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
920124 Ecart 3.27 +1
920127 Ecart 3.00 +1
920131 Ecart 3.00 +1
920205 Ecart 3.40 +1
920211 Ecart 3.12 +1
920213 Ecart 3.41 .X
920214 Ecart 3.12 +1
920218 Ecart 3.12 .X
920219 Ecart 3.27 +1
920302 Ecart 3.64 +1
920325 Ecart 3.40 +1
920406 Ecart 3.00 +1
920428 Ecart 3.00 +1
920519 Ecart 3.54 -3
920520 Ecart 3.00 +1
920527 Ecart 3.15 +1
920609 Ecart 3.00 -3
920612 Ecart 3.15 .X
920613 Ecart 3.00 +1
920617 Ecart 3.00 +1
920622 Ecart 3.00 +1
920716 Ecart 3.00 +1
920720 Ecart 3.00 +1
920723 Ecart 3.00 +1
920810 Ecart 3.02 .X
920818 Ecart 3.15 +1
920824 Ecart 3.00 +1
920826 Ecart 3.15 -3
920827 Ecart 3.15 +1
920903 Ecart 3.15 +1
920904 Ecart 3.00 +1
920909 Ecart 3.00 +1
920915 Ecart 3.18 +1
920923 Ecart 3.02 +1
920924 Ecart 3.00 +1
920930 Ecart 3.29 +1
921002 Ecart 3.12 +1
921005 Ecart 3.88 +1
921005 Ecart 3.15 +1
921014 Ecart 3.70 -3
921022 Ecart 3.50 .X
921024 Ecart 3.65 +1
921027 Ecart 3.00 +1
921030 Ecart 3.00 .X
[/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)/ (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.
I just tested yesterday's options, manually played several sessions, and reached new high 166 units, using hitnrun.
Is it possible for hitnrun to make a difference?
I was wondering if you'd run again the same amount of results for both, stop after 1 and stop after 2 losses, would you found the same again??
It could be coincidental that stopping after 2 instead of 1 loss came out on top.
You should run simulations again because it doesn't make sense, why is better?
Parlaying wins is a way to make your wins count more, personally I'd not expect to win only with flat bets a negative expectation game.
I also do not know why the results are better.
I tried after 1 lose and after 3 losses, but only after2 losses works.
I play RX RNG and after 2 losses and virtual win results ar positive, with hitnrun even more.
Try parlaying too.
Quote from: ozon on June 02, 2017, 03:14:15 PM
Is it possible for hitnrun to make a difference?
Depends on how fast you can run. :cheer:
H&R makes no difference. One person playing 8hrs a day is the same as another playing 4 two hour days.
It would make sense only if we knew what's coming up next.
Since we don't know this we cannot base a long term win strategy around something such as: when +10 quit session, because random doesn't provide fixed amounts to be won.
You might lose much more by trying winning your session's +10 units, and/or you could win much more than 10 units from time to time.
Therefore by playing for fixed amounts, like expecting a paycheck, firstly would prevent you win more and secondly won't save you from the really bad sessions.
It's only negative in the overall, you should apply an adaptable, flexible strategy which prolongs winnings as much as possible on favorable sessions and circumvents losses as soon as possible on not favorable sessions.
One such strategy is the plateau(s) concept, originally perceived and applied by Nick the Greek back on 60's.
This is all in theory, all the simulations done on the RX are in fact swept in a moment. In online RNG.
I treat this as a hobby, do not see the possibility of win in longrun with online casino RNG. Disconnetions and many weird things. Online roulette in reality works like slotmachine not real wheel.
With a good bet selection this concept can work if we could come up with a way to mix in a positive progression this would be interesting.
This topic was one of the most interesting in this forum, MIKE's claim in the first post concerned that after three losses we have a delicate edge, playing against such an event, after 3 losses.
I do not know what it looks like in reality and I was thinking how to bite it.
If I would have to come to this.
I would play so I would like to table with la partage rule.
I would play only Black, the triger would be 3 times Red, and one time black against the reds series
If the edge really occurs then I would add 4 step positive progressions , one step for one trigger.
5
11
24
55
But I'm really curious if the edge really exists
This question is already addressed to MIKE
I think I have a good bet selection in 600 games played never busted the progression went to 10 ,3 times .
I'm trying something different with this I'm keeping a flat bet Until the results go to a-4 then I kick in the progression keeping track still on what the flat bet side is doing and using this progression according the results as soon as the flat be side becomes positive I stop with the progression and go back to flat betting . It's a little hard to explain .
hi folks,
it's been a while ... well .. quiete a while. :)
do you remember C.E.H with his C.W.B. I'm sure you do. and I don't want to stir old things up again. but as I read this topic I remembered one thing that ol' charly e. hamster once wrote:
"Now as promised I will help you in that direction. I have no doubt that SOME idiots will take this as an actual bet or some hidden clue.
THIS IS NOT A BET....BUT A PROPER GUIDE TO WHAT A "Bet Within a Bet" is all about.
As a pure EXAMPLE ONLY let us take a 50/50 bet like the penultimate which is fairly stable in the results as IF...you where betting it (NOTE IF !)
Taking the results ( Wins & Losses) as IF you where betting it, you may SEE that for INSTANCE....perhaps after three losses, IF you bet you THEN .....you would win say seven out of every ten. IF that was a FACT ? You would then have a consistent winner you could use to make a great deal of money.....IF you was a Professional ?
THAT IS AN EXAMPLE OF A " BET WITHIN A BET"
So IF we take Mikes assumption that after 3 losses somehow mr. edge waits around the corner and ADD this statement here, it seems to me, it needs one or two bits more than just wait for 3 losses to start betting.
cheers :)
hans
"So IF we take Mikes assumption that after 3 losses somehow mr. edge waits around the corner and ADD this statement here, it seems to me, it needs one or two bits more than just wait for 3 losses to start betting":
It needs a huge amount more! It does not work that way in the casino. People try all the time.
The people mix reality with fallacy and dreams all while they are in the wrong, 'frame-of-mind'.
I have literally seen well established, smart, long time players at baccarat lose 6 to 12 hands repeatedly. True they do not have to wager but their ego-mood-bank roll-past experiences and much more----all comes into play. On top of it all people do not take very lightly to buying in with $10,000.00 or much more and than losing it. I watched a female baccarat player last week actually point to the board at midway and verbally cite, "Look it has never went past 4 repeats for both banker and player". It was at hand 43. I told her, please understand things change and very seldom does the board hold true the whole shoe, 80 hands. She wagers table max in 4 spots, which was $8,000.00 for the cut to the players side and 4 more bankers came out. The time to do what she did was when it was happening in the sections that already prevailed. But, people look for what they convince themselves are 'solid' and 'great' wagers to make and then bet on them. That is why the casinos put those boards there, that is why they provide pens and score cards, they want you to do that. Simple, no? I have written about it all and many people will not truly understand or believe me, because they have not been in a real casino or their exposure to a real casino is not very much.
I truly think it takes longer than 10 years of casino play to even start to understand the casino, the game, and yourself. But hey--I might be totally wrong! I don't know.
The "avant dernier" or "before last" or "penultimate" selection is trying to catch chops and streaks and its nemesis are pairs of EC's, EC's occurring in couples.
Therefore, like any other bet selection, has its weakness and is no better, BUT what if we would separate it in 2 different bets?
1 bet covers the streaks and the 2nd covers the chops simultaneously.
What and when is the most important and I'm going to tell you;
You might wonder why to let you know, just because it's good it doesn't mean that there is no better, so that's why I'm willing to share freely something simply decent, good, because I've the exceptional and I have no need and/or obligation to sell or give away a thing.
Let's say that you see a change in the dozens, let's say that this change was from 1st to 2nd, this change is the trigger, as a matter of fact every change in dozens/columns is a trigger.
So in this case you should bet the last dozen/column PLUS the opposite EC, for this example, after 1st and 2nd dozen the opposite EC would be HIGH, therefore 1 unit on 2nd dozen + 1 unit on HIGH.
Another example with columns, 1st spin 1st column and 2nd spin comes 2nd column, in such case you would bet 1 unit on 2nd column + 1 unit on the opposite EC which is RED.
I hope it's clear.
hi bleu angel,
thank you very much for replying. :)
You explained your approach perfectly clear. I've been experimenting with simiilar ideas for some time. but it never got me anywhere. well, I surely will take the variables you suggested into consideration and see what happens. :)
cheers
Hans
Quote from: HansHuckebein on March 12, 2018, 06:12:36 PM
hi bleu angel,
thank you very much for replying. :)
You explained your approach perfectly clear. I've been experimenting with simiilar ideas for some time. but it never got me anywhere. well, I surely will take the variables you suggested into consideration and see what happens. :)
cheers
Hans
Hello Hans, what I've described on my previous post it has been tested flat bet.
It has ups and downs but the ups are more than the downs, thus it accumulates net profit over the time.
If you try it the way I described you might find yourself a lot of opportunities to end your session with a profit. 8)
Ozon any new info on this progression?
Hello Warrior
I have recently tested positive progression a little, but unfortunately if bet selection without edge, they are not able to overcome the house edge.
I even found selections on 2 dozens with positive progression, which withstood 500 k spins, but on the wheel without zero.
If there is a zero in my simulations, everything loses.
I have several options for very aggressive versions of positive progression to be tested, but rather they will not bring long term profit.
Hi Warrior - i have 60.000 placed bets flat betting and with positiv progression that overcome the house edge with La Partage Rule.
Even Money - maybe you can learn from that - i can pm you the author name if you want - i base all my testing upon similar methods and principals.
I just did a test where i gain 100 units with 1000 placed bets flat betting ...
Cheers
Quote from: Sputnik on March 23, 2018, 01:34:15 PM
Hi Warrior - i have 60.000 placed bets flat betting and with positiv progression that overcome the house edge with La Partage Rule.
Even Money - maybe you can learn from that - i can pm you the author name if you want - i base all my testing upon similar methods and principals.
I just did a test where i gain 100 units with 1000 placed bets flat betting ...
Cheers
For sure send me a pm I would like to test it thankyou.
Quote from: ozon on March 23, 2018, 10:00:16 AM
Hello Warrior
I have recently tested positive progression a little, but unfortunately if bet selection without edge, they are not able to overcome the house edge.
I even found selections on 2 dozens with positive progression, which withstood 500 k spins, but on the wheel without zero.
If there is a zero in my simulations, everything loses.
I have several options for very aggressive versions of positive progression to be tested, but rather they will not bring long term profit.
Thanks for the reply ozon ,that pesky zero.
PM Sent ... Cheers
Sputnik = satellite of EC bets ;D
You will never become rich like Richard if your repertoire contains only outside bets, unless you have open your third eye...! :glasses:
This topic was probably one of the most important topics in this forum.
I wanted to refer, however, to the matter related to this topic.
In the first post Mike, he wrote that it is possible to reach the edge, absorbing losses from the first 3 losses of bets.
I think he tried to do it himself, but I do not know if he achieved the goal.
He also wrote that waiting for 3 virtual losses does not make sense. But he wrote about roulette, where the distribution of even bets is equal , minus zero.
And I mean baccarat, where the bets are not equal, The simulation shows that runs of the banker are longer, which translates to a slight edge in this direction.
My question is this.
Whether using virtual losing bets for banker, we are able to reduce the casino's advantage.
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.
https://web.archive.org/web/20170420212412/https://betselection.cc/even-chance-8/how-to-get-an-edge-flat-betting-(in-theory)
edit: The URL link is not archived or something along those lines, however you can still access it manually if that makes any sense!
There most definitely is a way to get ahead by flat betting.
Just almost all players, at least those in all the B&M's I go to and have ever been at, main floor bac and high limit bac, I would have to say an unofficial 98 out of 100 will never stop with a few units.
Once again, I have written extensively, IMO about psych and reality of bac gaming and how to get the best chance of gathering up some sizable wins, capitalizing on groups, sections and opportunities, etc. I have experienced almost a turn around in leaving the table with a profit in sizable amounts versus that of a few units.
But, yes. Flat betting can work the same as anything else with less risk, but less chance to win larger amounts.
Time is the players enemy #1. Everything falls behind the time factor.
+1 and reversal +0 works most of the times, but sooner or later the sequence comes and gives you -8 or any value you set as stop loss.
You might win +13 and get -8 and then again +10 and again -8 and sooner or later you will find your self at even plus-minus the house edge.
The test has already been done with 1.7 house edge for 60.000 trails flat betting.
I can only see one way around this dilemma and achieve one-year gambling with no loss or even more, but then is not flat betting anymore.
My conclusion is that you can use a level accumulation strategy.
Cheers
Flat betting is my personal preference. On saying that, I will use a positive progression if a section of the shoe looks like it's heading for a run of a streak/chop or what I would define as a 'staggered' chop. Obviously nobody knows what's coming out beforehand, but you do need to have something in your armoury which can identify the switches quickly if you want to profit from flat betting. It's no good losing a few units at the end of one section just to possibly win one unit on the next few decisions before another couple of losses if you hope to be successful. Asym is right in one respect! You better know your 'first bet' is going to be a winning one the majority of the time because then you have some wiggle room.
Quote from: Bally6354 on March 02, 2019, 11:13:02 PM
Flat betting is my personal preference. On saying that, I will use a positive progression if a section of the shoe looks like it's heading for a run of a streak/chop or what I would define as a 'staggered' chop. Obviously nobody knows what's coming out beforehand, but you do need to have something in your armoury which can identify the switches quickly if you want to profit from flat betting. It's no good losing a few units at the end of one section just to possibly win one unit on the next few decisions before another couple of losses if you hope to be successful. Asym is right in one respect! You better know your 'first bet' is going to be a winning one the majority of the time because then you have some wiggle room.
Simply put, good logic in many ways.
Interpretation plays a huge part of baccarat, IMO.
Think, Know, Act on Gut, Cut out False and No Good Influences.
Quote from: alrelax on March 07, 2018, 02:05:23 PM
"So IF we take Mikes assumption that after 3 losses somehow mr. edge waits around the corner and ADD this statement here, it seems to me, it needs one or two bits more than just wait for 3 losses to start betting":
It needs a huge amount more! It does not work that way in the casino. People try all the time.
The people mix reality with fallacy and dreams all while they are in the wrong, 'frame-of-mind'.
I have literally seen well established, smart, long time players at baccarat lose 6 to 12 hands repeatedly. True they do not have to wager but their ego-mood-bank roll-past experiences and much more----all comes into play. On top of it all people do not take very lightly to buying in with $10,000.00 or much more and than losing it. I watched a female baccarat player last week actually point to the board at midway and verbally cite, "Look it has never went past 4 repeats for both banker and player". It was at hand 43. I told her, please understand things change and very seldom does the board hold true the whole shoe, 80 hands. She wagers table max in 4 spots, which was $8,000.00 for the cut to the players side and 4 more bankers came out. The time to do what she did was when it was happening in the sections that already prevailed. But, people look for what they convince themselves are 'solid' and 'great' wagers to make and then bet on them. That is why the casinos put those boards there, that is why they provide pens and score cards, they want you to do that. Simple, no? I have written about it all and many people will not truly understand or believe me, because they have not been in a real casino or their exposure to a real casino is not very much.
I truly think it takes longer than 10 years of casino play to even start to understand the casino, the game, and yourself. But hey--I might be totally wrong! I don't know.
I never followed this thread much - until the other day with nothing else to do I began reading when I came across the above. I'll be honest, I had to chuckle when I got to the anecdote about the lady who lost 4IAR betting against. Al is right, shoes seldom maintain a "signature." IMO, the only mistakes the lady made were continuing after the first loss and after losing the first bet she already was at table max so she had no where to go to do more than break even if she won the 2nd hand. But that's not what cracked me up.
What cracked me up was this statement by Al:
"The time to do what she did was when it was happening in the sections that already prevailed." Huh? So IOW as soon as you see a 4 IAR go once or maybe twice it is more likely to be a winner next time? Or the longer a "presentment" continues the less likely it is to go further?
So I guess the lesson is, PLAY THE HISTORY but play it sooner than later.
I will return to my last post.
My question was about assumptions.
If we determine the player series is the same as the banker series, we know that the banker series are slightly longer and more frequent, but this is the minimum percentage.
We know at the same time that the payment is not equal.
My question is whether we will save 0.15 unit if we play after three virtual failures of banker
Bet selection would be after 3 times the virtual loss of banker play till win for 2 or 3 hands.
Quote from: Bally6354 on March 02, 2019, 03:56:39 PM
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.
The question still remains.
Is using a virtual loss on the side banker, to some extent it changes something.
I do not know if this is a place for such an open conversation,
if it were so but by making selections by statistics, i.e. the single player is more popular than the single banker, you can create interesting selections