The Martingales Probability and Casino Strategy

There are a few articles about the Martingale System on this website, however here I wanted to cover a little bit more information on Martingales Probability and the flaws of using this method in an online casino.

But before we start a word on randomness, at the heart of the martingale strategy is a requirement for randomness, it is a system that will fail very badly in the light of any bias. So be sure your casino is fair and random and beware leaving your luck in the hands of a random number generator – if only for your own piece of mind.

The concept of the martingale strategy is quite straight forward, you play consistently on a single bet type – usually 50/50 one like odd/even or red/black. You are relying on the low probabilities of repetition and on a mathematical inequality. The amount – S is put on this single event, say on red being spun, if the bet does not win then the Stake (S) is doubled to S2 on the second spin. The third spin will require 4S (double the last bet) if it loses and so on, doubling the bet until the win.

When the winning bet does occur then the final amount will exceed the losses from all the previous games, a fact which is actually algebraically provable.

Here’s some sample odds from American Roulette (the odds for European are slightly different but not greatly)

Some Martingales Probability

For example, the probability of black occurring

  • 2 times in a row – 22.43%
  • 3 times in a row – 10.62%
  • 4 times in a row – 5.03 %
  • 5 times in a row – 2.38%

When we look at this system, the mathematical certainty of doubling the bet bringing a win eventually, and the low probability of consecutive repetition of the same color – it looks extremely tempting and some will say infallible.

There are problems though, as mentioned it suffers badly if there is any bias although it could be argued that any strategy would.   The reliance on randomness though makes playing ordinary online casinos with their computer generated spins less than appealing.   It should only be used in a real life casino or where you can play online roulette here – DublinBet which is a real online casino from dublin played in real time.

There are however some problems which actually exist outside the realms of probability and mathematical certainty of the Martingale system. The system actually carries a major risk of consuming all your cash before paying out, it can be surprising how many times you’ll see long consecutive streaks of the same color for instance. Be careful how you try this if you do play online roulette

Even with sufficient funds you could find yourself in the position of placing an enormous bet to make a very small profit. If your nerve fails you, the house blocks your bet or you do not continue doubling your stake for any reason – then you lose. These are very real reasons combined with the fact that wins are small but regular, that make the Martingale system great in the land of probability but more flawed in the real world.

How do you Bet in Roulette

Although when you see someone throwing hundreds of chips on a roulette table, it can look a bit daunting. It’s actually not that difficult, here’s some of the main number bets you can make in roulette –

    Single Number – Quite simply placing your chip on a single number, e.g 1, 5, 0 or 34 etc.

Number (Split)

    – Putting your chip on a line adjoining two numbers, you are betting on either of those numbers coming up


    – Betting on three adjoining numbers – to place this bet put your chips on the left line of the first number of the series.  For 16,17 and 18 you’d place your chip on the left line of the box around the number 16

Number (Corner)

    – A bet on four numbers whose position on the table make a square.   To make this bet you put your chips on the line in the centre of the square.


    – This is a bet on six numbers, made up of two rows of three.  Here you place your chips on the line to the left of the first number in the series and between the two rows.

Number (Dozen)

    – You have actually got some alternative to making this bet depending on which 12 numbers you want. You can either bet on the first, second or third twelve which has it’s own section. So the first group includes the numbers 1,2,3 -12, the next 13-24 and so on. Remember though none of these groups include the zero

Number (Column)

      – There are also three distinct column bets, to place on these numbers you simply put your chips on the first column (e.g. 1,4,7,10,13,16,19,22,25,28,31 or 34), or the 2nd, 3rd column. The bet is placed using the square at the bottom of each column)

These bets are classified as either ‘inside bets’ or ‘outside bets’ depending on which section they are in on the roulette table. I’ll put all the odds up in my next post on roulette betting. But remember if you play online roulette, then al the decent casinos have free games where you can test these for yourself without risking any money. One word of warning though, if you seem to be exceptionally ‘lucky’ on any roulette free game, be very cautious about using their real money game they maybe manipulating the odds deliberately. Personally I’d never trust any roulette game that did this.

There are many other bets