Hello All,

I've been successfully playing with two card effects--neither of which I know the actual mechanics behind. The first one is as such: A participant riffle shuffles a deck seven times and then starts dealing two cards at a time. You have predicted in advance that there will be a pair of cards that equal a 21 Black Jack hand. You are, of course, correct. I half-way understand this because if black jack hands did not come up nobody would play blackjack, right?

The second effect is a bit more curious. A Red deck of cards is given to one participant who shuffles seven times. The Blue deck is given to a different participant who shuffles it seven times.

Cards are flipped over one at a time from both decks and invariably two of the cards flipped match completely--suit and value. Now, this doesn't happen every single time but it happens MOST of the time from what I am understanding, seeing,and doing.

Can someone here help me find any source material as to the mechanics, hows, and why's of these effects? Thanks in advance.

Sincerely,
Dale A. Hildebrandt

Dale

The card matching happens about 63% of the time. I actually mention this phenomenon in my new book. It is based on e the base of the natural logarithm.

Larry

This page explains the math for the second effect.

http://www.johndcook.com/blog/2010/04/06/subfactorial/

Mike

I was going to bring up derangements but it's covered. As for the first effect, it's not sure-fire. Imagine the deck was stacked A-5-A-5-A-5-A-5 on top. There could be no blackjacks. What you're banking on is that of the 20 cards valued at "10," one of them will get paired with an ace. Seems like a safe bet but I didn't bother crunching it.

There's a brilliant card effect by Tomas Blomberg based on this fact. Even better, the workings and mathematics to that effect are buried somewhere in this very section of the Café. Happy hunting!