# Math Help - The holy grail or a dream?

1. ## The holy grail or a dream?

Hi guys,
I am totally new at this forum and I hope somebody can help me. I have been studying the roulette for many years (developing and testing systems only as I do not like to gamble or to play at all, just interested in the odds and statistics). In all cases so far I have been able to determine the chances of something happening or not happening but now I have developed a strategy to play for which I have difficulty to determine the chances and the odds. Below I describe the strategy and I add what I think (!) the odds are but I am very uncertain about this so please correct me when I making a mistake in my thinking process:

The strategy is as follows (and for easy of explaining I skip the zero!)

Red and Black have each a 50 % of falling

Clearly if we have a row of 8 spins than the chance of 8 R or 8 B (or any other sequence of R-B) is 1/(2^8)= 0,39%

A perfect spread of chances would be: R B R B R B R B R B R B R B R B etc.
In reality this will not happen for a long time so I thought of betting on a max number of single appearances of Red or Black
If one uses a progression (such as Martingale) the player can bet that a single B or R will not occur too often:

For example:
We want to play on Black:
We see: R R R B R R B and now we start betting that B will not be another single but a second B will fall. In principal we have a 50% chance of winning this time. If we win we start again, if we loose we wait for the next B and make another bet to win (double the bet to recoup the loss and make a small profit).

Now I am trying to find a method to calculate the odds that there are 10, or 11 or 12 subsequent singles of one colour.

My thinking is (similar to the first example of the 8 red or 8 black) that if we loose say 12 Blacks than the MINIMUM row of spins needed will be: 24 spins.

R B R B R B R B R B R B R B R B R B R B R B R B

If R has one or more doubles or longer rows than the total number of spins before we loose must be even greater than 24 spins.

Well, the occurrence of this specific row of 24 spins is 1/2^24 = 0.000000059604644775390625 so that is a chance of loosing of 0.0000059604644775390625% or in other words a chance of loosing of 1 in 16,777,216 ( If we only play for 12 R or B not showing than the chance of loosing would be 1/(2^12) = 0.024% or 1 in 4096 ! )

Am I right or am I making a mistake in this calculation. If I am right this method would reduce the chance of loosing with roulette to less than the chance of being killed in traffic.........

So far my problem/question. I hope somebody is out there who can help me with this. Thanks upfront.

Your strategy of doubling the bet each time you lose so that eventually when you win you recoup all your losses suffers from a fundamental flaw - namely that you must have infinite wealth for this to work. Suppose you first bet $2, then if you lose you next bet$4, then $8, etc. If you lose 12 in a row then you've already lost$8190 and your next bet requires 2^13 = $8192. The odds of losing this many in a row are long, but when it does happen if you don't have the cash you must quit and you are wiped out. There's also the practical aspect that casinos have limits on the size of the bet you're allowed to make, so the strategy gets cut short. As for the mathematics: your example of losing 12 in a row does not require precisely 24 spins - that's the minimum number of spins to lose 12 times, but it may actually involve more (if there are multiple reds in a row). The upshot is that the odds of losing 12 in a row is actually (1/2)^12 = 1/4096 , not one in 16 million. And keep in mind that once you've lost, say, 5 in a row the odds of getting to 12 is now (1/2)^7 = 1/128. So as your losses mount the odds of a catastrophic wipeout gets higher. 3. ## Re: The holy grail or a dream? Hi Ebaines. I am fully familiar with the risks involved when playing martingale. I have been studying roulette and systems/strategies for many years and am very familiar with these risks. Fact remains that there are practical limits when the roulette spins. IN B&M casino's the highest row ever seen is 26 x RED . Of course many people lost fortunes. IN RNG ( On-line casinos the max row ever seen seems to be 31). Of course that does not mean that 32 red cannot occur but the chances (!) of it occurring are extremely small. So suppose I wait until I see 30 REDS and then start a Martingale with a bankroll to double say 10 times ( So i can survive to 40 REDS than my chances of winning are not bad. I now it can still happen but the chance is small. But you have a point. Real players always should have a STOP LOSS limit in mind. No doubt about that. Having said all that lets go back to the real question here: I agree again that 24 spins is the minimum to loose against 12 singles falling. I hear you when you say that the chance of loosing 12 singles is (1/2) ^12 but I do not understand this as this can only occur when I have a row showing a specific sequence of at least 24 numbers ( or even more) The chance that this specific row occurs is 1/2^24. Your last statement is obviously correct as when I have lost 20 times with every next spin the chance of loosing is always 50% That is the nature of the game. Nevertheless what are the chances that a specific row of 24 numbers occurs. Because if that specific row does not occur there must be at least one double black in the row which makes me win. I appeciate your help but I do not think that this answers my question yet. Thanks 4. ## Re: The holy grail or a dream? Originally Posted by Gezondverstand Having said all that lets go back to the real question here: I agree again that 24 spins is the minimum to loose against 12 singles falling. I hear you when you say that the chance of loosing 12 singles is (1/2) ^12 but I do not understand this as this can only occur when I have a row showing a specific sequence of at least 24 numbers ( or even more) The chance that this specific row occurs is 1/2^24. The chance of getting the exact sequence BRBRBRBRBRBRBRBRBRBRBRBR is (1/2)^23. (Note the exponent is 23, not 24 - reason being that the first 'B' is a given - if the first result is an 'R' you woudl ignore it and wait for 'B' to come up). But that's not the only way to lose 12 in a row. You might also get: BRRBRBRBRBRBRBRBRBRBRBRBR, or BRRRBRBRBRBRBRBRBRBRBRBRBR or BRRBRRBRBRBRBRBRBRBRBRBRBR or ... There are an infinite number of ways that you can lose 12 in a row. And if you add up the odds of each one of these possible combinations occuring you'll find it adds to (1/2)^12. We can demonstrate this quite easily using more manageable numbers. What's the probability of losing 3 in a row? The combinations and their probabilities are: BRBRBR (1/2)^5 BRRBRBR (1/2)^6 BRBRRBR (1/2)^6 BRRRBRBR (1/2)^7 BRRBRRBR (1/2)^7 BRBRRRBR (1/2)^7 BRRRRBRBR (1/2)^8 BRRRBRRBR (1/2)^8 BRRBRRRBR (1/2)^8 BRBRRRRBR (1/2)^8 BRRRRRBRBR (1/2)^9 BRRRRBRRBR (1/2)^9 BRRRBRRRBR (1/2)^9 BRRBRRRRBR (1/2)^9 BRBRRRRRBR (1/2)^9 etc. The sum of this infinite sequence is: $( \frac 1 2 )^5 + 2( \frac 1 2 )^6 + 3( \frac 1 2 )^7 + 4( \frac 1 2 )^8 + 5 ( \frac 1 2 )^{9} + ... = 0.125 = (\frac 1 2 )^3$ 5. ## Re: The holy grail or a dream? not to dispute any of the math displayed so far, but most roulette wheels have "house numbers" 0 and/or 00, which are neither red nor black (typically green), and which gives the house (gaming establishment/web-site) a buffer against people playing red/black strategies. this lowers the chances of a (single) win at all (on just a red or black bet) from 50% to 48.6% (with only 0) or 47.4% (with 0 and 00). because of this, martingale strategies are pretty much doomed to failure. 6. ## Re: The holy grail or a dream? tes, the 0 and 00 are what give the house the advantage over the players, as the payouts for winning are all calculated as if those slots weren't there. Without them the casino would have no incentive to offer the game. 7. ## Re: The holy grail or a dream? yes, but my point is: from the perspective of the thread at hand, the 0 and 00 (if present) count as extra reds. this means that just doubling a bet is insufficient (over the long run, you will gradually lose 2-5%, even in a conservative betting scheme, with an infinite bank). which means a slightly larger base for exponentiation than 2, which becomes significant fairly fast in even a small amount of "trials" for example, on the 13-th bet instead of$8,192 dollars, one is already up to \$11,697 dollars to "break even" (for a wheel with only a single 0). that's...a lot. most people have no intuitive idea how exponential growth works (or how geometric series work, which is largely the same thing). the devil is in the details, so to speak...

yes, casinos run games to make money. yes, they make money even when people play "smart" (with the possible exception of blackjack, which is why large casinos play with multiple decks, and frequent deck changes). the holy grail...the sure-fire way to "win"...is to be the house. open a casino (if you can afford to), they're proven money-makers.

tl,dr version: the house packs the wheel with extra colors that are guaranteed losers for red/black bettors. it's NOT 50/50, and strategies based on 50/50 will come up short, eventually.

8. ## Re: The holy grail or a dream?

Hello Ebaines,

Thank you for your very clear explanation. This is helpfull and I fully understand what you are saying. And I can only agree that in theory you are absolutely right indeed. But nevertheless i have the impression that the real world somehow is not always following these statistical laws. I have been studying and observing many many spins ( both outcomes form real casinos as well as RNG spins and the fact is that I have often seen rows of 14, 15 or more RED or Black but I have never (!!) seen a a row of single RED or BLack ( as I described) of more than 14. I have no explanation for this observation as in theory ( as you describe so well) the odds are exactly the same. I have developed another game playing on dozens and columns and in theory it also have exactly the same odss compared to playing on a "dead"dozen or column. And strange enough my method seems ( so far) to give much more security than assuming that a dozen will certainly within so many spins. I have an alteration system and the highest bet I ever needed was bet 17 ( this is progression 17) where I hev seen dozens or columns not showing for more than 30 spins.
So I still have difficulty to grasp the different result between mehtod which should have exactly the same odds ( based on laws of statistics).

Cheers