Tuesday, April 6, 2004 Imagine the following card game. Your opponent holds two cards, one saying "saved" and the other saying "damned." You hold two cards, one saying "I believe; I live a painfully virtuous life" and the other saying "I don't believe; I indulge in all my favorite sins." Play proceeds as follows: Your opponent selects one of his cards and lays it FACE DOWN on the table. You then select one of your own cards and lay it face up on the table. Finally, your opponent flips over his card on the table to reveal which one it is. You score 1 point if you selected "I don't believe" and 0 points if you selected "I believe." Completely independently of your selection, you also score 1000 points if your opponent selected "saved" and 0 points if he selected "damned." So in all, there are four possibilities, scoring 0, 1, 1000, and 1001 points respectively. The tricky point is that when your opponent makes his selection, he first tries to guess which card you will pick. If he predicts that you will play "I believe," then he plays "saved," and if he predicts that you will play "I don't believe," then he plays "damned." He scores 1000 points if he guesses correctly and 0 points if he guesses wrong. Now suppose that you have observed your opponent play this game with many people, and every single time, the opponent has guessed correctly. The opponent seems to be an infallible guesser. What should your strategy in this game be? Argument 1 is that everyone in the past who has played "I believe" has walked away with 1000 points while everyone who has played "I don't believe" has walked away with only 1 point. Why should you be any different? Join the ranks of the 1000- pointers and play "I believe." Argument 2 is that once your opponent has played his card, there is nothing either he or you can do about that choice. Whichever card it happens to be, you'll come out an extra point ahead if you play "I don't believe." So your best strategy (in game-theoretic terms, your "dominant strategy") is to play "I don't believe." - * - If you have heard of Newcomb's paradox, you will have already recognized the above game as a thinly disguised version. I have not read all the literature on Newcomb's paradox, and I know that some of it does address the issue of free will versus determinism, so it is entirely possible that what I have said, and am about to say, is old hat, but it has not occurred to me before to state it in precisely this form. The card-game analogy has given me some new insights into the predestination/free-will debate. For example: 1. It suggests that it might be helpful to think of God as *potentially* fallible in his predictions of how we exercise our free will, but *actually* infallible. That is, in theory our free will is "absolute" and in theory God *might* make a mistake in predicting the future, but in practice he never errs. 2. It illustrates quite sharply that even the divine foreknowledge theory of predestination, in which God exercises no control at all over our actions, still suffers from the feature of predestination that most disturbs its detractors, namely the notion that your eternal destiny seems to have been locked into place before you were even born. It also illustrates, though somewhat less sharply, that a strong theory of free will does not necessarily eliminate paradox. 3. It potentially allows proponents of predestination to distance themselves from fatalists, by declaring fatalism to be analogous to a different card game, in which the second step of choosing "I believe" or "I don't believe" is carried out *by the opponent*. Amusing note for those who know some game theory: The fact that the unique equilibrium has everyone going to hell might partially explain why "few there be that find" "the way which leadeth unto life." [Postscript: I should acknowledge that the concept of the "Predestination Card," which I first heard of in a talk by Peter Winkler, helped inspire the precise formulation of the above card game. Also, a quick web search after I wrote the above article revealed that William Lane Craig has written a long essay on Newcomb's paradox and its relation to the doctrine of divine foreknowledge and fatalism.]