Trope-ic Thunder: The Mexican Standoff

By Drew Parton

As most of you probably know, on Monday I reviewed and discussed the phenomenal and influential Western film The Good, The Bad, and The Ugly. The climax of the film involves a three-way quickdraw gunfight between the main characters. Director Sergio Leone dubbed this kind of gunfight a “Mexican Stand-off” (despite Leone being Italian). The intensity and drama of the climax rests entirely on this Mexican Stand-off.

United Artists

United Artists

So what’s so special about a Mexican Stand-off?

To discuss this, we have to touch on a field of mathematics called “Game Theory.” Game theory is exactly what it sounds like- mathematicians use algorithms to optimize and predict everything from the economy, to ethical dilemmas, to Connect Four.

A Mexican stand-off has profoundly different game theory implications from a normal gun duel.

Say that Bob and Alice are in a quick-draw duel where the goal is to draw your gun, and shoot your opponent before they shoot you. In this example, let’s say that Alice draws her gun first, shoots Bob dead, and avenges her cattle. In a gun duel the advantage lies with whomever draws their gun first.

duel

But now let’s throw Charles into the equation. In this scenario, let’s now say Bob draws his gun first. He might be able to shoot Alice, but there is no way he’s going to turn and shoot before Charles guns him down. In a Mexican Stand-off, the disadvantage lies with the individual who draws first- and this is where the high-tension comes from in the climax. In The Good, The Bad, and The Ugly, Blondie (Clint Eastwood), Angel Eyes (Lee Van Cleef), and Tuco (Eli Wallach) are locked in such a stand-off with the highest of stakes (their lives, and $200,000 in gold coins).

standoff1

standoff2

This is why the final duel is so phenomenal. On the surface, it’s three individuals looking at each other and slowly reaching for their guns, but once you understand the mechanics of the Mexican Stand-off, it becomes one of the most satisfyingly dramatic climaxes in the history of film. That, and the soundtrack doesn’t hurt:

Of course, all of that up there was assuming that every gunfighter was equally skilled- equally accurate. But what if they weren’t? Well, then things get really weird. Let’s now assume that Charles is the most accurate: he hits his target 95% of the time. Alice is still a crack shot, she hits 90% of the time. And let’s assume that Bob has really shaky hands, he only hits 15% of the time. But what Bob lacks in accuracy, he makes up in speed, and pulls his gun first. Now what? If Bob shoots at Charles, it’s rare that he’ll even hit- and if he does, then Alice will still be accurate enough to kill Bob no problem. Believe it or not, Bob’s best bet is either to draw and miss, or draw and not fire. With a lot of luck, Charles and Alice will shoot at each other rather than Bob. It’s still a lot of luck, but much better odds than he had before.

Now! The moment all (some) of you have been waiting for. In the review, we announced a contest to win a blu-ray copy of The Good, The Bad, and The Ugly for the first person so send in a comment, I’m happy to announce that the winner is: Jessica Dudek  out of Buffalo, NY. Thanks to everybody who entered and participated, and we hope to do more stuff like this in the future. You fans make this worth everything, without all of you, we’d just be old college friends talking to each other.

Anyway, be sure to check out my review column: Mindless Action Mondays

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