Roulette gambling system: Triple Martingale

[Eric Blair]

A couple of years ago I developed a gambling system for roulette based on the popular http://en.wikipedia.org/wiki/Martingale_(betting_system).
I never could get it to work consistently over one million spins but I haven't come across any better system for roulette so I thought I would explain it in the hope that some math wizard can suggest improvements.

In the Martingale system, the gambler assumes that given enough time, the desired result will eventually appear.
And that by increasing his bet every time he loses he will eventually win enough to recover his losses and make a profit.
Sometimes this is simply double the previous bet and sometimes it is determined using The Fibonacci Sequence (madness!).

This is no good for roulette however, because roulette has a maximum bet (usually about 1000x the minimum bet).
So even if the gambler has a substantial bankroll he will quickly exceed the maximum bet allowed by the house.
A popular innovation for the martingale system is to increase your bet just enough to cover your losses and make the smallest possible profit on winning bets, and to bet on one third of the table rather than a single number.
This way you can withstand about 17 losses in a row and still continue profitably (when betting on one third of the table that is).

This was a bit of a waste of time when BTC was worth only a couple of dollars so I expanded the system across all 3 thirds of the table.
Which may seem silly at first glance because betting the same amount on each third will yield a neutral result.
However, each time one third gains a profit, the bet on that third is reduced to 1 while the other thirds are still betting at higher values.
It is this imbalance of risk which yields profits.

The fundamental problem with this system, like many gambling systems is the http://en.wikipedia.org/wiki/Gambler's_fallacy which states that past results of a random system are not indicative of future results, no matter how much you want them to be!
If you have suffered 17 losses in a row, you are NOT more likely to encounter a win!
All results have an equal chance of being successful each and every time.

So unlike the snake oil salesmen I learned from, I am not going to tell you this system will work consistently given enough time.
In fact, the opposite is true, given enough time this system is guaranteed to fail!
It seems to work best in short bursts, but as I explained above you can easily encounter 18 losses on your first 18 spins, and yes that does happen!
From testing the system over 1 million spins I've found that the maximum bet is exceeded on average once every 500 spins.
That number is significantly lower when there is no ZERO on the table, however I am putting my efforts into finding a better way to distribute risk after X number of losses.

MOD NOTE:
Be careful when downloading software from unknown sources

I've built an application to demonstrate the system which you can download at http://www.filedropper.com/triplemartingale.
Disclaimer: I do not endorse the use of this system. I am not liable for any decisions you make. You are responsible for your own decisions.
However donations are welcome if you do find it to your liking.

The application assumes that you have an infinite bankroll, that the minimum bet is 1 unit, and the maximum bet is 1000 units.
It will tell you how much to bet on each third of the table.
Click on one section of the table to tell the application where the ball landed and it will update your balance and determine new bets for you.
If one third loses 18 times in a row you will accrue those losses and the bet figure will return to 1.

Now with all of that said, is there anyone with some voodoo math skills who can suggest improvements?

[Foxpup]

I don't have voodoo math skills, just regular math skills, but I'll suggest an improvement anyway: Don't gamble, dummy!

The Martingale strategy (and all others like it) do not and cannot alter the expected value of a particular bet. The only difference they make is that instead of having a small chance of winning a large amount and large chance of losing a small amount (as when betting normally), you instead have a very large chance of winning a small amount and a very small chance of losing your entire bankroll, which balances out so that the expected value is exactly the same (the assumption that you have an infinite bankroll does not apply in the real world, and any results you derive from that assumption are bogus). Note that this chance is exactly the same regardless of how long you've been gambling, so you have small chance of going bankrupt on the very first round of betting, before you've even won anything. Whoops.

[murraypaul]

This was a bit of a waste of time when BTC was worth only a couple of dollars so I expanded the system across all 3 thirds of the table.
Which may seem silly at first glance because betting the same amount on each third will yield a neutral result.
However, each time one third gains a profit, the bet on that third is reduced to 1 while the other thirds are still betting at higher values.
It is this imbalance of risk which yields profits.

This makes no sense.
The fact that a particular third of the table won last time has no effect on whether it is likely to win again soon.

[Eric Blair]

This was a bit of a waste of time when BTC was worth only a couple of dollars so I expanded the system across all 3 thirds of the table.
Which may seem silly at first glance because betting the same amount on each third will yield a neutral result.
However, each time one third gains a profit, the bet on that third is reduced to 1 while the other thirds are still betting at higher values.
It is this imbalance of risk which yields profits.

This makes no sense.
The fact that a particular third of the table won last time has no effect on whether it is likely to win again soon.

I'm confused, I thought I explained that already.
It is an assumption of the Martingale system, and a flawed one.
While it may be quite possible for the ball to land on ZERO 18 times in a row, or inevitable given enough time, I consider it unlikely enough to risk some money on the assumption that it won't happen.

And while I don't consider this system reliable enough to put decent money into, there may be some gamblers with a higher risk tolerance who enjoy it.
Gambling is not just about money, it's about risk and anxiety, for me it's mostly about strategy.

The single martingale system records your losses and determines your next bet accordingly.
The triple martingale does not lump all of your losses into one account.
It is three separate accounts recording three separate losses.
If you bet 1,1,1, respectively, and the ball lands in the middle, you lose 3 and gain 3 - neutral result.
However your next bet will be 2,1,2, and if the ball lands in the left, you lose 5 and gain 6 - positive result.
Then if you bet 1,2,3, and the ball lands on the right, you lose 6 and gain 9 - positive result.
So you see how a neutral risk ratio yields a neutral result, but an imbalanced set of bets yields a positive result.

If the ball misses the right of the table 10 times, your accrued losses on the third account will be -92 units and your next bet will be 1,2,47.
If the ball then lands on the right you will lose 50 and gain 141, which brings the third balance back into positive numbers and the discrepancy is a result of the 1st and 2nd accounts still betting.

One of the properties of random numbers is that they will yield the same result several times in a row, streaks you might call them.
Long streaks happen less often than short streaks.
That is to say, that the ball landing on the left twice in a row is more likely than 3 times in a row, which is more likely than 4 times in a row, and so on.
This is not a predictive pattern, it cannot be used to determine future results.
It is simply a property of randomness which can only be determined retrospectively.
But we can infer that 18 losses in a row is an unlikely event, inevitable yes, but on average we can expect X number of wins between those streaks.

[Damnsammit]

One time at a live casino I was getting a lot of strange looks because I was drinking and decided to do Martingale on Red and Black at the same time.

It was pretty funny, after I was up like $40 one guy looked really puzzled.  I told him I was crazy... don't think he ever figured it out.



Edit:  An example in case anyone is confused.

Code:

red	black	r+b	ttl	result	won	ttlwin	p/l
5	5	10	10	red	10	10	0
5	10	15	25	red	10	20	-5
5	20	25	50	black	40	60	10
10	5	15	65	black	10	70	5
20	5	25	90	black	10	80	-10
40	5	45	135	green	0	80	-55
80	10	90	225	red	160	240	15
5	20	25	250	red	10	250	0
5	40	45	295	black	80	330	35
10	5	15	310	black	10	340	30
20	5	25	335	red	40	380	45

[Eric Blair]

I don't have voodoo math skills, just regular math skills, but I'll suggest an improvement anyway: Don't gamble, dummy!

The Martingale strategy (and all others like it) do not and cannot alter the expected value of a particular bet. The only difference they make is that instead of having a small chance of winning a large amount and large chance of losing a small amount (as when betting normally), you instead have a very large chance of winning a small amount and a very small chance of losing your entire bankroll, which balances out so that the expected value is exactly the same (the assumption that you have an infinite bankroll does not apply in the real world, and any results you derive from that assumption are bogus). Note that this chance is exactly the same regardless of how long you've been gambling, so you have small chance of going bankrupt on the very first round of betting, before you've even won anything. Whoops.

Well the system tested over 1 million spins, on average yields a balance of -300,000 units so I would be absolutely delighted to discover that the results are bogus.
I wasn't trying to imply that you are a central banker with an infinite supply of cash, it's just that the application records your gains and losses relative to ZERO rather than having you input your bankroll at the beginning.
I could make a roulette simulator with fake cash if you like, it would only take a couple of hours but that isn't really the purpose of the thread.

And yes, I do note that the chances are the same at each spin.
Again, I thought I explained that quite clearly.

The system is there and available for anyone who likes gambling systems.
And it is explained so that it is open for improvement by anyone who is already familiar with the inherent nature of gambling.

[Damnsammit]

Another fun thing to do is just play any two numbers over and over again.  I usually 7/10 and play the adjoining bet (17:1) and also do martingales on the 1st third and 1st column.  With the 3:1 bets you can go pretty deep, but with the adjoining bet you can go 44 deep for 129x the original bet.

I usually only do these silly things at online gambling sites since I need a spreadsheet to keep track of what I am to bet next.

Live roulette is much more fun because you get to drink while you lose money

[Eric Blair]

Another fun thing to do is just play any two numbers over and over again.  I usually 7/10 and play the adjoining bet (17:1) and also do martingales on the 1st third and 1st column.  With the 3:1 bets you can go pretty deep, but with the adjoining bet you can go 44 deep for 129x the original bet.

I usually only do these silly things at online gambling sites since I need a spreadsheet to keep track of what I am to bet next.

Live roulette is much more fun because you get to drink while you lose money

Hmm, would like an application to keep track of your strategy for you?
Might be ideal for drinking purposes.

[Foxpup]

Well the system tested over 1 million spins, on average yields a balance of -300,000 units so I would be absolutely delighted to discover that the results are bogus.
I wasn't trying to imply that you are a central banker with an infinite supply of cash, it's just that the application records your gains and losses relative to ZERO rather than having you input your bankroll at the beginning.

Oh, I see what you mean now. I was confused because you said earlier:

The application assumes that you have an infinite bankroll

Still, losing 300,000 units over 1 million spins is not exactly what I call a good result.

[DannyHamilton]

Still, losing 300,000 units over 1 million spins is not exactly what I call a good result.

It is certainly worse than if you had simply placed a single unit on "Red" (or "Black", or any other bet that pays "even money" every round).

That strategy should result in a loss of approximately 53,000 units over 1 million spins.  So this "Triple Martingale" system does a pretty good job of making your results 5 times worse.

[Eric Blair]

Still, losing 300,000 units over 1 million spins is not exactly what I call a good result.

Agreed, that's why I don't recommend it.
It is significantly better on a table without a ZERO.
Just tested that over 10 million spins and it seems to have about a 50/50 chance of a positive result in the long run.

[DannyHamilton]

It is significantly better on a table without a ZERO.
Just tested that over 10 million spins and it seems to have about a 50/50 chance of a positive result in the long run.

This is true of ANY and ALL "systems".

If you play a fair game that has no house edge, the "system" you use doesn't matter. You'll always have a 50/50 chance of a positive result in the long run.

[Eric Blair]

If you play a fair game that has no house edge, the "system" you use doesn't matter. You'll always have a 50/50 chance of a positive result in the long run.

Fair point.
Either way though, the martingale system is fun and doesn't require much thought.
If you play on a table with a large minimum bet say $1,000, you only need to win 20 times to make a years salary.
And given that it takes about 500 spins to hit a losing streak, that's enough to work for 200 years, given a bit of luck.

[Viccanddarl]

Real board is obviously worth playing but about virtual systems, well I don't? Been tryna earn some dough lately, anyone heard about http://www.moneyblowers.com/  You should try it sometime, and get some break from all the fasad...I am not a mathematician but I have some common sense on which one to choose. Again I would still recommend a table without a zero, Cheers

[InwardContour]

I have tried the normal Martingale system in some dice sites but I have always hit streaks of about 20+ losses...
I won't gamble anymore with the purpose of gaining money, I'll do it just for fun and with a fixed amount of cash.

[notlist3d]

Gambling is gambling.  You might have a better chance of not losing... but when odds are still higher on losing it makes no sense.

If doing gambling it should be for fun as you can not count it as a investment.

House always wins.

[Zebra]

I have tried the normal Martingale system in some dice sites but I have always hit streaks of about 20+ losses...
I won't gamble anymore with the purpose of gaining money, I'll do it just for fun and with a fixed amount of cash.

If you are doing thousands and thousands of bets with automated bets, it is pretty normal to see some long losing streaks.
And martingale and any other strategy don't change the fact that the game has a house edge and the house is winning in the long term.