This is a example of a dilemma seen infrequently in chase stories. I can't remember the name of the dilemma (if it even has one) but I know an extremely similar case appears in the movie Collateral, specifically this scene starting at 11:00 and ending at 13:08:
There are two iterations of this dilemma seen in these two minutes, but both are dealt with the same way, and Tom Cruise's character chooses correctly in both situations because he recognizes the strategy involved. Though not 100% the same as the medic / townie case, it is similar enough in that there are two paths for the medic to take, and two paths for the goon to take. The goon must take into account the medic's choice in his own, and it is because the medic has to make a choice "first" that the goon has an advantage.
The first choice happens when the good guys get to the bottom floor. There is a diverging of paths: take the street or the subway? The most important thing here is the potential for escape. The street offers the greatest potential for escape, because the good guys can just keep running and hide in a manhole if necessary, or they can quickly grab a taxi. The subway offers the least potential for escape because there is no way to know whether a train will be there on time for the good guys to keep running, and there is a high chance that they will be caught up to if they take this route. But they know that the "goon," Tom Cruise, is close behind. So Jamie Foxx attempts to trick Tom Cruise by taking the path that offers the least potential for escape, the subway.
The second choice is between the upper (same level) or lower (different level) trains. Again, the medic wishes to fool the goon by picking the least obvious choice. But the medic just chose the least obvious choice. If, then, the goon has picked correctly between the street and subway, then the goon is onto the medic's game and it is to the medic's advantage to pick the most obvious choice, thereby attempting to trick the goon again.
The second choice is more difficult, but the principle is the same. At first, the good guys run down the stairs so as not to be spotted, in case the goon has chosen correctly. Then, the upper train arrives first. The most obvious choice for escape in this situation is the upper train, which the good guys will pick to trick the goon. It is always the medic's advantage to attempt to trick the goon. This is why Tom Cruise is able to choose correctly, though it takes some brainpower as you can tell by the video.
In the first case the street choice represents the medic taking action to defend himself. The subway represents the medic acting to protect the townie. The medic isn't sure whether the goon knows he is the medic. So the medic can assume one of two things:
1. The goon doesn't know that he is the medic, or
2. The goon does know that he is the medic.
The medic notices that in the first case, it doesn't matter who he decides to protect, as the result will be a coin flip. So he decides that it is best to assume [2], that the goon knows he is the medic. The medic will most likely then decide it is in his best interest to trick the goon by protecting the townie. In the medic's mind, it is most likely that the goon will decide to kill the medic if he knows his role.
The goon's situation happens to be far superior. By assuming the medic will try to trick the goon, the choice becomes as simple as the one between the street and the subway in Collateral. The medic will pick the least obvious route of escape, which is to protect the townie. The goon can then choose to kill the medic, and he will probably be right.
EPT
