loss +1
L   take the loss    0
L   take the loss   -1
W                         0
L   take the loss   -1
W                         0
W                       +1
L   take the loss    0
L   take the loss   -1
L   take the loss   -2 3rd consec. loss - start progression (next bet 1u)
L   4th consec. loss,  (step 2 of prog: 1u)
L   5th consec. loss,  (step 3 of prog: 2u)
W  You have now cancelled all losses > 3. Balance is back to -2
L   take the loss   -3
W                        -2
W                        -1
W                        0
W                       +1

 
This is very similar toward my strategy that i post at this forum board.

Interesting concepts.....


Is there a mathematical way to come up with a suggested life time bankroll for this? And if there is not what do you think a good BR would be, 3 times 10 losses in a row?

Big EZ,


3 times 10 losses in a row might be ok. But there's no guarantee that you will be ahead even if you don't lose it.


If you're using a martingale, the bet amounts to this progression:


1,1,1,1,2,4,8,16,32,64


Return to step one on any win. My analysis above was incorrect when I said you don't need to make a profit after the 3 consecutive losses, because you have to take into account the 'wasted' win. i.e., You need to have made one unit profit when the stake start rising after the 3 consec. losses in order to make up for the win which you would have made had you not been involved in the recovery.

Quote from: Mike on November 21, 2013, 08:19:55 AM



If you're using a martingale, the bet amounts to this progression:


1,1,1,1,2,4,8,16,32,64

Did anyone ever try this?

This thread is certainly one of the more interesting ones on the forum.

It could work well in conjunction with the '2nd's + 3rd's' idea posted here.....

http://betselection.cc/bally's-blog/2nd's-3rd's-(for-e-c's)/

......and possibly a few other filters thrown into the mix as well.

I will attempt 500 placed E.C. bets at dublinbet and see how things pan out.

cheers

Mike what ever happen  with this.

A few days ago I made simulations.
I only played red, after 2 loss wait for virtual win.
To my surprise after 500k spins and was about 500 units on plus.
Biggest high was after 150k spins 670 units
Max drawdawn from top was 350 units.
In the first 150k the trend was increasing, after that trend was neutral.

Observe, even if there is a slight edge, we can not use any real progression.
  I do not know what progression is able to withstand the drawdown of 350 units.

@ Ozon,
I've 2 suggestions which could improve the overall picture:

1) Stop after 1 loss and restart after 1 virtual win

2) When you have drawdown parlay your wins up to the win which will create a new bankroll high, then bet 1 unit and don't parlay if you have no drawdown.

Hi Blue Angel
I did simulations of 200k spins with the first option, ie after one lose wait for virtual win.
Biggest high was 50 units after 50k spins, max drowdawn -300 units, and ended -110 units.

Yesterday I did something else I decided to use fallacy like hitnrun is.
I use RX
Bet selection is what I described 2 loss and virtual win
Bankroll 100 units
Session target profit +7 units, stoplose -14 units
I always ended sessions when reach TP or SL, and reset spins.
To my surprise after several sessions I doubled my starting bankroll.
The tests were not long, but the results surprised me a little

But how about parlaying wins up to the point where you have recoup any losses and reach new bankroll high?

I did not use the second option, I quickly made only simulations for first option from your post.