Why does a protocol droid know odds and statistics so well?

Question

C-3PO is a pretty sophisticated piece of kit. Not only does he know six-million forms of communication and act very convincingly like a nervous butler, but he seems to be a tactical statistician too. Now, K-2SO's analysis of odds makes sense, but is presumably based somewhat on C-3PO's. But why does Threepio know such things?

Examples:

C-3PO: Sir, the possibility of successfully navigating an asteroid field is approximately 3,720 to 1.

C-3PO: Sir, the odds of surviving a direct assault on an Imperial Star Destroyer are precisely— Princess Leia Organa: Shut up!

He also quotes R2-D2's analysis at least once - but he is away from R2 during the other two quotes during Empire.

Answer 1

C-3PO is a pretty sophisticated piece of kit. Not only does he know six-million forms of communication and act very convincingly like a nervous butler, but he seems to be a tactical statistician too.

There is a huge difference between being a statistician and being a tactician.

I can tell you that the odds of dying in Russian Roulette are 50% (assuming you play the game between two opponents, alternating shots until one dies). But that is not the same as telling you whether you should play Russian Roulette or not.

Similarly, I can tell you the odds of drawing a given hand in poker, and the odds that your opponent has drawn a better hand than you, but that doesn't help you with deciding on how much you should bet.

C3PO is logical in nature, and is therefore inherently capable of analyzing what he perceives. Assuming that droids still use the underlying principle of computing (which seems fair to assume), every computer (in the broad sense of the word) analyzes its input in order to render output.

C3PO has shown to be capable of doing more than just his primary purpose. He can have meaningful conversations (unrelated to his primary purpose), he can learn, he has opinions, he can be sarcastic or wistful (mostly to R2), he is shown to (at least try to) be a fair judge of character. This proves that C3PO is technically capable of learning anything he wishes to learn (as long as his body is not physically incapable of it, of course)

If anything, tactics is about playing the opponent, instead of playing the odds. This is almost perfectly encapsulated by Han's well-known quote:

Never tell me the odds.

Notice that Han doesn't say that C3PO is wrong, he merely dismisses it as irrelevant (to him). Han is an emotional character, not a logical one, and therefore has no use for C3PO's statistical feedback.

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A slightly more direct answer

While it is true that tactics are often influenced by the odds of success, that does not mean that the odds of success are the sole factor in deciding your tactics.
C3PO is good at one skill (calculating odds). But he has no military expertise, nor is he particularly experienced in combat or navigation.

Sir, the possibility of successfully navigating an asteroid field is approximately 3,720 to 1

C3PO has little to no navigational skill. It is very likely that C3PO was listing statistics of past events (e.g. of all recorded flights where a ship manually navigated an asteroid field, only 1 out of every 3721 flight records did not mention a crash).

That says little about the current situation:

• Han's skills
• This particular asteroid field
• The hull strength and maneuverability of the Falcon
• The inherent dangers of not flying into the asteroid field
• ...

All of these factors can influence the odds dramatically. If C3PO is listing statistics based on past events, then he is overgeneralizing.

Edit
If this overgeneralization is the best that C3PO can deliver, then I do believe that the Dunning-Kruger effect applies to the justification of why C3PO is speaking at all.
If C3PO is not aware of any better way to help, then he must logically believe that his way is the best possible way to help; which leads him to speak up about his statistical findings.
This seems logically valid. Because if C3PO was aware of a more meaningful response, there's no reason for him to not give that more meaningful response.

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Edit - A bit of offtopic pedantry

Sir, the possibility of successfully navigating an asteroid field is approximately 3,720 to 1

This also hinges on what C3PO means by "successful":

• Not hitting a single asteroid
• Not damaging any ship systems (but possibly hitting a few asteroids)
• Not rendering the ship inoperable (but possibly somewhat damaging it)
• Not killing any passengers (but possibly rendering the ship inoperable)
• Not losing your way (which seems the most literal interpretation of "successful navigation of an asteroid field", completely disregarding ship damage or loss of life, though it does seemingly exclude rendering the ship dead in the water)

The usefulness of his statistical analysis very much hinges on his definition of what constitutes a successful navigation.

Answer 2

One part of communication is knowing the best way to respond to another person based on stimuli. Since 3PO is a machine, he would do this with the aid of statistics. In fact, a protocol droid would need extremely powerful pattern recognition software to communicate properly with other beings, which heavily uses statistics.

This could explain why 3PO is almost always apprehensive about space travel. Statistically, it is a very dangerous method of travel. On the pattern recognition side, how many times has he been on a ship that has gone into danger? Several times.

Here is an example of how statistics and pr would help in communication: a protocol droid is being used to communicate with a human. The droid would already have statistics on basic human interaction, and be able to perform necessary calculations in determining the proper course of action for each but of speaking. After repeated conversations with the same human, the droid has learned certain patterns that one human has, even outside of direct conversation. Those patterns are then used to modify its previous statistics to be used in future conversations, whether the same or different human.

It is also clear that protocol droids can also communicate with a ship's computer, allowing it to potentially get the data that would allow it to learn the success rate of going through an asteroid field.

Answer 3

in very simple terms Game Theory is the application of maths (stats, probability etc) to real world situations involving decision making. Now it is not to much of a stretch to imagine that as part of his protocol programming C3P0 has had game theory included to allow him to help advise and take part in Negotiations between different parties. That way whoever owned him could then ask him to work out the probability the other party will agree or disagree to a particular deal, and the best action to take to improve the odds of a successful negotiation.

He could also have probability built into his decision making and be constantly working out the probability of events happening allowing him to choose the best course of action to take in any given situation.