Yahtze is an entertaining family dice game. The highest scoring throw is all five dice the same, for which you get 50 points, and 100 bonus points if you throw another in the same game. I think the odds of a Yahtze are 6^4, or 1:1296. The odds of throwing two Yahtzes are that number squared. Correct my maths if it’s wrong – but by any calculation it’s not a highly probable outcome. We used to play it when camping with the kids, since it used less skill than other games and so caused less tantrums. There’s nothing worse than mums and dads throwing tantrums. At times, though, It used to give me some parental qualms.
Maybe my conscience was oversensitive, but it was at the time the National Lottery began, and I was a little concerned at encouraging the children in games of chance. Partly this was for fear of their growing up to gamble their money away, but theologically my logic was that, since the Bible says every decision of the dice is from the Lord, a Christian in need of money is better advised to ask his Father for it than putting him to the test for it. One evening my son, then aged about twelve, threw five (honest) Yahtzes in one game, and said, “I’m scared – I don’t want to play this any more.” Somehow it seemed to confirm my scruples. He still does the Lottery sometimes, though. Kids nowadays…
Some time later I was intrigued to read that a similar episode cured the great Puritan Richard Baxter of gaming. He was living at Ludlow Castle at the age of seventeen (that would be in 1632), and decided to learn the art for lack of any other entertainment. The best gambler in the place undertook to show him the ropes. On the first or second game, Baxter was in such a hole that the bystanders were laughing and telling him to jack it in. But on the naive basis that it ain’t over until it’s over he ignored their advice, and let his opponent lay down ten shillings to his sixpence on the result:
As soon as the money was down, whereas he told me there was no possibility of my game but by one cast often, I had every cast the same as I wished, and he every one according to my desire, so that by the time one could go four or five times round the room his game was gone, which put him in such great admiration that I took the hint, and believed that the devil had the ruling of the dice, and did it to entice me on to be a gamester. And so I gave him his ten shillings again, and resolved I would never more play at tables whilst I lived.
Now, do statistics negate his sense of the significance of this? On average even over his game, if not during the last few throws, the dice favoured each roughly equally. And no doubt a bored statistician in Ludlow Castle counting all the die-casts over a month would find a pretty random distribution of results. But the fact remains that Baxter became renowned as a Puritan preacher and writer rather than lost in obscurity as a gamester because of a statistically unusual pattern within the greater distribution. Just as my son’s brief 1:1296^5 run happened to coincide with my theological musings rather curiously.
What happened in Baxter’s experience? Does the devil really get to control randomness? Well, in Job’s case he did, but only under the the permission of God. A more nuanced view of Baxter’s experience, then, would be that God used the devil’s enticement knowing that it would cure, rather than corrupt, him. Or maybe God doesn’t delegate natural phenomena to Satan, and acted directly to the same beneficial effect.
In Mike Gene’s model, God chose to create the very universe in which, at that particular locus, random chance had been forseen to produce that effect. OK, but it seems rather a sledgehammer to crack a nut that directly tweaking a few variables like muscle potentials and so on would achieve more easily.
Does Baxter’s interpretation, or these variants on it, violate science? Forget Elliott Sober’s philosophical concessions. In this example, “random” does not mean intrinisically undetermined, but unconsciously determined. We can probably assume that every throw of the dice was actually determined by the voluntary muscular activity of the two players, the only other factors being fixed values like friction. But those muscle potentials were regulated blind. One could imagine a machine so accurate that it could calculate every movement of a die from picking it up to thowing it unerringly to a predicted score – the ultimate determinist gambler. But since there was (and is) no such machine, merely the incalculably complex and highly inconsistent activity of two independent humans, invoking deterministic law is simply whistling in the wind. Science has nothing useful to say about why the dice fell precisely as they did, and can only comment on the large scale statistical pattern. Any claim that a “lucky streak” is undirected is without evidence. Baxter’s precise game-winning sequence of throws conformed, we may conjecture, to statistical norms but can still, to any Christian, be plausibly attributed to God’s (and/or the devil’s) influence.
So why is the situation any different in organic evolution on the Neodarwinian model? The non-involvement of humans, especially Puritan divines, hardly seems a rigorous criterion for distinguishing the situations. God willed a result (a spooky gambling victory) and used one of the proverbial examples of randomness (a specific sequence of dice throws) to achieve it. So what if he should will to create Homo sapiens sapiens (and every other species too) by the apparently stochastic nature of DNA mutations? What, indeed, if he should want to create Richard Baxter of Eaton Constantine (an idyllic hamlet, by the way) by a rather longer sequence involving the contingency of human reproduction, and indeed of every event in history up until then? What conceivable right has a scientist to proclaim that it was actually an undirected process, and that the result was in the slightest way fortuitous?
The sceptic could, of course, assert that Baxter was completely mistaken in attributing his dramatic win to anything more than superstition. But all Baxter would need to do in reply would be to assert the opposite. Bare assertions don’t carry much weight as evidence, especially when the contrary assertion helps explain the course of a uniquely useful life. And in the biological realm too, what is to be explained is not just one useful life, but an entire useful world. The matter still reduces to two competing assertions of undirected chance and directed providence.
Perhaps we should toss for it?