Watch the videos I linked above, or at least the first one or two. Sure, third parties can and do win in a first-past-the-post system, but it gets more and more rare until it becomes practically impossible for them to have any chance of success.
When was the last time a third party had any real chance of winning the Presidency of the U.S.? Theodore Roosevelt took second place in the 1912 election running as the Progressive Party candidate. He was previously a very popular President of two terms, who decided not to run for a third immediately. Instead he tried to run for a third term later only to miss the Republican Party nomination. He formed his own party, and despite his popularity among Republicans, all he could do was spoil the election... he split the Republican vote, and Democrats walked away the victors with a relatively low plurality.