The Martingale System
by Roy Brindley | Published: Feb 01, '10
Double up, double up and double up again… It’s the oldest betting strategy in the book. You know the craic – put a tenner on red – if it loses put a score on red next spin, if that loses forty quid, then 80, and then 160, 320, 640…
Eventually that little white ball should land in the red bit on the roulette wheel and you will win a tenner. Such is the popularity of this gambling scheme it even has its own name, the Martingale System.
Sadly the Martingale System is not infallible, far from it. To ensure success, players need infinite wealth and they also need to find a casino with no betting limits. Understandably such places do not exist. As it stands punters will either run out of money after a small series of losses or exceed the house betting limits after a similarly small series of losses.
Commonly the ratio of minimum bet to maximum bet on even money chances on a roulette wheel in a casino is less than 1-100. Meaning if a table has a £/$/€5 minimum stake the maximum bet often does not exceed £/$/€500. Likewise a £/$/€10 minimum table can have a £/$/€1,000 maximum stake or less.
With these limitations an initial losing bet sequence starting at 10 units may only go: 10-20-40-80-160-320 before your opportunity to recover your losses (and make 10 units profit has gone).
This is not the only flaw this system has. Red/black, high/low, odd/even may pay even money, but with the zero taken into account, the odds of return are significantly lower than the odds on offer.
On an American roulette wheel there are two zeros which see all even money shots lose. Therefore the odds of your red/black, high/low or odd/even selection NOT coming up are 20-in-38 or 52.6 percent.
If things are already looking shaky, ask yourself what is the chance that one can play Vegas-style roulette game using the Martingale Strategy and avoid a losing streak long enough to double your bankroll?
This purely depends on the likelihood of avoiding a sequence of six losing roulette spins. The odds of that happening, again using a double-zero wheel as an example, is just 2.12 percent (q = 20/38 = 52.6316 percent, so q6 = 2.1256 percent)
However if you play more and more spins, the odds of losing six times in a row begin to increase rapidly. Just consider:
In 73 spins, there is a 50.3 percent chance that you will at some point have lost at least six spins in a row.
Similarly, in 150 spins, there is a 77.2 percent chance that you will lose at least six spins in a row at some point.
And in 250 spins, there is a 91.1 percent chance that you will lose at least six spins in a row at some point.
So to double an appropriate bankroll of 630 units (10+20+40+80+160+320) a minimum of 63 spins will be required (in the unlikely event you win every time) and a maximum of 378 spins (in the even more unlikely event that you win every single round on the sixth spin).
Each round will last an average of approximately two spins, meaning you will need an average of 126 spins of the wheel to double your money and the probability is six losing spins will occur before the conclusion of a 126 spin sample.
The Martingale System cannot work on any table game within the limits imposed by casino rule makers.