Cheating buggers at William Hill
I'm not a gambler - never have been. There's never been any attraction for me in putting a bet on - don't get me wrong, I'm not anti-gambling, it just doesn't float my boat. I'm 25 and I've never even set foot in a bookies.

However...

Not too long ago, I got one of those spam e-mails advertising a guaranteed system for playing the odds, etc. etc. etc, and although I normally ignore these sorts of things, I decided to take a look. Of course, I couldn't access the information unless I filled in some surveys, personal details and all that guff - so my apologies to The Queen at SW1A 1AA, the spam mail you'll get is from me - but to my surprise I eventually got to the promised info.

Basically, the system is this. It's roulette, the only bet you place is red / black. You start with e.g. red, and bet 1p. If you win, you get your bet plus 100% of your bet back (2p in total). If you lose, you lose your 1p.

Now, if you win, then take your winnings and bet 1p on the opposite colour. If you lose, double your bet and stay on the same colour. After some thought, I realised this might work. E.g. see below:

COLOUR RESULT BET TOTAL

BLACK WIN 1p 2p
RED WIN 1p 3p
RED LOSE 1p 2p
BLACK LOSE 2p 0p
BLACK LOSE 4p -4p
RED WIN 8p 4p

... and over time, slowly, you'll increase your pot from nothing to a considerable amount. By betting 10p at a time, I worked out you could make about £7-£8 per hour ... not a great deal but more than some people earn at a job.

The only thing of course that could spanner this plan is a long run of results on one colour. This would automatically mean that you're making bets of 1p, 2p, 4p, 8p, 16p, 32p etc and of course this exponential rise means you'll quickly run out of cash. This system relies on the 'break' in the losing run that'll enable you to recoup in one win everything you've lost in the run.

Great idea, thought I, so I registered with William Hill online and started off with £2.00 in the pot, playing roulette as above at 10p per stake. After about 2 hours, I'd increased my pot to £17.50 and rising and I was beginning to smile.

Sadly, not to be. I think the casinos are onto this one since, amazingly, I got a run of 15 reds in a row. Now the odds of this are 2^15 or 32,768 (mathematicians, please correct me if I'm wrong). Sadly I ran out of cash long before the run ended and watched the play until the break with complete, angry disbelief on my face.

I honestly believe this would work over the short term at a real casino, but perhaps some technowizardry identifies these sorts of schemes and moves to block them?

I haven't gambled since. The money I lost was nothing but it made me so angry - and why do something that upsets you?

Would be interested to hear the thoughts of any b3tan statisticians on this subject ... What do you think - bad luck or something more sinister?
(hangableautobulb is an anagram of the best album ever, on, Fri 8 May 2009, 16:00, 20 replies)

.
The odds of each spin landing on red or black are slightly less than 50/50, whether you've had 3 reds in a row, or a million.

Someone the other week on this very forum was saying how he lost some huge amount trying this fail-safe plan!
( browser still relating boring anecdotes into a void on, Fri 8 May 2009, 16:05, closed)

indeed,
there tends to be a 0, and sometimes a 00, which tends to be green. iirc.
(thrain, Fri 8 May 2009, 16:07, closed)

It works for any 50/50 bet ...
... but you have to win before you hit the ceiling.

If you had bet red, black, red, black and kept doubling each time, you would always win your initial stake in the end.

However, on a losing streak, each time your chance of continuing your losing streak halves (i.e. on each red/black or coin toss), the cost of your staying in the game also doubles. You therefore have to have (and be able to bet) many times your anticipated profit to be "sure" you won't lose, 'cos when you do lose you will lose big (you'll lose all of your money or all of the table-limit). In a real casino the table limits will stop you reaching the point where you are pretty certain of not losing and I think they will throw out anyone with an obvious "system" in any case.

Edit - the "extra" numbers in roulette add an additional probability of a loss as those above point out, but even on a coin toss you need a very high earnings to limit ratio.
( Ugi , it's a game of give and cake, Fri 8 May 2009, 16:15, closed)

Phew.
Where to start?

1. Yes - the 2^15 is a statistical aberration (remember the infinite improbability drive from H2G2?) and the underlying program will have had something in it to identify it and screw you over.

2. As others have intimated, it's not a 50/50 game - there's always a green or "vigorish"(?) that I believe it's referred to as which pretty much ensures that the odds are always in favour of the house.

3. It's also not a continuous probability - for example, like bingo. In bingo, if you're betting on a specific number coming out like (say) No.8 from ten balls and two others have come out and are not eight then the probability that the next number is No.8 has increased marginally. With a new spin every time of the roulette wheel the probability of red / blue is "reset" every time.

As for luck or sinisterism? I'd suggest neither, and replace both with the phrase "information asymmetry".

Ed - homo mathematicus statisticus
(Eds Meds Mathskillz=1,Socialskillz=0, Fri 8 May 2009, 16:25, closed)

hate to point this out
but the odds of ANY combination of 15 reds and blacks are the same (2^15 or rather a little more, allowing for the green 0, or the green 0 and 00 on a US table)

You just wouldn't take any notice if you got red,black,red,black etc.

It's perception of likelihood rather than actual likelihood itself that's confusing here.

And as you say, the actual odds for each spin are "reset" each time, anyway, which means again we perceive a likelihood that isn't there. At any point, for any spin, the odds of red or black are simply 50/50 regardless of whether it was one red or a hundred reds in a row before.
( the mighty badger Aphrodite, on a bar stool, by your side, Fri 8 May 2009, 16:44, closed)

The Martingale System
Is what you're describing. It only works if you have unlimited funds, which sadly nobody has.

en.wikipedia.org/wiki/Martingale_(betting_system)
(Vice Admiral Sir Charles Cockbrush KCB MBE DSO, who is finding it increasingly difficult to log into b3ta.com wants to duck your aunt and kick your puppy, Fri 8 May 2009, 16:38, closed)

and if you did
then why would you be gambling
(TheManWithThePlan cussed your mum on, Fri 8 May 2009, 16:55, closed)

Yes
I didn't factor in the 0/00 slots which would, of course, devalue the odds somewhat. It's an interesting run of arguments here - the gambler's fallacy mentioned below and the arguments about the different types of probability above come down to the notions of conditional and non-conditional probability scoring, i.e. the bingo example mentioned elsewhere on this QOTW (or maybe above?) is an example of conditional probability, where one result influences another, and roulette is of course non-conditional probability. Well, it least it would be if WH and the likes didn't build in strategies to influence the probabilities! I'd never heard of the Martingale system before but I knew this couldn't be unique - sounds too good to be true!
(hangableautobulb is an anagram of the best album ever, on, Fri 8 May 2009, 17:31, closed)

Even with unlimited funds it wouldn't work for roulette
Because of the 0 (and 00) as mentioned above. Also, of course, the whole switching colours thing is a red/black herring - it makes no difference whether you keep betting the same colour or switch colours.

I've mentioned before in another qotw that I've always had a problem with the whole 'every run is equally improbable' argument about statistical aberrations, by the way. It isn't true that ten reds in a row is as likely as any other combination, in the sense that ten reds in a row is 'interesting', whereas most sequences are interchangeable. That means that yes, a run of reds genuinely is improbable and worthy of surprise in just the way that common sense says it is. What it isn't is any less probable than any other *particular* run, but of course that's not what people mean at all. Arguing against that is just smug pedantry (and I speak as a fully paid-up smug pedant)

I think people confuse this with the Gambler's Fallacy, which is to say that *after* a run of reds, a black is more likely. That's a genuine error.
( flatfrog Staring vacantly into space, Fri 8 May 2009, 17:04, closed)

yes. you have a point
but the a 1 in 30,000 event isn't statistically particularly rare or significant. Particularly because, as is pointed out below, you can't regard that probability in isolation.

you've got a 1 in 30,000 probability off 15 spins. How many times does a roulette wheel spin in a day? I'll get the maths wrong here, as I'm doing it off the top of my head, but I think that you only need the wheel to spin something like 2000 times for the chances of a 1 in 30,000 sequence coming up to be more or less evens.
( the mighty badger Aphrodite, on a bar stool, by your side, Fri 8 May 2009, 17:29, closed)

I tried this...

I had a slightly more complex system but with the same principle, and more money - speculate to accumulate is what I thought. Went in with £100 and had made £800 in 2 hours. Great!

Next day - a string of straight colours (and it doesn't matter if you swap colours either as of course you have an equal chance of losing either way) and I'd lost it all again.

I think I've just about sussed how to make money without reaching the maximum bet but at the moment I don't have the money as it's all gone on my other gambling habit of dicing with death on my motorbike...
( Turquoise Hexagon Sun has just dropped acid on, Fri 8 May 2009, 16:41, closed)

Ah, the wonders of "coincidences"
Yes, if you only do 15 spins, the odds of getting 15 in a row are 1 in 32,768. However, you played more than just 15 times. For someone playing 114 times, there are 100 stretches 15 spins long, of which any could be all reds.

Also, you would be saying much the same (probably) about a shorter run (say, for example, 10), which increases the probability of this occurring at some time further.

As for roulette in general, due to the 0, your average return is less than 1p for every 1p bet, there is no system that will go over this on average. They merely tend to limit the amount you lose at any one time. In fact, your expected return is just a good from playing the numbers.

edit: With 100 plays, at leat one run of at least 10 will occur approximately one time in ten. 6.54% if not including the "0" (i.e. a run of one colour), 10.96% if including the "0" (i.e. a run of losses)
( Tedium Alduce me to interlow myself., Fri 8 May 2009, 17:12, closed)

It's something more sinister.
Not that you got a long run of one colour - that's just blind chance.

The sinister thing is the guy who sold you the method: as the others here have pointed out, it is statistically flawed.

There's no technique that will beat roulette. Doubling up and its variants (like this one) look good for a while, but once you hit the house limit you're screwed.

If you're going to bet in a casino at all, then mathematically speaking roulette is the best table to play at. The optimal technique is as follows:

1. Amass all the money you will ever bet in a casino in your entire life.
2. Put it all in one massive heap on red (or black - doesn't matter which).
3a. Profit!
3b. ... or loss.
4. Never ever bet in a casino again.
( teedyay, Fri 8 May 2009, 17:29, closed)

I like the idea
But I have a better alternative.

1. Amass all the money you will ever bet in a casino in your entire life.
2. Put it all in your pocket.
3. Walk past the casino.
4. Turn right into the Ferrari dealership and at least know that yes, your car will lose money almost faster than you'll lose it in the casino but, in ten years time even though your car is only worth 20p, you'll still be driving a Ferrari.
(hangableautobulb is an anagram of the best album ever, on, Fri 8 May 2009, 17:34, closed)

Haha!
Yes!
( teedyay, Sat 9 May 2009, 16:37, closed)

It's not 50/50
The double zero sees to that. The house always wins.
( idonthaveafunnynickname Drink-Aware? Sure. I'm aware I want another drink., Fri 8 May 2009, 19:36, closed)

Casinos are wise to this
If you look at any real world or online casino they state minimum and MAXIMUM table bets, e.g. $5 and $500. The maximum is not there from the goodness of their hearts. They know all about doubling up so they stick a maximum in there to stop people from constantly doubling up to recoup their losses. I'd add that it would be trivial for a casino to spot someone doubling up and simply tell them to piss off, probably at the worst moment.
(MagicMoose, Fri 8 May 2009, 19:36, closed)

Why?
They'd tend to get the house edge anyway, and most of these systems give a way of "ensuring" a small win, so even if it works the house loss is small. (in the system above, each time you win, your pot goes up by your initial bet compared to what it was after the last win).
Since someone on a limited table will keep this bet small to prevent short runs from scuppering the plan, the house won't pay out too much.

Note that the "get your initial bet after each win" nature does mean that doing the same system but staying on red (to make the example simpler to word) would allow you to add (say) £1 to the pot each time red came up, but would require large amounts in the starting pot to get anywhere.

If any maths genius wants to calculate the odds of getting 100 reds before a run of 10 blacks comes up, it would be rather interesting (that amounts to winning £100 from an initial pot of £1024).
( Tedium Alduce me to interlow myself., Fri 8 May 2009, 23:48, closed)

^
"most of these systems give a way of "ensuring" a small win"

No they don't. The odds are stacked in the Casino's favour. The only potential for profit is when you manipulate your stake [Martingale or any other of a plethora of LOSING plans] AND quit as soon as you're ahead. Roulette is a game of chance and not skill.

On a standard European wheel there are 37 slots. 18 red, 18 black and a slot marked 0, normally green. [US wheels also have an 00 slot further putting the odds in the Casino's favour.]

You don't need to analyse a series of outcomes, the 'game' comes down to a single spin. You're betting on a colour - either red or black - you have 18 out of 37 chances to be correct, which is 48.64%. Ignoring the Casino's policy on stake returns when 0 lands, the house has 19 out of 37 chances to be correct, which is 51.35%

Red/black pays evens [1/1] which equates to a 50% chance. You're backing at 48.64%. Every time. No matter what colour landed before. No matter what stake you have on.

The Casino is offering you 50% [when it's true chance is 51.35%] on you being correct when the true chance of you being correct is 48.64%.

Simplistically, 51.35% minus 48.64% gives a house advantage of 2.71% EVERY TIME THE WHEEL SPINS. Which as the clued up will have worked out is the same advantage as the house zero against the 36 other slots, 1/37 gives ~2.7%.

On such small percentages are vast fortunes made.
(SalRossi Laughter the best medicine? Nurse, penicillin....., Sat 9 May 2009, 11:49, closed)

aye, thats why the quotes.
However, if you are aiming for a certain amount, with a practically infinite pot (or at least much larger), then these give you a systematic way of betting until you amass the number of wins needed to get that amount.
Unfortunately the amount you get each win must be much less than your pot, or the casino maximum, and if the casino minimum is 1/100 of the maximum, then a run of 7 scuppers you, which will happen 58.9% of the time in 100 spins. To make a profit after one of these runs you need to have won 64 times before this happens (since you cant place the 7th bet for 128 times the minimum, and have just lost a bet for 64 times the minimum).
I cant do the calculations for that, but whatever happens the house edge comes out unchanged in your expected final profit.
( Tedium Alduce me to interlow myself., Sat 9 May 2009, 23:17, closed)