Discussion Main / ArtisticLicenseStatistics

Linking to a past Trope Repair Shop thread that dealt with this page: Rework page:, started by Unknownlight on Aug 25th 2011 at 4:19:02 AM

So, would whoever added this gem care to make a few bets?

• "One book on recreational mathematics described "the college bet", so-called because its inventor supposedly made enough money from it to put his son through college. If you select three card ranks randomly, and then draw a card from a fair 52-card deck, the chance that it will be one of your ranks is 3 in 13, right? Thus (the book claimed) if you draw three cards, the chance of at least one being one of your ranks is 9/13 (0.6923), and with four cards this rises to 12/13 (0.9231). If the author of the book had followed this "logic" a bit further, he would have seen that this gives the chance of one in five cards being one of yours as 15/13, or more than certain — which is clearly nonsense. (In truth, if each card draw is independent of the others (that is, the card is replaced and the deck shuffled after each draw), the three-card probability is 2170/2197 (0.9877 — substantially better than the naïve calculation), the four-card probability is 28480/28561 (0.9972), and the five-card probability is 371050/371293 (0.9993).)"

What is actually described there is the chance of getting at least one card that isn't what you picked. The chance of getting a selected card three times out of three is (3/13)^3 = 27/2197, so the chance of not getting three out of three is 2170/2197. The actual chances of success are 1 - (10/13)^3 = 1197/2197 (0.5448), 18561/28561 (0.6499), and 271293/371293 (0.7307).

The first point made in the Civilization entry is simply not valid, as it fails to take into account that the benefit of victory and the penalty of loss are very unequal. Sure, a 75% chance means you're more likely to win than lose that individual battle, but overall if you always take those 75% chances, you will lose heavily.

Can remove basically any of "this game's rng seems to favor the enemy", with any actual proof (a line in the games code, a fan studying the odds with 95% certian or higher, etc) that this ACTUALLY the case, not just people's recollection bias which I'm pretty sure about 99% of them are.

In the A Gift of Magic listing, how does telepathy - the ability to read and send thoughts - affect the characters ability to draw random cards from a deck?

Another commons statistics mistake. Is there a name for this?

Equal probability fallacy: Assuming that, if there are X possibilities, every possibility has a (100/X)% chance of happening, even when the probabilities are obviously not equal. Often seen as "There's a 50% chance that this will happen: either it will or it won't." Probability doesn't work this way, as can be shown by simply putting something obviously absurd (or obviously inevitable) in place of "this".