I have been studying and collecting chain letters for some time, and I've even been developing a sort of Linnean taxonomy of the critters. One thing I've always wondered about is just how many people who forward them actually believe in them, and my informal surveys seem to suggest it's actually relatively few who actually claim any kind of sincere belief. More often than not, people seem to forward them "just in case". That is, they tend to doubt the threats of bad luck for breaking the chain, but they don't want to take any chances.
The reasoning here is actually the same as that in Pascal's Wager. Blaise Pascal, who made wonderful contributions to mathematics and probability, is also known for his argument for why one should believe in God. Now, it's not actually a cognitive argument, in the sense that it provides no evidence whatsoever as to whether or not God is likely to exist. Rather, it's an instrumental argument about the respective costs and benefits of belief versus doubt.
The argument is, of course, mathematical and probabilistic in character. Pascal divides up the possibilities and creates a payoff table, now familiar to students of game theory. There are two variables: Belief/disbelief, and Existence/nonexistence of God. You can either believe or not believe, and in either case you can either be right or wrong (that is, God may exist or not exist).
If you believe, and God exists, your payoff is going to Heaven when you die, to which we assign an infinite positive payoff value. If you believe, and God does not exist, well, then you die and cease to exist. Payoff is zero, just as it is for the nonbeliever who turns out to be right. But pity the nonbeliever who is wrong, for the payoff is the infinite negative of eternal damnation!
So, Pascal argues, looking just at the payoff table, the rational choice is to believe, because the worst that can happen is you're wrong and you just die and cease to exist, whereas you have an infinite positive payoff if you happen to be right. Even if it's 99% certain that there is no God, you're still better off believing than not believing, because at worst your payoff will be the same as the non-believer's best possible result.
What's wrong with this argument? Well, it doesn't actually take into account all of the possible payoffs. How do we know, for example, that God actually will reward people for believing and punish them for doubt? Perhaps after going to such trouble to create a universe in which there was no unambiguous empirical evidence for His existence, He actually wants us to doubt, and so the doubters will be rewarded and the believers punished for their irrational wishful thinking. The thing is, we just don't know the actual payoff table for Pascal's Wager, and so there's no way to conclude that we're actually playing it safe by believing.
The same applies to superstitious practices like chain letters. People look at the text of the chain, and assume there are only two possibilities: True or Not True. Either it'll give you bad luck if you break the chain, or it won't. Yet no one stops to consider that maybe it's telling the very opposite of the truth. Assuming for the sake of argument that a chain letter can actually influence your luck, perhaps the letter lies about the nature of the influence, and maybe breaking a chain is actually good luck. Maybe passing it along brings bad luck.
We simply cannot rule out that possibility. What do we really know about crazy magical concepts like luck and how it works? What reason is there to believe that a magic letter has to tell the truth about its effects? Maybe magic works on the Opposite Day concept, where it has to lie to have its effect. There's really no way to know anything about these mystical powers, and pretty much by definition, we're not supposed to. They're maaaagic!
If you do the math, the infinitely unknowable possibilities are equal on both sides of the equation. You are not playing it any safer by carrying on the chain letter than you are by breaking it. Nor are you actually playing it safer by believing in God, if that's your motive for believing. (Seriously, don't you think an omniscient being will know what you're up to, and see how cynical and self-serving your "belief" is? Is that really what God wants from us? Well, maybe, but it's just as likely it isn't.)
I've heard people say they'll pray for someone who's sick, and cheerfully remark that while it might not help, it can't hurt. Well, if it can't hurt, then it probably can't help, either, at least not in the way they think. Of course, it's nice to have someone care about you, and to know they're thinking warm thoughts about you, and that's good in itself. But if some mystical or supernatural power is involved, then it's just a mistake to assume that power can only work in the way one chooses to imagine it working; if weird magic stuff is in the cards, all bets are off.
The lesson here, if there is one, is that we should simply ignore superstitious considerations when we make decisions. Just because a chain letter threatens bad luck if you break it doesn't mean you won't have good luck for breaking the chain. It's okay to wish for things, to pray for things, and so on, but don't get trapped into thinking that wishing or praying by themselves have any kind of causal effect. They might, of course, but if they do, they're just as likely to have the opposite of the desired effect. So just let those unknowables cancel themselves out of both sides of the equation, and decide based on what you do know.