The martingale staking technique is a betting technique that involves increasing your bet each time you lose, so that when you eventually win a bet you will recoup all prior loses plus win an amount equal to the initial bet. Of course this technique wont work in the long run because eventually there could be a sequence of consecutive losses that completely destroys the bankroll, unless you have an infinite bankroll. This is partly why casino tables have maximum bet limits, to nullify any martingale technique at an early stage.
As an example, lets looks at using the martingale staking technique for continuosly betting on the toss of a coin. The odds offered for heads (or tails if you prefer) always remain equal for each bet (i.e. 2.0 in decimal odds, 50% chance). We will use an initial betting stake is £2 and double it each time we lose. Supposing the coin lands on tails 5 times consecutively, then finally lands on heads on the 6th bet:
1st bet: stake £2, it loses, so cumulative losses so far are £2
2nd bet: stake £4, it loses, so cumulative losses so far are now £6
3rd bet: stake £8, it loses, so cumulative losses so far are now £14
4th bet: stake £16, it loses, so cumulative losses so far are now £30
5th bet: stake £32, it loses, so cumulative losses so far are now £62
6th bet: stake £64, it wins £64, so now all prior losses have been recouped and the trader has won £2 overall.
As you can see, in this example the plan fails if the trader only had a maximum betting bank of £62, he would have been unable to place the 6th bet and thus became bankrupt after the 5th bet.
Supposing a trader uses the martingale staking technique such that he will be bankrupt if he hits a run of 'n' consecutive losses. From a mathematical point of view, given certain information such as the traders historical win / loss ratio and the number of bets he makes per day, it is theoretically possbile to calculate the likelihood of n consecutive losses actually occuring in his trading lifetime. What cannot be certain is whether it will occur on his first day of trading, or his last, or not at all.
Anyone considering using a martingale technique would be well advised to avoid doing so. There is a well known phrase declared by the economist and investor John Maynard Keynes, "markets can remain irrational for far longer than you or I can remain solvent".
Happy trading,
Gavin