This is a helpful article. But there is a minor problem with this exposition:
"Gamble A has first-order stochastic dominance over gamble B if for any GOOD outcome x, A gives at least as high a probability of receiving at least x as does B, and for some x, A gives a higher probability of receiving at least x. In notation form, P [A \ge x]\ge P [B \ge x] for all x, and for some x, P[A \ge x]>P[B \ge x]. " (My capitalisation of "GOOD".)
The notation form does not capture the notion of a "GOOD" outcome x; it quantifies over ALL x, "good" or otherwise". 
Would the problem be fixed simply by deleting "good" in the initial characterisation?