You are "ruined" if your account size dips below a size that you consider intolerable, a drawdown that will put you out of the trading business, at least for now.

Kelly

For a "Kelly" better, it is fairly simple to calculate your risk of ruin.

If A is your account, and xA is the lower limit that you will tolerate (your ruin), but yA is your profit target, then your risk of ruin is:
Probability that a Kelly better achieves yA before xA = P = 

            y * (x - 1)   
       P =  -----------   
              (x - y)
If x is 1/2 and y is 2, this means you will quit trading when you are down 50%, but your chances of doubling your money are 2*(1/2 - 1)/(1/2 - 2) = 67%
Your chances of tripling your money before losing 2/3 of it are 3*(2/3 - 1)/(2/3 - 3) = 3/7 (43%)

Fractional Kelly

If you are betting a fraction of a Kelly bet, say 1/2, the formula for risk of ruin is a little more complex.

Probability that your balance reaches yA before it reaches xA.
             x^((2/f) - 1) -1   
       P =  -------------------   
            (x/y)^((2/f) -1) -1
With a half-Kelly bet (f=.5), you have an 88% chance of doubling your money before you lose half of it.