1
vote
2answers
93 views

What is the probability of going bankrupt in roulette?

Imagine that the bank has the money $M_1$ and the player has the money $M_2$. The rules are the following: You win with a chance of $\frac{17}{36}$ and lose with $\frac{19}{36}$ each round. Now you ...
0
votes
1answer
30 views

Board Game Markov Process - Transient Probabilities

I need to write an essay on the Game of Life board game, and so I studied up on Markov Chains to help me calculate the probabilities and average payoffs for the spaces; however I'm not sure whether ...
11
votes
5answers
405 views

The Price is Right optimal play

The following situation happened on the Price is Right and I was curious about the optimal response. The rules are: A contestant rolls a wheel with 5 cent increments from 5 - 100 (20 numbers total). A ...
0
votes
1answer
42 views

Prove that a Modified Cantor Distribution is Atomic.

Consider a measurable space $\{\mathcal{I},\mathcal{B}\}$, where $\mathcal{I} = [0,1]$ and $\mathcal{B}$ are the Borel sets on $\mathcal{I}$. And also, denote $\mathcal{C}$ as the cantor set on ...
9
votes
1answer
131 views

Can we qualitatively predict the strategy of the German and US teams in today's World Cup soccer match?

In today's World Cup soccer match between Germany and the US, both teams only need a draw to advance to the next round. There's been speculation about possible collusion, especially given the friendly ...
1
vote
1answer
52 views

How to calculate the expected utility for $3$ player game?

I do not understand how to calculate the expected utility of $3$ or more players game. For a $2$ player game, it is easy. Suppose I have two action $\{A, B\}$ and my opponent has two action $\{C, ...
0
votes
1answer
27 views

Maximum payoff for safe bet

I'm having a hard time choosing a good strategy for this problem: assume that you have $m$ money that you can bet on $n$ mutually exclusive outcomes, all with unknown probabilities, and that each ...
2
votes
4answers
82 views

How does one explain basic probability theory to a layman?

I have recently been involved in a number of discussions with people with little or no background in mathematics when we considered a problem of the following shape. A random event is going to ...
52
votes
3answers
5k views

Mathematical research of Pokémon

In competitive Pokémon-play, two players pick a team of six Pokémon out of the 718 available. These are picked independently, that is, player $A$ is unaware of player $B$'s choice of Pokémon. Some ...
1
vote
0answers
36 views

What is the optimal strategy?

There are $m+n+1$ cards numbered $1,2,\ldots m+n+1$. Participants A and B respectively get $m$ and $n$ cards. Meanwhile, they only know what they get. The remaining card is face down on the desk. ...
0
votes
0answers
59 views

Application of Markov Chain to Game of Life Board Game

I need to calculate the expected outcomes for the Game of Life. I believe that if I multiply the probability of landing on a particular square with the payoff of said square and add up all these ...
0
votes
5answers
120 views

game theoretic die rolls

Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever ...
3
votes
2answers
60 views

Alice and Bob card game

I came across this puzzle online in an online Princeton thingy (course?): Alice writes down two integers between 0 and 100 on two cards. Bob gets to select one of the two cards and see its value. ...
1
vote
1answer
41 views

need help with zero sum game

Tom chooses an integer in {1,2,3} and Bob chooses an integer in {2,3,4}. If the chosen numbers are the same, no money changes hands If the numbers are different the person who picks the bigger number ...
1
vote
1answer
91 views

Optimal strategy for dominoes game

Here is the basic principle of the game I'm trying to find an optimal strategy for: Two players (say P and Q) are given a 2x3 grid and a domino. Then P chooses one way of positioning the domino on ...
2
votes
0answers
120 views

What is the optimal strategy for this 2 player game?

Let some finite array of integers is given initially. There is a number k which is initially '0'. In a move, a player will select a number from the array arr[i] and change k to gcd(k,arr[i]). Also, ...
0
votes
2answers
380 views

Game of cards and GCD

Alice and Bob play the game. The rules are as follows: Initially, there are n cards on the table, each card has a positive integer written on it. At the beginning Alice writes down the number 0 on ...
2
votes
1answer
44 views

Spinner game outcomes: What has the best chance of winning with your last two coins?

We are discussing probability and odds in my elementary math class. The students came up with two scenarios. They are as follows... In a spinner wheel game based on the days of the week, students bet ...
4
votes
2answers
297 views

The Last Man Standing

This is my second question following this post. Three players are playing a game. They all have small amounts of money, let say: player 1 has $\$a$, player 2 has $\$b$, and player 3 has $\$c$, ...
1
vote
0answers
32 views

Game theory:Baye's rule for tournament

I'm having challenge with the following computations from the book I'm using. How are the steps obtain from the preceding step? In the expressions below, $E_i$ and $E_j$ are independent, random ...
2
votes
1answer
94 views

Unbalanced game: probability of winning over an infinite number of possible match sequences

We have 2 players, A and B, competing. The probability that A wins a match is p, making the probability that B wins a match (1-p) = q. The game is won by player A as soon as he gets one more win than ...
3
votes
1answer
73 views

Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
1
vote
2answers
39 views

Committee Voting Choice

Let's say you're in a group of 20 people, and each person has 3 votes for different people. They're all voting for a 5 member committee, and the 5 people who get the most votes win. Ties are resolved ...
0
votes
1answer
268 views

What is the probability of a $4$ appearing in the game $2048$? [closed]

I'm not sure if this is the appropriate SE, so please suggest a more appropriate website if not. I'm making a facsimile of $2048$, and I've just one question I've been unable to work out: what is the ...
0
votes
1answer
19 views

A game of lines and points

Consider the following scenario: $\mathcal{A}$ and $\mathcal{B}$ play a game inside the unit disc $\mathcal{D}: $ $\mathcal{A}$ chooses a point $p_0\in \mathcal{D}$. At step $n, ...
1
vote
0answers
47 views

Dilemma at the dining table

I created this problem while I was having my supper a few days back. So there maybe flaw in the formulation. Please point them out as you see one. Suppose, there is a circular dining table with ...
1
vote
2answers
48 views

Existence of a winning strategy against the probability of winning

Edit: I've made the question clearer. Suppose a game is played between $A$ and $B$, in which there exists a winning strategy for $A$. Suppose $A$ and $B$ play their moves at random, do we have ...
0
votes
1answer
32 views

What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
3
votes
1answer
217 views

Game Theory/Bayesian approach to a bluffing game

Two players play the following card game with a deck consisting of (A,2,3,4,5). A dollar is placed in the pot by some third party, and player 1 is dealt a card. If it is an A, he has a winning card, ...
3
votes
2answers
115 views

Finding optimal thresholds for “guess if number is highest” game

Consider the following game: five numbers are chosen randomly in the interval [0..1] with uniform distribution. The player is shown each number in turn and asked if it is the highest. The game ...
1
vote
1answer
72 views

Card game: How much will you pay to gamble?

You turn over the cards 2 at a time, if they are both red, you keep the cards, if they are both black I keep the cards. If one is red and the other is black then neither you nor I get a card. If you ...
4
votes
1answer
90 views

What is a good strategy for this dice game? [duplicate]

I learned the following dice game from another forum. It was not solved there. The dice game is as follows. You start tossing six dice. After each toss you must put aside at least one of the dice ...
0
votes
0answers
43 views

Waiting Time For Computer Cluster

There are $n$ computers. Computer users stay on their computers for a certain amount of time, $t$, throughout the day. Computer users come and go. How long will I have to wait, min/max, for a computer ...
7
votes
5answers
5k views

Help: rules of a game whose details I don't remember!

In a probability course, a game was introduced which a logical approach won't yield a strategy for winning, but a probabilistic one will. My problem is that I don't remember the details (the rules of ...
2
votes
2answers
62 views

Expected value and optimal strategy for red/blue game

Firstly please excuse my ignorance if I'm posting this to the wrong exchange site. If this doesn't belong here let me know and I'll move it. Now as for my question, today during a short course that I ...
1
vote
1answer
98 views

Card game question with conditional probability

If I have a standard deck of 52 cards with ace being 1 and jack being 11, queen 12, and king 13. I know the expected value of any card I draw to be 7. However, how does this change with each ...
4
votes
1answer
394 views

Deal or No Deal: Monty Hall?

This question was inspired by another question posted today: Monty Hall Problem Extended. So I thought that the comments an answers brought up a great point about increasing the doors to 100 or ...
1
vote
1answer
59 views

Finding social cost in game theory paper

From theorem 3 in http://cgi.di.uoa.gr/~elias/publications/paper-kp09.pdf Let $w_1$,$w_2$ = 1. I have interpreted the above paper as saying that the social cost is the same thing as the expected cost ...
2
votes
0answers
50 views

Optimally Efficient Tournament Strategies

Consider a fair symmetric game between two players that always results in exactly one of the players winning, i.e. there are no ties. When two players $P$ and $Q$ play each other, $P$ wins with a ...
1
vote
0answers
24 views

Playing Connect 6?

Say I'm playing Connect 6, a variation of Connect 4, and I get to go first. For a $n \times n$ board, which position should I place my chip on to maximize my odds of winning? Note than unlike Connect ...
0
votes
1answer
42 views

probabilistic behaviour

I am trying to understand what 'probabilistic behaviour' in a 'deterministic model' means. I am reading this paper http://www.ulb.ac.be/sciences/use/publications/JLD/16.pdf but i find myself unable ...
0
votes
1answer
65 views

Finding Mixed Strategy Nash Equilibria

Okay, so I was working through this problem: Now, I understand the computations. What I don't understand is why the solution says that each player will play H with probability p=2/3. I would have ...
1
vote
1answer
99 views

A game theory question about tiles, part 2

A recent question asked about the following game: There are six tiles, face down. Three are type A and three are type B. Each player turns over three tiles, and wins if they match. Otherwise, they ...
0
votes
1answer
75 views

A game theory question about tiles

So if there are two players playing a tile game where there are two sets of matching tiles $a_1, a_2, a_3$ and $b_1, b_2, b_3$, what would the optimal strategy be to maximize winning probability? Go ...
0
votes
0answers
57 views

Optimizing a population to maximize probability of achieving certain samples.

Preface: I'm reasonably comfortable with mathematics on the whole, but I don't know too terribly much about probability theory, or optimization. I play Magic: The Gathering, and am trying to apply a ...
2
votes
1answer
76 views

Game Probability Problem

Consider a game played by two people $X_1$ and $X_2$. Against the general population, $X_1$ wins with probability $0.51$ and $X_2$ wins with probability $0.49$. We have no knowledge of the ...
0
votes
3answers
95 views

solutions poker texas hold'em

Is there any equation that characterizes the poker game in terms of variables such as the strength of the hand, the amount of betting money in the pot, etc? Is there any solution that says what the ...
17
votes
4answers
374 views

Salvaging a damaged cable

Let's say we have a cable of unit length, which is damaged at one unknown point, the location of which is uniformly distributed. You are allowed to cut the cable at any point, and after a cut, you'd ...
2
votes
1answer
106 views

Up to how much would one pay to play this game? 30 red and 30 blue marbles

There are 30 red marbles and 30 blue marbles. Your opponent may arrange these marbles in any way he/she chooses into 2 urns. You then pick one of these 2 urns. You get 10 dollars if you draw red and 0 ...
4
votes
2answers
192 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...