1. Gilbreath principle
(a) Arrange cards so that colors alternate
(b) Cut the deck so that the bottom of each half is a different color
(c) Riffle shuffle
(d) Remove the cards in pairs from the top. Each is of different color.
(e) Why?
i. assume that first card to hit table is red
ii. if next card comes from same side, it's black
iii. other side is also black
iv. in any case, the bottoms of the halves are still different colors
2. more general Gilbreath
(a) order deck in suits (spades, hearts, clubs, diamonds, spades,
hearts, etc).
(b) deal cards to form a pile (reversing order)
(c) riffle shuffle
(d) draw quadruplets - will get sets of all four cards
(e) can extend to two entire decks
3. non-messing-up theorem
(a) shuffle
(b) deal cards face up to form a rectangle
(c) sort each row in increasing order
(d) sort each column in increasing order
(e) notice that rows are still ordered
(f) why?
4. dilution
(a) dived deck into red and black halves
(b) take n cards from black half and put into red
(c) shuffle red half
(d) take n cards from red half and put into black
(e) does the red half have more red cards than the black half has black
cards?
5. Monty Hall
(a) guess which of three cards has the ace
(b) reveal which non-guessed card does not have an ace
(c) what is the best strategy to find the ace now?
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