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Hey guys. I enjoy your shows including this one. Just a word on statistics, you don’t quite have it right. On your solitaire game, you are correct, you have a 1 in 13 chance the first draw of losing and a 12 in 13 chance of not losing. After 13 cards, there is a 35% chance of still being in the game. The chance of making it through all 52 cards is only 1.6%. This just goes to show how unintuitive statistics are. And when people say what are the odds that Joseph Smith did xyz, they have no idea.

Unless you are C3PO quoting R2D2 on the odds. In that case he has been known to be wrong from time to time.

Can I interject comments like this is reddit?

Great podcast and I too was getting the furrowed brow listening to the math statements. I know math is definitely a perishable skill. I loved Calculus and Statistics and Probability. I now work in accounting and haven’t used those skills for a decade- poof – gone. I seem to remember Stats and Probability being related like cousins. Stats being more historical and probability being predictive. Thus the use of the solitare game would be probabilities. I was trying hard to recreate what the set up would be in my head – remember perishable – then I came and saw Josephus Smythe already nailed it.

My favorite parts are when you laugh RFM. Thank you,

In this podcast, RFM provides a nice analogy for the Church of Jesus Christ of Latter-day Saints’ claim that Book of Mormon “hits” provide evidence for its veracity, in the form of a solitaire game. The point is so clever that it would be a shame if it were marred by a miscommunication of the probabilistic analysis. Unfortunately, there are some problems with the discussion in the podcast. (Basically, RFM mishandles probabilities by adding them instead of multiplying them.) However, an accurate derivation of the probabilities involved isn’t too hard to generate. I’ll try to do so here.

The solitaire game proceeds by the player announcing a card value (A, 2, 3, etc.) as each card in the deck is dealt, with a hit occurring when the announced number matches the dealt card. The game is won if there are *no* hits. What is the probability of winning the game? Intuitively, the probability should be high, as the probability of a hit on any given card is so low, namely, 1 in 13, a probability of 1/13. Nonetheless, as RFM says, the actual probability of winning the game, getting no hits in 52 cards, is quite low. The explanation is as follows:

The game is won if there are no hits, that is to say, 52 non-hits in a row. The probability of a single non-hit is 1 minus the probability of a single hit, that is 1 – 1/13 or 12/13, which is about 0.92. Getting two non-hits in a row requires a non-hit on the first and a non-hit on the second, with probability (12/13) x (12/13) or 144/169. The probability of two non-hits is thus 0.85, still quite likely, though somewhat lower than the 12/13 of a single non-hit. Continuing on in this way, the probability of 52 non-hits in a row is (12/13) x (12/13) x (12/13) x …, with 52 12/13s multiplied together, that is, 12^52 / 13^52, which turns out to be about 0.016 or slightly less than 1/64. (I’m using the caret “^” to represent taking a power. You can see the calculation at http://bit.ly/2HrY2VT.) So if you played this game 64 times, you’d expect to win only once, a very low probability of winning indeed. Conversely, the probability of there being at least one hit (losing the game) — and this is really RFM’s point — is quite high, 1 – 0.016 or about 98 times in 100, even though the probability of a single hit is extremely low.

The point can be made even more starkly if we imagine an even “easier” version of the solitaire game, one in which we announce not only the value of the card but also its suit. The odds of a hit is now a very small probability indeed, only 1/52. But the odds of winning the game, getting 52 non-hits in a row, is still only about 1 chance in 3! (By the same argument as above, the odds are 51^52 / 52^52 = 0.36. See http://bit.ly/2LeudJc for the calculation.)

On the other hand, as the notion of what constitutes a hit gets looser — let’s say by allowing a hit when the announced card is within plus or minus one of the dealt card, as RFM mentions — the tiny probability of winning gets truly vanishing. The odds of winning are now 10^52 / 13^52 or only about one in a million!

RFM is right about the general point: given a bunch of unlikely events, you’d still expect a few of them to occur, whether these hits be announced cards or announced plants in the Book of Mormon. Without much more careful analysis, seeing a few such hits is no evidence for the predictive power of the card announcer or of the scripture.

Thanks for the elucidating podcast!

Thanks so much for the statistical analyses! (That is plural for both of you!)

Statistics are not my strong suit, so I am very glad you weighed in. I did think that winning one out of four in playing this version of Solitaire did strike me as high.

You showed me the odds are much lower than that, by which I mean it is much harder to win than the odds I gave in the show.

Here is the part I didn’t mention–Imagine my dad’s surprise when, after showing me how to play this solitaire game when I was in fourth grade, I shuffle the cards and won the first time!

Talk about beginner’s luck!

He immediately wanted me to do it again!

I did.

And failed.

Every single time after that!

Well guys, that was quite the smack-down. 10 mins vs four hours.

It’s funny how you articulate the things that are on the back of my mind. Too bad I have no one to bounce these thoughts and ideas with, but I’m glad that they are expressed so eloquently here.

RFM,

In this quote:

“Kids, fiction is the truth inside the lie, and the truth of this fiction is simple enough: the magic exists.”

Why did Stephen King chose “the” instead of “that” magic exists.

Wouldn’t it make more sense to use the word “that”?

I think “the magic” to which King referred was the power of imagination in children–which in “this fiction” was ultimately the magic that was needed to defeat a certain dancing clown.

One thing that was implied, but not explicitly stated, as I recall, was the fact that Joseph also had approximately 10 months between the loss of the 116 pages and the renewal of translation in April 1829. So the short time frame given by apologist for the translation process is even longer than claimed.