DrREC Wants to Play Poker
|December 14, 2011||Posted by Barry Arrington under Intelligent Design|
DrREC writes that the concept of “specification” is a tautology, because in determining if something is designed, ID proponents start from the assumption that it is designed. He gives a poker example to illustrate his point: “A straight flush is an interesting example – out of 2.6 million poker hands, there are 40 straight flushes. Which is the specification – getting one of them, or any of them? Or any hand better than your opponent’s? Choosing the specification inserts a design assumption – that 1 of the flushes, or all of them are what was ‘specified.’”
Let’s take DrREC up on his challenge and consider what a design inference might mean in a poker game. First, we need to consider what a search for “design” in poker even means. To do this I will define a “fair game” as a game in which the cards are properly randomized (i.e., thoroughly shuffled) and properly dealt to the players in each hand. In a fair game, by definition, the hand each player receives in each hand is completely random. On the other hand, we are warranted in making a design inference ONLY if we find evidence that leads us to conclude that a player has received a hand or series of hands that are not random AND the cause of that deviation from randomness is the intentional acts of an agent (commonly called “cheating”).
Let’s look at the math. DrREC is correct in at least two respects. There are approximately 2.6 million five card poker hands (2,598,960 to be precise) and of those hands there are 40 combinations that result in a straight flush (including royal flushes, which some people consider a different hand). This means that on any given hand the odds of being dealt a straight flush are 40/2,598,960 or 1/64,974. Now those are pretty long odds, but they are well within the powers of simple chance. And in fact this is verified by our experience. We also know that players regularly receive straight flushes in fair games.
Therefore, using the explanatory filter to make a design inference based upon a player being dealt a single straight flush is not possible. In other words, if all we know is that one player (let’s call him “Larry”) received one straight flush, we have no warrant to conclude that the null hypothesis (i.e., that it is a fair game) has been falsified. We must conclude that the best explanation for this event is “chance.”
But that is not the end of the analysis. Suppose on the very next hand Larry gets another straight flush. What are the odds of that happening? It is important to keep in mind that we are not talking about the odds of the single event. If we look at each event independently, the odds for each event are the same (i.e., 1/64,974). Failing to understand this leads to the ruin if many gamblers like a craps player betting on “12” because it is “due.” On any given roll of the dice the odds of getting “12” are 1/36 whether “12” has not come up in an hour or it came up on the last roll.
This is not to say, however, that we cannot calculate the odds of a particular series of events. Take a coin flip for example. The odds of getting heads is ½ and the odds of getting tails is also ½. This is true on any given flip. But are the odds of getting three heads in a row also ½? The answer is “no.” The odds of a series of events is simply the odds of each of the events multiplied together. Thus, the odds of getting three heads in a row is ½ X ½ X ½ = 1/8.
In the same way we can calculate the odds of Larry getting two straight flushes in a row. Those odds are 1/64,974 X 1/64,974 = 1/4,221,620, 676 or about 1 in 4.2 trillion. Those are very very long odds. Still, however, the odds are not long enough to warrant a design inference. With millions of poker players in the world, billions of poker hands get played every day. Therefore, over the course of a not-too-long time, trillions of hands will be played and common sense says that over the course of 4.2 trillion hands there is an even chance there will be two straight flushes in a row. This too is confirmed by experience. I searched the internet and it did not take me long to find a story of a game in which a player received two straight flushes in a row in a game everyone believed was fair.
We’re not done yet. What if Larry gets 10 straight flushes in a row? What are the odds? The odds are 1/64,974^10 or approximately 1/1.34^48. That’s 1 in 1.34 raised to the power of 48. If every person who ever lived played one poker hand per second from the big bang until now, we would not expect any of them to receive 10 straight flushes in a row. Now, perhaps, we are warranted in making a design inference.
But wait! This is where DrREC’s objection comes in. We cannot make a design inference merely because the sequence of hands is highly improbable, because if we take ANY random set of 40 hands, the odds of receiving one of those 40 hands ten times in a row is EXACTLY THE SAME as the odds of receiving a straight flush ten times in a row. Therefore, we are not warranted in making a design inference.
Well, if I were playing Larry and he kept getting straight flush after straight flush I would have a strong intuition that someone was cheating. But is that intuition grounded in anything other than my feelings? Is there a rigorous way to demonstrate design?
First, let’s give DrREC his due. He is correct. The odds of receiving one of the hands in any random set of 40 hands is exactly the same as the odds of receiving 40 straight flushes in a row. He is also correct that merely because an event is extraordinarily unlikely, a design inference is not warranted, because the probability of ANY series of ten hands is extremely low and that series of ten hands will probably never happen again from now until the heat death of the universe.
So is it really true that our design inference is based on nothing but a feeling in our gut? This is where William Dembski’s work is so important. Dr. Dembski would say that a design inference is warranted if the event in question displays “complex specific information.” Here everyone agrees there is “information.” Within the rules of poker the cards contain a clearly recognizable semiotic system. Everyone also agrees that our event is complex (i.e., highly improbable). The only issue is whether the complex information is also “specified.” Dembski writes: “The distinction between specified and unspecified information may now be defined as follows: the actualization of a possibility (i.e., information) is specified if independently of the possibility’s actualization, the possibility is identifiable by means of a pattern.”
In our case we have a pattern. The pattern is called “ten straight flushes in a row.” This pattern is not post hoc, because the concept of “straight flush” was clearly known and defined well before the ten hand series was ever dealt. Therefore, ID theory posits that the ten hand series displays a high degree of complex specified information and therefore the best explanation for its existence is “design by an intelligent agent.”