32
votes
Accepted
Alice and Bob invent a game
So building on kristinalustig's answer they are indeed playing
The cards are assigned as follows
Alice's first turn
Bob's first turn
In particular
Alice's next move produces
Bob's next move ...
23
votes
Accepted
Minigolf Solitaire
Whilst I tried to split things logically into blocks (e.g. working forwards to a point, then working backwards from the end to see what else was left, and thus needed to be used first), this was ...
19
votes
Accepted
Captain Pun plays cards
I believe the message being communicated is
Getting the message took a bit of guesswork, but it checks out:
Since
18
votes
Accepted
Pick one card magic
If cards are not prearranged then it is impossible to do this trick.
It is so simple arrangement that you wouldn't notice.
Because
Lan got your card by
This way
17
votes
Accepted
Unique representation ID for 5-card poker hand using combination without sorting
If we take the IDs to be
and the result to be
then you can find the card IDs by
and the number will be at most
We can actually do better than this while using the same basic idea:
A little better:...
17
votes
Accepted
17
votes
Accepted
How many different kinds of hands can appear in a single Texas Hold 'em game?
I believe the maximum number of different hands is 7
Here is one such example:
16
votes
Alice and Bob invent a game
I spent quite a while working on this yesterday and today. I only have a partial answer.
I started with the assumption that
I chose this assumption because:
Given this assumption, I tried:
However:...
15
votes
Accepted
Card trick: guessing the suit if you see the remaining three cards (important is that you can't move or turn the cards)
Step 1:
Step 2:
Step 3:
Step 4:
Example:
13
votes
Accepted
Transform a pile of cards in reverse order
The optimal strategy takes
Here's why this is necessary:
And here's a way to do it:
Fun fact:
13
votes
Accepted
12
votes
Accepted
A retroanalysis problem in bridge
6 rounds have been played and no-one has any voids before you sit down. There are therefore at most 1 round of spades and hearts (if there were 2 then 8 cards are played + 4 visible + 2 with the ...
12
votes
Accepted
5 people each have 5 equal cards
Assuming each player wants to maximize their personal win probability for the single game...
The reason I chose this approach is
11
votes
5 people each have 5 equal cards
Assuming he respects his friends, he assumes they play just as he will.
In order for him to have the highest chance of victory, he needs to be able to select each card with a random probability. The ...
11
votes
Accepted
Twisty puzzle composed of hexagonal prisms, with As and diamonds
It was first released in June 2004 by Mefferts under the name Jackpot, and later it was renamed Platypus, and after that the New Generation Puzzle. It probably was sold under other names as well.
See ...
11
votes
Accepted
Mind Reading in Three-Handed Pot Limit Omaha
Suppose the board is:
with Charlie (last to speak) holding
To see how Charlie could infer the contents of Alice and Bob's hands, consider that...
As a consequence, Alice's winning hand must be
Bob,...
10
votes
Accepted
Card Passing Game
Let us begin with this observation: with 13 pair of cards in play, that accounts for every card in the half-deck. There are no cards remaining out of play.
So let's construct a scenario in which ...
10
votes
Accepted
10
votes
Accepted
What happened today? Asked the magician
The magician and the assistant need not memorize 36 phrases, because they have memorized the following simple table:
Note that every sentence contains two nouns (or nominal phrases), and a verb.
To ...
10
votes
Accepted
Pick cards from a table
I can get
My thought process is
I believe this is the maximum because
I've made two pictures to help illustrate what's happening.
8
votes
8
votes
What is the minimum High Card Points needed for a partnership to be able to claim all 13 tricks in Bridge?
7S can be forcibly won with five HCP:
...
8
votes
Accepted
Number of cards to be pulled
Here's my solution based on expectations.
First,
The calculation steps are shown below:
Next, let's think about A's strategy.
Then,
In conclusion:
7
votes
Accepted
6 Cards, Top to Bottom
Order
(Am adding explanation)
Step 1
See clue #3
Step 2
See clue #4
Step 3
See clue #2
See clue #6
Step 4
See clue #1
merging steps 3 and 4
since the last card is the king, we get the ...
7
votes
A cooperative guessing game - Guess your order and card
As a starter, there is a strategy to make
specifically
to guess correctly.
The strategy is
By doing that,
Take a note that
The next step is
by calling
Hence,
For bonus question, the above ...
7
votes
A cooperative guessing game - Guess your order and card
- So, the answer is six? - said A. - What are we aiming for now? It's no use trying to increase the six, since, ha-ha, there are only six of us here. And if there were more of us, I suppose, we could ...
7
votes
Accepted
A cooperative guessing game - Guess your order and card
Let's do better. I claim that we can fully win when:
This can be done as follows:
This seems to be tight:
7
votes
Minigolf Solitaire
I found a different answer by writing a python program to brute force find the solution using a depth first search(go as deep as possible until you can't make any more moves and then backtrack). I ...
7
votes
Mind Reading in Three-Handed Pot Limit Omaha
Supercat's answer is correct. Below is a more rigorous proof of its correctness.
An example board is:
On this board, the best possible 2-card holdings, in sorted order, are:
In order for Alice to ...
6
votes
5 people each have 5 equal cards
Looking at this from a statistical standpoint we know that we should never play a card higher than a 3. In all cases an A, 2 or <...
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