# Blackjack and Fixed Fractional Position Sizing



## Milk Man (3 June 2006)

Hi guys,

I wanted some feedback about a fixed fractional position sizing idea i've been toying with. It is similar to my casino method when playing blackjack.

Basically when playing blackjack, every time I lose I increase my bet. E.g- I bet $10; if I win the bet remains at $10, if I lose then the bet increases to $15 then $20 then $30 and so on until I win. The premise being that each time a loss is incurred, a win is more likely next hand. This is because the odds of the losing streak continuing are less than it breaking. Just like when you flip a coin; the outcome is either heads or tails, the statistics of such experiments show that larger streaks are a lot less common as numbers increase. The odds increase dramatically each time up (13 of one side in a row is the highest reasonably possible). The theory has worked well a couple of times now. 

Now it is my intention to apply the same logic to forex trading. Basically using normal fixed fractional position sizing except that the position size is never decreased. The logic being that when a loss is incurred the most likely outcome next time out is a winner. The system im using has a 60-70% win rate so this makes it all the better, I believe. I wouldnt use it with systems with larger numbers of losers though as the drawdowns would likely be horrendous. 

Anyways, if you had the energy to read through all my prattle, can I have some feedback? C'mon, one of you academic types has to have a major in statistics.


----------



## tech/a (3 June 2006)

Well no major but some systems experience.

I'm suprised your Blackjack method works as your returns at best can only be 1.5 x stake. at worse you can be risking massive amounts for only the initial stake price.Its only a matter of time that you blow up unless your Kerry Packer,last I heard he wasnt playing a great deal these days.

As for FOREX there would be no need to increase your position size as you are not limited to win % over risk.Unless you have done this.
IE you exit the trade at Y times Risk.

Infact *the exact inverse * I believe has been successfully employed by many.

That is decrease position sizing in losing trades (If you have consecutive losing trades generally its not moving consistently in the direction your attempting to trade) and Increase it during winning streaks (If you have consecutive winners then generally the instrument your'e trading is moving consistently in the direction your trading).

In my discretionary trading I will decrease position sizes during losing streaks--LIKE NOW.


----------



## bvbfan (3 June 2006)

Position sizing why 1.5times initial bet?
If you have two losses in a row say $10 and $15 you''ve lost $25, on third bet you bet $20 and you win but you are still down $5.

My friend plays a similar system but doubles his bet if he looses.

Now on the theory on winning streaks, I can see what your saying but each event whether a toss of a coin or spin on the roulette table is mutually exclusive to any event prior.
Even if by chance you had 10 reds in a row, the chances of the next spin being red is still the same ~49%.
I was at the casino last year and I think I saw 11 reds in a row, if you were playing that system you would need to bet $20480 to try to make a profit of $20, if started with a $20 bet


----------



## son of baglimit (3 June 2006)

re:bvb's 11 in a row - once the table limits kick in, you cant get it back.

just do what i do - go every blue moon, win when you do, and be happy.

SEE ITS SO EASY

(tongue firmly in cheek)


----------



## tech/a (3 June 2006)

> Position sizing why 1.5times initial bet




Maximum return on anyone hand--Blackjack,then even money then Stand off then loss.

Thats why card counters look for better than average decks so they get their win rate up and as they do hit the amount risked.

*What Milk * is describing isnt fixed Fractional position sizing it is Martingale position sizing.
What Im professing is Anti Martingale (in this case).


----------



## GreatPig (3 June 2006)

bvbfan said:
			
		

> My friend plays a similar system but doubles his bet if he looses.



That technique's as old as the hills, and while the basic procedure is sound and works in theory, in practice there are other conditions that can stop it working: namely available funds and betting limits.

If you double your bet with each loss, a run of losses can put a serious dent in your funds. Remember the story of the rice on the checker board? If your first bet is $1, your bet after 10 losses would be $1024, after 20 losses more than $1m (and also remember they're cumulative, so as you placed your bet for $1m, you'd have lost nearly that amount again in bets already). Chances are betting limits would have cut in before then too.

Now you might think that a run of 20 losses on something like black & red on a roulette table is highly unlikely, and indeed it is. However, you'd be unlikely to bet just $1 as well. If you put $100, then after 5 consecutive losses you'd be betting $3200, having lost $3100 already. Five consecutive losses is relatively common, and would you be prepared to risk another $3200 on an almost 50/50 bet by that time - if you lost, you'd be $6300 down and looking to bet $6400? That's a long way from your starting punt of $100.

Essentially you're trading a high probability of small wins against a small probability of a big loss. Casinos have deeper pockets than you, and the odds are in their favour, so if they're not too busy, they may well be happy to let you take that chance.

Cheers,
GP


----------



## GreatPig (3 June 2006)

Milk Man said:
			
		

> 13 of one side in a row is the highest reasonably possible



Why do you say that?

13 of one side in a row has twice as much chance of happening as 14 in a row, and half as much chance as 12 in a row. What's so special about 13?

GP


----------



## tech/a (3 June 2006)

GPs right you have to double up.

Lets take your idea of $10,then $15-,$20-,$25,-$30
and you then win on $35 so in 5 bets youve lost $100 and then on 6th bet youve returned $35---ooops

If you double.
10,20,40,80,160 total outlayed = 320
 next bet 320 win 320---ooops.


----------



## Milk Man (3 June 2006)

Glad I asked. Blackjack system needs work then huh? I never fully crunched the numbers; I was just going by feel. Oh well, no harm done, im a few hunge richer anyways. See what happens when you get reward for doing the wrong thing? 

GP- I think the whole 13 in-a-row works exponentially but im no rocket scientist.

Anyways, I guess what I propose is more anti-martingale not martingale like I was playing. Just to clarify; im not staking any more when I lose just not any less then previous risked.


----------



## GreatPig (3 June 2006)

Milk Man,

People have been working on systems for Blackjack ever since the game was invented, so it's highly unlikely that you'll ever find anything that actually works consistently . And as Tech keeps saying about share trading, it's _consistent_ profits that are important (if you're going to do it regularly), not just having a few successes now and again.

Regarding you original premise that "each time a loss is incurred, a win is more likely next hand", you may want to take a look at this PDF file.

And for actually using the Martingale system in casinos, you might want to note the last line here. 

Cheers,
GP


----------



## Realist (3 June 2006)

> Infact the exact inverse I believe has been successfully employed by many.




Yes, I use the exact inverse, and I have read alot about this, and play alot of blackjack. Was in Vegas only 10 days ago.

IMHO if a coin is tossed 1000 times and each time it comes up heads I'd be betting on heads next time. Not tails!!

Trends in all aspects of life occur, everyone knows it, people do get on winning streaks and losing streaks. Betting againt trends is unwise unless you get better odds for it (which occurs on the stockmarket, but not at a casino odds are fixed).  If you lose 3 in a row leave the table, if you are winning bet more - simple as that.

However with Roulette, you can double your bet after a losing bet (on red or black 49/51 odds cause of 0) until you win, because the odds of you losing 8 in a row are very very small, if you had unlimited cash and did this on an unlimited table you could basically never lose. But there are table limits!! And losing 8 in a row means you can't bet again and you've lost alot of money! The odds of this are small of course, but if you keep doing it, it is bound to happen making this theory unwise.


----------



## tech/a (3 June 2006)

> However with Roulette, you can double your bet after a losing bet (on red or black 49/51 odds cause of 0) until you win, because the odds of you losing 8 in a row are very very small, if you had unlimited cash and did this on an unlimited table you could basically never lose. But there are table limits!! And losing 8 in a row means you can't bet again and you've lost alot of money! The odds of this are small of course, but if you keep doing it, it is bound to happen making this theory unwise.




Sorry but I TOTALLY disagree Ive seen 27 straight black and well over 8 times everytime I walk into a casino.If you went to Caesar's or MGM in Vagas
and told them you wanted the limit increased so you could play martingale they would usher you into a private table area fully serviced fasted than you could sign a cheque.
Odds can be less in the US many tables have 00

Dice (not Craps) is the only 50/50 game in town that I know of.

Least with the markets I can get better odds and a better edge.Well I "think" I can.


----------



## bullmarket (3 June 2006)

Realist said:
			
		

> ...............However with Roulette, you can double your bet after a losing bet (on red or black 49/51 odds cause of 0) until you win, because the odds of you losing 8 in a row are very very small, if you had unlimited cash and did this on an unlimited table you could basically never lose. But there are table limits!! And losing 8 in a row means you can't bet again and you've lost alot of money! The odds of this are small of course, but if you keep doing it, it is bound to happen making this theory unwise.




There are 18 red, 18 black and zero on a roullete wheel - therefore the mathematical probability of a red or black on any given spin is 18/37 = 48.6%

Regarding losing on 8 spins in a row betting on either black or red and not at all on zero, the probability is:

(18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37)

= 0.153%

Consequently the probability of picking red or black correctly 8 times in a row is 0.153% assuming an evenly balanced wheel and ball.

cheers

bullmarket


----------



## dubiousinfo (3 June 2006)

20 reds in a row were spun at a roulette table in the Alice Springs casino one night. The bloke doubled his bet till he hit the table limit and then bet the limit on each spin ($800.00 I think as it was 20 years ago). When the 21st spin came up black, he picked up his chips and left.


----------



## wayneL (3 June 2006)

I haven't done the maths ( incapable is a better description) but I am told that martingale, and other staking plans do not remove the negative expectancy. The odds (and capacity risk) will get you sooner or later.

But I would love to do some statistical studies on distributions of runs of one colour.

One would expect to see normal distributions , but I suspect there would be a rather marked degree of kurtosis. The number of long runs observed seems higher than the pure mathematical probability.

Any statisticians care to comment?


----------



## markrmau (3 June 2006)

LOL. Should have realised it was discovered previosly. I once thought up the same system for Keeno at the club (doubling up after each loss). Worked fine a few times, but darn it wouldn't you believe I lost 7 times in a row and came to the maximum bet limit! (which I didn't know existed). Fortunately I had a friend with me and we split the last bet. I won the last one, took my $10 reward (for a $600 final bet risk   ) and vowed never to be so silly again. Then the stockmarket came along.....


----------



## GreatPig (3 June 2006)

bullmarket said:
			
		

> (18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37) x (18/37)
> 
> = 0.153%



For a losing bet you have to include the zero, so the chance of a loss is 19/37. Losing 8 times in a row has a probability of 0.484% (your answer should have been 0.314%).



			
				Realist said:
			
		

> because the odds of you losing 8 in a row are very very small



Over the longer term, if you're a regular player, the odds are irrelevant. It's the average return that becomes important. With the house having the zero on the wheel, their long-term return is 1/37th, or about 2.7%. Therefore, on long-term average, for every $100 you bet, you'll lose $2.70. This means that if you start with a fixed amount and keep playing with it as long as you can (which means rebetting any winnings), you'll always eventually lose the lot.

The only certainty with gambling (on casino games) is that the more you play, the more you'll lose, as you'll gradually start matching the average return.

GP


----------



## GreatPig (3 June 2006)

wayneL said:
			
		

> martingale, and other staking plans do not remove the negative expectancy



That's correct. Martingale only works where the probability is exactly 50/50 - no house advantage.

Although you could perhaps compensate for that by slightly more than doubling each bet. However, you'd still be stuck with betting limits and potentially exhausting your funds in a run of losses.

GP


----------



## robots (3 June 2006)

hello,

you need variable odds for each bet
i
e. 1/5, 1/21, 1/10, this makes it far more effective

and a constant item

thankyou
robots


----------



## bullmarket (3 June 2006)

Thanks GP - you are right 

the probability of losing in my example is actually 19/37 = 51.3% and so my (18/37)s should have been (19/37).

What I calculated originally is the probability of picking red or black correctly 8 times in a row and I think I did one too many multiplications in my original example.

(18/37)^8 = 0.314%

(19/37)^8 = 0.484%

The method is correct but the numbers used were not 

cheers

bullmarket


----------



## Realist (3 June 2006)

> Consequently the probability of picking red or black correctly 8 times in a row is 0.153%




Exactly, the probability of losing 8 bets in a row is less than 2 in 1000.

Of course on the other times you win small amounts of money to cover that 1 or 2 losses.  So doubling up after each loss is not that silly. Still not wise either.



> Sorry but I TOTALLY disagree Ive seen 27 straight black and well over 8 times everytime I walk into a casino.




First of all that sounds unlikely to me, the odds are less than 2 in 1000 of 8 blacks in a row happening apparently, you must sit at the roulette table for hours each time.    

What are you disagreeing with exactly?  I said I do not think the theory is wise, I certainly don't do it, and of course you could just move to another table with higher limits.  You could do this theory and it'd maybe pay off for a while, but when that one unlucky day comes along you'll get shat on!!

Of course it is possible you will lose 27 times in a row. But that possibility is so small it is not even worth calculating. I'm not sure I believe you when you say you saw 27 blacks in a row, that must have been a freak day indeed!


----------



## GreatPig (3 June 2006)

Realist said:
			
		

> Of course on the other times you win small amounts of money to cover that 1 or 2 losses.



That's the problem though: with the house advantage (the zero), on average those small amounts _won't_ cover the 1 or 2 losses.

GP


----------



## macca (3 June 2006)

It really is this simple, if doubling up worked, every casino in the world would be out of business.

Instead of that, they are busting to build them everywhere.

Trust me,  it doesn't work mate !!


----------



## macca (3 June 2006)

I just remembered something, about 10 years ago, 3 guys I know went to the casino in Hobart.

Their plan was to wait until 2 of the same colour came out, say 2 blacks, they then started betting on red.

They played for 3 days over a long weekend, lost $23,500.00.

Expensive weekend


----------



## Realist (4 June 2006)

> They played for 3 days over a long weekend, lost $23,500.00.




 Oh dear!!    

Dumb bastards!


----------



## RichKid (4 June 2006)

Milk Man said:
			
		

> Hi guys,
> 
> I wanted some feedback about a fixed fractional position sizing idea i've been toying with. It is similar to my casino method when playing blackjack.....................
> ............
> Anyways, if you had the energy to read through all my prattle, can I have some feedback? C'mon, one of you academic types has to have a major in statistics.



Milkman
Have you read Ryan Jones' The Trading Game? It explains the gambler's fallacy and the differences between martingale and anti-martingale systems with worked examples and tables of coin flips etc- seems to address your strategy. If you search ASF you'll find the book discussed with a link to a copy. He also discusses the effect of varying the position size according to a certain formula (talks of futures contracts but shows how to apply to other instruments too) but that part of the book has been criticised in the past, his basic statements are clear and worth reading. Let me know if you haven't read it and would like to.


----------



## kgee (5 June 2006)

Are we talking blacjack or roulette...the only thing I've heard about proffesionals winning at roulette is when a crew scoping a casino found a wheel that kept up throwing statistical anomalies...ie they figured the wheel was weighted wrong or slightly off balance....it was a book i read the ...table was shut down after a couple of day's
other than that I figure the law of big numbers is always in favor of the house and to break it you'd need a huge bankroll


----------



## Milk Man (5 June 2006)

RichKid said:
			
		

> Milkman
> Have you read Ryan Jones' The Trading Game? It explains the gambler's fallacy and the differences between martingale and anti-martingale systems with worked examples and tables of coin flips etc- seems to address your strategy. If you search ASF you'll find the book discussed with a link to a copy. He also discusses the effect of varying the position size according to a certain formula (talks of futures contracts but shows how to apply to other instruments too) but that part of the book has been criticised in the past, his basic statements are clear and worth reading. Let me know if you haven't read it and would like to.




Yeah definitely. Although considering my so called skills involving position sizing they may just stay as theory for now. I did come up with a way of beating the casino though, first I go down to the psych ward and find an idiot savant(sp?) that can count cards.... Seems to work according to Tom Cruise.


----------



## money tree (5 June 2006)

Forex is not a random market. It is strongly LEPTOKEUROTIC (tendency to come up the same as previous result). Forex trends last for LONG periods.

A good betting strategy may be a Fibonacci sequence.

1,2,3,5,8,13,21

eg, bet 1, lose,
bet 2, lose,
bet 3, lose,
bet 5, win.....get back previous 2 bets (3 + 2), reduce bet by 3 positions (to 1)

you need a good table limit and lots of capital. I used to use this system betting on 2 dozens.


----------



## macca (5 June 2006)

kgee,

The only way you can ever break the bank is if they do something stupid.

As long as the casino stays within their budget restraints and don't risk to much on any one game then they will always win.

Just like in the stock market, don't over expose yourself to temporary risks and you will survive a lot longer 

Just an aside, to win big on roulette you must play the numbers and pray, just be aware that any good croupier knows when to throw the ball if they want to avoid a number. 

Thats why the wheel spins at a constant speed, they will land it in a certain quarter of the wheel about 60% of the time. So if you are ever going to have a BIG bet on a wheel, put your chips down after they release the ball and on a number away from the number that had the most chips on it before they let go.

Most of the times the high rollers play blackjack or bacarrat and if they get on a roll they can win big  

Good luck


----------



## RichKid (5 June 2006)

Milk Man said:
			
		

> Yeah definitely. Although considering my so called skills involving position sizing they may just stay as theory for now. I did come up with a way of beating the casino though, first I go down to the psych ward and find an idiot savant(sp?) that can count cards.... Seems to work according to Tom Cruise.




Milkman

lol, we need some sort of 'hire a savant for the night' service...the psych ward is probably where we'll end up if we think we can beat the house that easily..we'd have to be lunatics to donate money to the Packers and Ainsworths of this world, they've got enough money as it is.

Here are some links to threads on ASF, one of them has the link to the book, free download. It's one of the first books of its type that I read and I found the main concepts easy to understand, which is good as it means it's written for novices (but I did have to read some chapters several times!! Still need to re-read it myself). I don't trade futures directly so I have no idea about the validity of his system but I've heard that he's had some disasters trying to trade it publicly (the money management system that is). Google the web for some critiques but only after you've read the book. At least read the first few chapters and some of the coin flipping chapters near the end if you don't have time- see if you can spot some errors (probably typos). Feel free to start a new thread on Ryan Jones' The Trading Game so we can pull apart his theories if you like, I'm keen to delve deeper into this important topic.

A brief mention of the book:
https://www.aussiestockforums.com/forums/showpost.php?p=10491&postcount=14

See today's post for the link to the free copy of The Trading Game: https://www.aussiestockforums.com/forums/showthread.php?p=49155#post49155


----------

