I used to work in Leos casino in town, and on the roulette a lot of people tend to double on even bets ( i.e red/black, odd/even).
For example go to the table with 100 pound worth of chips, bet 2 pound on red, if it doesent come in bet 4 pound on red, 8 pound on red ETC the odds of black coming in 10 times on the run most be in the hundreds so most of the time you leave a winner!
This system can work in the short term but it falls apart on the fact that most casinos are wise to it and therefore place a limit on the maximum bet. Most of them will let you double up about 5 maybe 6 times them you asre limited out. I have used this system and have been winning loads then 13 reds came in on the bounce. I was, lets say., pissed off to say the least.
That is why i sat down and did the maths and came up with my system where the starting point is the Martingale system but with some very important differences.
Let us remember all the time that in the long run the casino always has the advantage and the maths cannot be fiddled in the betters favour, this is because of the 0. But that is not to say that the odds cannot be "bent in our favour.
Take a simple bet of £1 on the number 5 to come in. The odds the house are giving on that is 35/1 when in reality the mathematical odds of it coming in are 1 in 37, so the fair odds would be 36/1. with most obvious simple bets on the roulette wheel we see this trend where the odds given by the house are slightly in there favour.
Let us consider a more prudent bet of £1 on red. The house offers even money but the maths says the odds of it coming in are 18 in 37. Let change the way we state odds here and start using decimal odds. Even money is now stated as 2.00. This is the money you get back from a £1 bet. So for even money you put£1 on and if it comes in you get £2 back. Sorry if that is stating the obvious but this is important for the maths. So the house offers 2.00 but the maths says that a fair price would be 2.056 (rounded up).
So for a bet on a single number the house offers 36.00 when we should get 37 and for a £1 bet on red we get 2.00 when we should get 2.056. So the house wins every time over the course of time because they have a percentage advantage on each bet. If we take a ratio of the real odds versus what we get we can see this. So fo a single number 37/36 = 1.028 giving the house a 2.78% advantage. For a bet on red we get the same number of 1.028.
So we could say that the lower we get the ratio the more value there is in a bet, and if we get a ratio lower than 1.00, we get the advantage in the bet.
Right, let try and find the best ratio we can get for a single spin. What you will find if you do the maths is that we have already found it for any bet on a single spin of the roulette wheel the house always has a 2.8% advantage because of the extra number (i.e The Zero)
Let us now move on to the Martingale system. What we do here is bet £1 on red if we win we pocket our £1 winnings and start again with another £1 bet on red, if we loose we bet £2 if we loose again we bet £4 an in theory on and on til we win. In reality there is either a limit on the table or we dont have enough money to go on, so lets say a reasonable giving up and leaving the casino in a bad way are to go up to a £64 bet. So if we go all the way to the £64 bet we will still after that bet only win £1 scince our last winning spin.
This means that to win this £1 we were prepared to risk £1 + £2+ £4+ £8+ £16+ £32+ £64 = £127. All to win £1. we could see this as the house giving us odds of 1.007874016 (128 won / 127 bet) on us being wrong 7 times on the trot. The mathamatical odds of being wrong 7 times are (expressed as a decimal with 1.00 being a certainty) 0.009416 therefore making the odds of winning at some point along the way (expressed in the same way 0.9905841 to make this number into betting odds in the form of a decimal we take the reciprical of it (do 1 divided by it) giving 1.009505431. We can now calculate out real odds to given odds ratio and it is 1.009505431 / 1.007874016 = 1.00161867 giving the house an advantage of 0.16%. Smaller indeed. But needing a bank of £128.
Got to go now. Get you heads round that and i will finish the story another time.