The probability of guessing correctly is not necessarily 1%. People are very bad at generating random numbers. They tend to prefer odd numbers that end in 1, 3, 7 or 9. If you remember that, you might win 2% of the time!
Dan W
Nice. I love xkcd. Someday, if I have nothing better to do, I might try this on someone, just for the lulz.
I think it’s fascinating that people trying to be random and unguessable intuitively reach for numbers more likely to be prime.
I wonder what the connection is.
Zadius
@Camels
I would think it’s because we use a base-10 number system, so people think numbers divisible by 2 or 5 to be too obvious. But then the guesser is probably thinking the same thing, so he’s not going to guess the “obvious” numbers either.
There are definitely ways to narrow the odds of this down considerably.
I used to do tricks like this all the time.
There are also ways to present certain tricks to seem more impressive than it really is.
Consider the probabilities involved in the Monte Hall game. Better yet, consider Three Card Monte where an astute player will paradoxically get the best odds by following the card they know for certain is not the special card. Many games can be ‘gamed.’
medussa
I thought the point of the panel was that any number between 1 and 100 qualifies as a number between 1 and 100.
ChameleonDave
The probability of guessing correctly is not necessarily 1%. People are very bad at generating random numbers. They tend to prefer odd numbers that end in 1, 3, 7 or 9. If you remember that, you might win 2% of the time!
The extra punchline (contained in the image tooltip, as with all XKCD strips) says as much.
Yes, it is more likely to be prime because otherwise it cannot be prime.
If an integer ends with 5 and isn’t just 5, it can’t be prime, because anything that ends with 5 is divisible by 5. If it’s even, unless it’s the number 2, it can’t be prime, and any integer ending in an even number is even.
Therefore, you can end a prime number with 1,3,7,9.
Without doing primality testing, any integer x has a (1-1/2)*(1-1/3)*(1-1/5)*(1-1/7)*…*(1-1/p) where p is largest prime smaller than x chance of being prime.
I saw this exact trick in a card trick book when I was a kid. Let someone pick any card from a deck, let them shuffle it all they want, then you draw a random card out claiming it to be their card. It only works 1 in 52 times, but when it does you will look amazing.
I think you can narrow that list even more. Most people, when asked to pick a number “between” aren’t likely to pick a number near either end of the string, so you can probably eliminate anything below 20 and above 80 and have a higher chance of guessing correctly.
GreyTheory
wait.. the answer isn’t 42?
Siamang
Better yet, consider Three Card Monte where an astute player will paradoxically get the best odds by following the card they know for certain is not the special card. Many games can be ‘gamed.’
As a magician, I don’t recommend you try this.
You’re assuming that the winning card is actually in play. You’re further assuming that they will pay you off, when in likelihood half the crowd are in on the con, and will knock you over in the alley.
3 card monte isn’t a game. It’s a con.
Play Vegas or Atlantic City, if you want an honest gamble where you actually do get to keep the winnings, and you actually can calculate the odds against you fairly. Of course, the House always comes out ahead in the long run.
But don’t play a con game trying to win. That’s foolishness. The winning card isn’t in play.
Even if it IS in play, they’ll just use another card to flip it over, whereupon it is no longer the winning card (since they swapped the two cards during the flip).
adam felix
on the flip side, if anybody ever asks you to pick an number between 1 and 100, to foil anyone who is trying to show they are “psychic” just pick a non-integer answer like 5/7 or e or pi or gamma. there are many other examples like any transcendental number or irrational number.
Siamang
Good one, Adam.
Also you could choose two, and write them down. Or three.
Then pick some nice round boring numbers. Like 1, 10 and 40.
Give them three guesses. Even if they get one right, they had 3 guesses at it, and the majority of them are wrong. If they get all three wrong, then you’ve completely destroyed their claim.
Siamang, of course I wasn’t advocating trying to con a con artist.
If Three card monte is played “legitimately” with three cards (say amung friends), the simplest slight of hand is during the throw when you can’t know whether the first card dropped is the money card or a dummy card. If you can successfully follow the third card which you know isn’t the money card, you have a 50-50 shot at picking the money card.
on the flip side, if anybody ever asks you to pick an number between 1 and 100, to foil anyone who is trying to show they are “psychic” just pick a non-integer answer like 5/7 or e or pi or gamma. there are many other examples like any transcendental number or irrational number.
Well, assuming you’re working with the real number line. If you’re working with irrational numbers as a vector field over the rationals, then a vector that went through 1 and 100 wouldn’t hit a single irrational number. And the reals as a vector field over the rationals doesn’t have a finite basis, so there’s no finite vector with which to describe pi or any other transcendental number.
Laura
The real problem here is that *you* guys start hitting on girls with “I’m psychic” lines, then we’ll have no way to tell you apart from everyone else. Jus’ sayin’.
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