Generally speaking, the effects of ionizing radiation to human bodies (which are invariably detrimental to health) can be classified into two categories: "Deterministic effects" and "Stochastic effects".

Based on a large number of experiments involving animals and other researches, further supplemented by theoretical studies, it was discovered that certain effects on human beings will always occur when the radiation doses absorbed by a human being reaches a certain level, the "threshold". The severity of these effects will increase with increasing radiation doses. However, below the threshold, the effect will be absent.  This kind of effects is called "deterministic effects".  Examples are cataract and  erythema. The International Commission on Radiological Protection (ICRP) considers that if the annual radiation doses to the lens of the eyes of radiation workers are restricted to 150 mSv, cataract is unlikely to occur during his/her life assuming a working period of 50 years. 

Deterministic effect is analogous to hitting somebody's head with your fist.  When you hit him very gently, there is basically no effect on him.  If you increase the force a little, there is still no effect on him.  However when you increase the force to a certain point, he will feel painful.  As you further increase the force, he will be injured.  Pain and injury are bound to occur when the force is increased to a certain extent.

Studies also show that certain effects may or may not occur when somebody is exposed to ionizing radiation. These are called stochastic effects. The probability of having the effects is proportional to the radiation dose absorbed. There is no threshold in that even the smallest amount of radiation absorbed may slightly increase the chance of stochastic effect. On a contrary, the severity of stochastic effects is independent of the absorbed radiation dose. One example is radiation induced cancer. ICRP considers that the chance of contracting fatal cancer will increase by 5/100,000 for 1 mSv of radiation dose absorbed.

Stochastic effect is analogous to winning the Mark Six. When you bet on Mark Six,  there is no guarantee that you will win.  You may or may not win.  When you put on more bet, the chance you will win also increases.  Again, there is no guarantee that you will win with more bet. On the contrary, reducing your bet does not mean that you will not win.  You still have a chance to win albeit the chance is smaller.