Risk of ruin calculation for roulette.

Here is a rough and easy way to calculate the risk of ruin of your progression or roulette system.

If you plan to win X units by risking in total Z units. The risk of ruin that you will lose your Z units before wining X units, is:

R(risk of ruin)= 100*X/(Z+X)
Example: We have a progression that when wins offers 5 units profit (X=5). And our Bankroll is 100 units (Z=100).
The risk of losing the progression is:
R=100*X/(Z+X)=100*5/(100+5)=500/105= 4,76%

(This number does not take into account the house edge. The effect of the house edge in the risk of ruin is minimal. In the example above with the house edge the risk of ruin gets closer to 5%)

Another approach and a calculation tool you can find here.
In this great essay we explore the types, reasons and effects of gambling losses in all types of gambling.