3
votes
1answer
41 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
37 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
93 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
18 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
40 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
44 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
28 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
174 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, ...
2
votes
2answers
96 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
64 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
84 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
40 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 ...
1
vote
5answers
143 views

Help: Rules of a Game Which I don't Remember Its Details!

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
46 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
70 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
213 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
58 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
47 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
23 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
0answers
40 views

elemental weakness combinations game theory and probability.

Suppose a game has a setup of elemental strength and weaknesses such as fire beats ice. given a circular elemental wheel A - B - C - D - E - F, such that a beats b, b beats c and so forth to f beats ...
0
votes
1answer
40 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
60 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 ...
0
votes
1answer
92 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
67 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
52 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
74 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
92 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
368 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
101 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
162 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 ...
1
vote
0answers
47 views

Game tie probability

If we have 3 players, playing extreme RPS game like image below: How much tie probabilities? Thanks
3
votes
0answers
85 views

Unexpected hanging paradox maxmin strategies

I have a question about strategies of the players of Unexpected hanging paradox (I am very sorry for a long topic, topic exist already for a while, during this time I try to develop idea how to solve ...
6
votes
1answer
106 views

Find the value of a function with definite integrals

I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals: ...
3
votes
1answer
37 views

Is it necessary to state that $y_i \leq 1$

In a class test for Linear Programming, my professor deducted some marks because I missed the condition $y_i \leq 1$ in the mixed strategy games solution. $ y_i $ stands for the probability of any ...
2
votes
1answer
113 views

What is the general formula for electoral districts tying.

I apologize if this question is a bit of a read. (You might want to get a frosty beverage.) Professor Alan Natapoff of MIT demonstrated, if 9 Voters are districted into 3 electoral districts of 3 ...
6
votes
3answers
327 views

Game theory games with very counter-intuitive results?

I have heard of an interesting game that produces a very counter-intuitive result. It is an auction of a 100 dollar bill, but one in which both the first person in the auction and the second need to ...
0
votes
1answer
249 views

What is the optimal strategy for this game?

You are playing a game where you put in a certain amount of money $m$. A random number in $[0, 1]$ is chosen. If the number is greater than $p$, you now have k% more money, otherwise, you lose all ...
0
votes
1answer
97 views

Deducing probability of an event, when opponent's type is uncertain

Suppose, two players I and II, given a state space of three states$\{a,b,c\}$ with a common prior, $p(a) = p(b) =p(c) =1/3$, are endowed with two partitions of state space, $\mathscr{P}_\text{I} = ...
6
votes
2answers
309 views

What is the Nash Equilibrium of the Monty Hall Problem?

The Monty Hall problem or paradox is famous and well-studied. But what confused me about the description was an unstated assumption. Suppose you're on a game show, and you're given the choice of ...
6
votes
2answers
647 views

game theory - coin flipping game

Lets say 2 players $A$ and $B$ make a bet, who can have more money at the end after playing the following game: a coin is flipped: with 51% probability it lands tails, with 49% probability it lands ...
0
votes
1answer
57 views

Which distributions should be used to model the winning & 2nd bids in second price auctions?

With second price auction which distributions should I use to model the winning bids and 2nd bids (separately)? I'm thinking of using Gaussian. However for the winning bids r.v, it has to satisfy: $$ ...
7
votes
1answer
186 views

Why is the best position for LCR not the last person?

For the uninitiated, LCR is a game in which each player starts with three "tokens" and rolls up to three dice (at most as many as tokens they have). Each die has three sides which indicate that ...
1
vote
0answers
105 views

Card game-ordering a deck [duplicate]

Possible Duplicate: Game Theory Matching a Deck of Cards Suppose we take a blank deck of $52$ cards, write the number $1$ on the first card, $2$ on the second card, and so on until we write ...
1
vote
0answers
167 views

On a zero-sum game betting market

I'm trying to come up with the rules for a betting game. My problem is to figure out under what constraints that game has zero-sum game properties: in other words, I want to make sure that no money is ...
3
votes
1answer
272 views

Game Theory Matching a Deck of Cards

Moderator Note: This question is from a contest which ended 1 Dec 2012. Suppose we have a deck of cards labeled from $1$ to $52$. Let them be shuffled in a random configuration, then made ...
2
votes
1answer
118 views

Nash equilibria in games with infinitely many strategies

As a simple example, suppose two players A and B play a game wherein each picks a positive integer, and if they both pick the same integer $N$ then B pays $f(N)$ dollars to A, for some given payoff ...
0
votes
1answer
71 views

How do we prove that e = RPC, in game theory?

Here e is the expected value of the game for the row player, P is the payoff matrix from the perspective of the row player, R is the row matrix containing the probabilities for each of the row ...
8
votes
3answers
133 views

Seemingly similar but different probability games

Burger King is currently running its "family food" game in which each piece can be modeled as a scratch off game where exactly one of three slots is a winner and you may only scratch one slot as your ...
10
votes
2answers
245 views

Strategy for a game of breaking sticks

Two persons have 2 uniform sticks with equal length which can be cut at any point. Each person will cut the stick into $n$ parts ($n$ is an odd number). And each person's $n$ parts will be permuted ...
6
votes
2answers
672 views

Simple dice game: Optimal strategy?

Here's the description of a dice game which puzzles me since quite some time (the game comes from a book which offered a quite unsatisfactory solution — but then, its focus was on programming, so this ...