discrete geometry - Do the last three remaining cards in a game of Set always form a set?

Question (brief introduction to the game Set is given after the question) When a game of Set gets to a point that there are only three cards left on the table, and all other cards were already removed as part of a Set, do these three cards always form a Set?The game of Set can be described by a finite four-dimensional affine space with each line containing three points. Every Set then is in correspondence with one of the lines in this space.When fiddling around with a two-dimensional case (i.e. an affine space consisting of nine points), the q...Read more

Card Probability in Magic: The Gathering

I'm playing with a deck in Magic: The Gathering which can be seen here: http://tappedout.net/mtg-decks/21-05-15-robots/The deck has sixty cards. I'm trying to find the probability of pulling 5 specific cards in my opening hand of 7 cards in any order. There are 6 copies of one card (either memnite or ornithopter), 4 copies each of the next three (springleaf drum, and ensoul artifact, mox opal), and 17 copies of the last card (any land card).What is the Percentage Chance of me pulling the cards I need?In summary:7 card hand need five specific ca...Read more

Drawing self-improving cards: get good or remove bad first?

Suppose there is a single player card game in which there is a deck of $n$ cards. A card is either red, green or blank. Initially, the deck consists of $r_0$ red, $g_0$ green and $b_0$ blank cards such that $r_0+g_0+b_0 = n$. All cards initially are put into a draw pile. If variable numbers are difficult, we may assume $n=20,r_0=9,g_0=1,b_0=10$.Each turn, the player draws cards from his draw pile until the number of drawn red cards is equal to the number of drawn green cards plus 3 (or until there is nothing left to draw). For instance, he may ...Read more

Determining the order of cards in a deck of shuffled cards

Once a deck of cards is shuffled, can the order of all of the cards for that specific shuffle be determined by only knowing perhaps the order(sequence) of $4$ of the cards in the deck? How many possible shuffles would include these $4$ cards in sequence? What is the math behind it?I would assume that the number of shuffles would be far less than 52!. I am considering options like $52*51*50*49 (6,497,400)$ possible shuffles given the 4 card sequence...I am a very math novice.Thank you....Read more

Playing Cards question

Say I have a hand of X playing cards drawn from a standard 52-card deck, where X can be 1 through 10.Then say I also have a second deck of the 52 standard playing cards, and draw a card from there. (alternately, say I rolled 1d13)I need to calculate the odds (at least approximately) that at least 1 card in my X-card hand will A: MATCH the number drawn/rolled, or B: BE WITHIN ONE OF that value. (So if I drew/rolled a 6, B would be satisfied if the cards in my hand included a 5, 6, or 7)...Read more

Can you explain this card trick?

Can you explain the card trick that is explained here?Edit: Here's a summary of the trick as explained in the video: Start by asking a spectator to pick any three cards they like out of a standard 52-card deck, without showing them to you, and write them down (to make sure they won't forget them). (Ed. note: You can shuffle the deck if you like, or even let the spectator shuffle it, but you don't have to.) Divide the remaining cards into four piles, so that first pile will have 10 cards, the second and third piles will have 15 cards each, ...Read more

How does this "basic" card trick work

I am a bit confused on how the attached cardtrick works, if anyone can explain that would be amazing, thanks! (im in 7th grade btw so its probably simple to most of you)Step 1Remove all face cards and the tens cards from a standard deck of playing cards.You will not need these cards for the trick. Check that you have 36 cards left.Step 2Have an audience member select any of the 36 cards at random without showingyou the card.Step 3Ask the audience member to follow these directions using the number from thecard. (An ace counts as 1.) Multiply th...Read more

card games - Is it possible to get the largest conceivable score in Hearts?

I should explain the necessary rules: in the four-player game of Hearts, the object is to get as few points as possible. The points you receive are determined by the cards you pick up through a hand: hearts are worth $1$ point each, and the queen of spades is worth $13$ points. Players can thus receive any score between 0 and 25 on a given hand. However, if on a hand a player obtains all 13 hearts and the queen of spades, then that player receives $0$ points and all other players receive $26$ points, an act referred to as "shooting the moon".Th...Read more

card games - perfect riffle shuffle problem

A perfect riffle shuffle, also known as a Faro shuffle, is performed by cutting a deck of cards exactly in half and then perfectly interleaving the two halves. There are two different types of perfect shuffles, depending on whether the top card of the resulting deck comes from the top half or the bottom half of the original deck.An out-shuffle leaves the top card of the deck unchanged. After an in-shuffle, the original top card becomes the second card from the top. For example:OutShuffle(A♠2♠3♠4♠5♥6♥7♥8♥) = A♠5♥2♠6♥3♠7♥4♠8♥InShuffle(A♠2♠3♠4♠5♥6...Read more

Collection all cards in a cardgame

Imagine we have a cardset of 140. Every card has 1/140 chance of being drawn every time. When a card is drawn, it is shuffled into the deck of cards again. This would be like when you buy a set in a store, you can get the same card multiple times. How many cards do I have to draw, before I have drawn every card in the deck?...Read more

card games - Maximizing the product of two numbers in a set given their differences

This is an interview problem from Glassdoor that I've been unable to solve. You have all the clubs from a deck, 13 cards, and you can choose 2 from the deck and get paid their product, where all face cards are considered to be 0. You can pay $1 to reveal the difference of any two cards you choose, how much would you pay to play this game?The answer given is "$79, because the 9 and 10 cards can be found in 11 steps", with no further explanation. Is this answer correct, and if so, how does one arrive at it? I tried diagramming out possible c...Read more

I don't understand why this card trick works

So a friend of mine showed me a very interesting card trick that I don't quite understand.You have 52 normal cards from any regular deck you can buy anywhere. The Ace is worth 1 while 2 through 10 are worth their number value. Jack is worth 11, Queen is worth 12 and King is worth 13.You shuffle the cards any way you want. Then you take the first card from the top of the deck and put it down on the table face up. Now, if it's a king you put it back in the deck and try again. If it's anything else you read the value on the card. Lets say you pick...Read more