The power of prophecy: the one where you know how many cards were taken

The magic effect

In this stunning three-phase prediction, you reveal the exact number of cards freely chosen from the pack by the spectator...even though your back was turned when they took their cards.

The mechanics

Ask a spectator to grab a small number of cards from the top of the pile and hide them while your back is turned. They don't know how many and so you can't know either. You take a bunch of cards too, secretly making sure you take more than they did. You told them to take a small number, so you take a large number.

You now count your cards. You need to work out a 'target' number that is three less than the number of cards you hold. If you have 18 cards, your target is 15. Next pick a suit where you have at least three of those cards but not many more. Turn to your spectator, explaining that you are going to make the prediction in three parts. You make these three statements:

"I've got as many cards as you..."
"I've then got another 3 hearts..."
"...and I'm then left with just enough cards to make your number up to 15."

For each statement you prove what you said was true and move on to the next. So the performance goes as follows:

"I've got as many cards as you..."

Ask the spectator to count their cards and place them on the table. Say they have 7 cards. You deal out 7 cards, and put them aside. Part 1 of your prediction is true: you have as many cards as them.

"I've then got another 3 hearts..."

You deal 3 more hearts from what's left of your pile. That's part 2 of the prediction correct.

"...and I'm then left with just enough cards to make your number up to 15."

In your pile you have 18-7-3 = 8 left. Count your remaining 8 cards onto their 7 cards, and the total is your stated target number 15. Part 3 of your amazing prediction is correct.

Prove it works!

The trick here is in the 3-part prediction that looks like you are making three separate but true claims. This step-by-step process builds the suspense and camouflages the simple maths going on. We saw it works if they took seven cards and you took 18. Are we sure it works for any numbers? We could keep checking different combinations (for ever!) or we can do a bit of algebra and prove once and for all it's sure to work.

Say you choose x cards and the spectator chooses y cards. The x and y can stand for any number actually chosen.

The first step - "same as you" - means you deal ycards down from your pile to match their number, y, cards (whatever y is). You originally had x cards. You are left with the difference. That means you have x-y cards left. This step only works if you have more cards than them (i.e., x > y). Otherwise you run out of cards.

The second step - "another 3 hearts" - means you deal 3 more cards down. Subtract 3 from the x -y left from the first step and you have x-y-3 cards remaining in your hand (so actually you need x > y+3 to have enough cards). Now for the final step - "just enough to make your number up to...". You did a secret calculation to work out the target number in this step. You counted your cards to get the number x (whatever x is) and subtracted 3 from it to get the target announced. So it is just x-3. You add your remaining cards to theirs.

Will it add to the target number x -3 you have predicted? We worked out above that you have x-y-3 cards in your hand and they have ycards. Add them together to give a total of (x-y-3)+y cards. The yscancel out leaving x-3 as you predicted.

Algebra wins again, hidden in your prediction. It's really quite simple and will always be true.

Showmanship

You can do this trick with other objects too. Ideally you want to be able to say something specific in the middle step though, like "I have three more broken matches", or "I have three more 10 pence pieces". That makes the way the prediction is split seem more natural, and precise.

You've seen the trick, now find out about the science!