The big casino

I often use poker to field objections to miracles. That single metaphor can illustrate multiple points. In this post I'd like to collect my previous thoughts on the matter into one place, as well as making a couple of newer points. 

i) Let's begin with Sagan's oft-quoted trope that extraordinary claims demand extraordinary evidence. There are several problems with that assertion. He fails to explain what makes a claim extraordinary. He fails to explain why an extraordinary claim demands extraordinary evidence. And he fails to define extraordinary evidence. Yet atheists routinely quote his statement as if that's a knockdown objection to miracles. 

What does he mean by an "extraordinary claim"? Since he's attacking miracles (or supernaturalism), he's apparently using "extraordinary claims" as a synonym for miracles. But that would amount to saying a claim is extraordinary if miraculous, and miraculous if extraordinary. If so, that does nothing to explicate what makes something extraordinary. 

ii) What are the odds that a player will dealt three royal flushes in three consecutive games? That's a deceptively simple question. Seems like a simple question of math. But the question is ambiguous. It contains a hidden premise. The odds depend on whether the deck is fair or stacked. If the deck is fair, then the odds are astronomically improbable. If, however, the deck is stacked, then it's a dead certainty that a player will be dealt three royal flushes in three consecutive games. Therefore, it's a question that can't be answered in the abstract, because it depends on how we answer a preliminary question. 

iii) Apropos (i-ii), a fair deck is analogous to a closed system. The odds in case the deck is randomly shuffled. That's what happens in the natural course of events. 

A stacked deck is analogous to an open system in which an outside agent manipulates the variables to produce a more discriminating outcome. 

iv) Assuming that it's extraordinary to be dealt three royal flushes in three consecutive games, what kind of evidence would suffice to establish that fact? Does it require extraordinary evidence that a player was dealt three royal flushes in three consecutive games? I don't see any logical connection. Wouldn't eyewitness testimony or security footage from casino cameras suffice? 

v) Apropos (ii-iv), verifying the "extraordinary" feat that a player received three royal flushes in three consecutive games needn't meet a higher evidential threshold than verifying an ordinary hand. For one thing, whether or not that's extraordinary depends on the cause. If the deck was stacked, that's an ordinary explanation. It needn't meet a higher evidential threshold to account for that outcome given that utterly mundane cause. 

"Mundane" in the sense that personal agency can take shortcuts. Events that are naturally improbable or even impossible may be possible or probable given personal agency. 

v) Some Christians, as well as many atheists, think you first need to establish the existence of God before you can justifiably entertain the possibility that a given event is miraculous. But let's revert to our illustration. Must I establish in advance that the dealer is a cardsharp before I'm entitled to infer that the deck is stacked? Surely not. If a player is dealt three royal flushes in three consecutive games, that, in itself, is reason suspect cheating. 

vi) Some critics object to intelligent design theory on the grounds that we can't infer design unless we know the intentions of the designer. An analogous objection could be raised to the recognition of miracles. 

Using the poker analogy, must we know the motives of the dealer to infer that he stacked the deck? Surely not. The fact that the same player was dealt three royal flushes by the same dealer is sufficient evidence of cheating, regardless of his motives. Indeed, we'd expect his motives to be hidden. 

Perhaps the player and the dealer are colluding. They will split the profits. A voluntary partnership. Maybe the player took the initiative. He made the dealer an offer.

Or maybe the dealer is in debt, so he took the initiative. He made the player an offer.

Perhaps the player put a squeeze on the dealer. The player kidnapped his family. Threatened to harm the hostages unless the dealer helps him win. 

Or maybe the dealer hates the player, and deals him winning cards to get him in trouble with the mob boss who runs the casino. 

vii) Atheists often say appeal to divine agency is a God-of-the-gaps argument. By that logic, we should never infer that the deck is stacked. To be dealt three royal flushes in three consecutive games is sheer coincidence. To conclude that the dealer was a cardsharp is cheating-of-the-gaps. 

Or they might say that's sample selection bias. Sure, it looks suspicious, considered in isolation, but when you compare it to all other the hands in which players don't receive three royal flushes in three consecutive games, that's just a random anomaly. Flukes happen.