# Tagged Questions

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### Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
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### Probability that 20 sided die beats 12 sided die with reroll

Alice rolls a 12 sided die (the faces labeled 1 through 12) and Bob rolls a 20 sided die (the faces labeled 1 through 20). After seeing their roll (but not the other person's roll), each person can ...
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### Guess the smallest number

Three people play a game where each of them writes down a positive integer at the same time. The one who writes a unique and smallest number wins one dollar from every other person. This means if two ...
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### Game theory: Bidding strategy during an auction in a card game

I'm trying to create a mathematical model for the auction process in a card game called Pitch. The specific question I'm interested in solving is: Let $p_i$ represent the probability of a specific ...
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### How to Find Symmetric Equilibrium Bidding Strategy in Mixed Auction?

N-bidders take part in a mixed auction (mix of first- and second-price auctions). The highest bidder (bidder 'i') wins and pays a*b_i + (1-a)*(max b_j) ('i' is not equal to 'j'), where 'a' is fixed ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
### 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 ...