Questions tagged [games]

Use this tag for sports and games like video games, poker, chess, go, and others similar. Do not use it for puzzles or enigma questions (see puzzle tag).

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Does adding Jokers into a normal 52 deck only add to the total # of possible hands, or does it also impact the existing hands' binomial coefficients?

The Jokers added to the deck in this case would be useless/junk cards, not wilds¹. My intuition is that there would be no impact to how we'd normally calculate the possible combinations/frequency for ...
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2 votes
1 answer
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Testing how well a sequence of observed word game solutions corresponds to expected word frequencies

Say we have a word game where each round involves finding a unique 5-letter word solution. (Wordle would be an example, for those familiar). For example, we may have a round where the word "magic&...
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What are the statistical fallacies of illusion of control?

Illusion of control* appears in gambling and events involving randomness. For example, choosing a lottery ticket which has an additional information that participant has a control of choosing, such as ...
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Can you do hypothesis testing when instead of a 'sample' size you have 'actual' size? Alternatively, how would you use statistics to compare means?

From chess se: What is white's increased advantage in chess90 as compared to chess870? (Chess960 can be split into 2 subsets, chess90 and chess870) Intro: It is known in standard chess that white has ...
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Why are rating distributions 'smoother' when there are more players?

Consider the following rating distributions by variant/time control on lichess. The bullet, blitz and rapid rating distributions look very, well, 'smooth' (or holomorphic/analytic or harmonic or ...
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How to model risk with Neural Networks (is there a better approach)?

What should be our target if we have our features and our return is variable. Suppose we have: ...
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1 answer
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Confused about geometric distribution [duplicate]

So I have a game that follows a geometric distribution. There is a probability, $p$, of winning a round. If the player wins, he earns \$1,000. As soon as there is a win, the game ends. If the player ...
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Computing score for chess moves based on statistics

There are statistics available for the chess moves that can be played for various opening positions. These stats include the number of games played as well as the number of each of the outcomes (white/...
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1 answer
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Three Envelopes Problem

In a game we have 3 envelopes, A, B, C, with a random number (from 1 to 100) sealed inside each. Nobody knows what number is inside. We win the game if we find the highest number, using only one of 2 ...
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3 votes
1 answer
82 views

D&D - Confidence Interval for enemy armor class

In dungeons and dragons, characters and monsters have two properties called Attack Bonus($AB \, \in \, \mathbb{Z}$) and Armor Class($AC \, \in \, \mathbb{N}$). Let $AB_c$ be the character attack bonus ...
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Calculating expected-value of an algorithm, not sure how to describe the distribution

For fun I was looking at the details of some stupid online betting game. To be provably fair they make a system where the bet outcome is a function of some hashes you can calculate yourself. They ...
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24 votes
3 answers
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Probability of defeating a dragon in one turn rolling a 20 sided die

In math class we were asked an optional problem I can't solve on my own: You are fighting a dragon with 250 hit points and are rolling a 20 sided die to deal damage. The dragon takes damage equal to ...
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What subjects in statistics should I focus on to determine the optimal time to to quit a game of chance while I'm ahead?

I am trying to answer the question: Given a game of chance with a "house edge" E (defined below), what is the maximum "amount ahead" ...
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2 votes
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Predicting outcomes of chess games based on engine evaluation of current position

I wish to train a classifier for chess games. For any given chess position, you can use one or more chess engines to give the position a numeric score (evaluation). A score less than 0 indicates that ...
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32 votes
3 answers
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How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?

Let's say we have a game with two players. Both of them know that five samples are drawn from some distribution (not normal). None of them know the parameters of the distribution used to generate the ...
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Head to Head Poker /w Special Rules

Is there a profitable strategy for this poker variant? If so, what is the most profitable strategy? Expressed as a percentage of your "special ante", how much would your strategy win on ...
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Expected Value of a Fundraiser Raffle Ticket with Three Prizes

The raffle ticket above represents a local fundraiser. The first prize is a smart TV valued at 1200 dollars, the second prize is a cooler valued at 200 dollars, and the third prize is a 100 dollar ...
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5 votes
1 answer
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Does Sampling with or without Replacement Have the Advantage?

You're playing a game where one person chooses coins and the other chooses cards. One flips a coin at the same time the other draws a card. The game stops once either the coins-player has got 4 in a ...
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4 votes
1 answer
154 views

Probability of winning a game for toddlers

Recently, my son got a game called Little Cooperation. The rules (see here) are very simple: We have 4 animals that need to travel from an ice flow to a safe igloo. Between a flow and an igloo there ...
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1 vote
0 answers
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Uses of MCMC samplers outside of Bayesian Inference? [duplicate]

I'm curious if there are applications of MCMC outside of Bayesian Inference? this conversation started when discussing Monte Carlo methods vs Markov Chain Monte Carlo methods with a coworker. He asked ...
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Analyzing lie in a cardgame

We are playing a card game in which cards can be of three categories — good, bad, neutral. A player draws a variable number of cards $n$ and then states the composition of his cards. The player does ...
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3 votes
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How can I include head-to-head data in a Regression? [closed]

I'd like to model Tennis results in a logit regression. How can I include head-to-head data? Simply taking the share of won matches between two players isn't ideal, because it doesn't take the number ...
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2 votes
0 answers
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Distribution of players in a computer game on different "levels"

Many computer games have different levels. Here is a description about levels on wikipedia, but I will explain more precisely what I mean below. The idea is this: to optimize the experience with a ...
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How to decide what is a "good move" or a "bad move" with supervised learning on a game?

Let's take an example game, like connect $4$, which is nice and simple. I know minimax is a super easy algorithm to program here, but let's say instead I wanted to create a Machine Learning model for ...
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1 vote
1 answer
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Finding a good extrapolation methodology for Clash Royale

I have assembled a database of Clash Royale games in an attempt to understand the outcomes of various match-ups. The game is composed of an 8 card deck drawn from 102 cards. As you can see from the ...
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Is there a method that seeks synergies among sports players?

I am going to gather data on the performance of individual lineups in NBA matches. I wanted the data to include the average statistics of the players depending on who was with him on the pitch and the ...
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0 votes
1 answer
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Chances of winning your money back on a double or nothing machine?

A double or nothing machine is where you place in one token, and on your next turn you either double your token or lose it with a probability of p, you can then repeat this until your final bet is 64 ...
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1 vote
1 answer
70 views

Probability of winning multi participant events

I will just start off with context about myself. I am currently studying further mathematics at A-Level and have a keen passion in statistics. I am sure most don't care about that, but just so you ...
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1 vote
1 answer
130 views

Significance of walks vs. strikeouts in FIP calculation

According to Wikipedia, the baseball FIP statistic is calculated using: $$ \frac{13HR + 3BB - 2SO}{IP} + C $$ Why should walks be more significant than strikeouts? If the equation were to include hits,...
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1 vote
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What happens to American odds when the point spread gets further from zero? [closed]

I am learning about American odds (moneyline odds) and point spreads. In Chapter 2 of Sports Betting for Dummies, I see: When the point spread on a game gets further from zero, the two moneyline bets ...
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1 vote
1 answer
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Statistical test for determining advantage from win ratio in a 4 player game

I have data from 1000 games, all performed on a group of 4 players (the group and the players are constant). For each game, I have 5 possible results -> player A wins, player B wins, player C wins, ...
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9 votes
1 answer
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Does machine learning on random situations require a cryptographically-secure random number generator?

I'm working on a project involving using machine learning to figure out optimal strategies to play board games, and after a few rolls of the virtual dice a thought hit me: For the games that involve ...
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9 votes
6 answers
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What are the chances rolling 6, 6-sided dice that there will be a 6?

More generally, what is the probability that n n-sided dice will turn up at least one side with the highest number ("n")? My crude thinking is that each side has 1/6 probability, so that 6 ...
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4 votes
1 answer
792 views

In Texas Holdem, what at the odds of 3 aces on the flop, then the 4th ace drawn on the first river card? [closed]

I played Texas Holdem with some friends last night. On one hand, the dealer burned a card, drew 3 aces on the flop, then burned a card and drew the 4th ace on the first river card. My question is, ...
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3 votes
2 answers
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De Finetti's Coherence Principle and Frequentist interpretation

So, without proof or citation, I often see that the Coherence Principle by de Finetti does not hold with Frequentist statistics. It is pretty easy to create examples of this fact. The exception ...
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2 votes
0 answers
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Proving Randomness in a Card Game

I recently came across a card game that is played as follows. For simplicity, assume that there are 4 players. The deck of 52 cards is split evenly between them, leaving each player with 13 cards. ...
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1 vote
1 answer
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Test to prove Poker deals are not random

I played on a mobile app of Texas holdem poker called pokerrrr 2. I suspect the game deals non-random hands. How can I prove the deals are not random? I prefer a test that can get an answer using ...
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Clustering Algorithm for data where each type has multiple observations?

I am trying to segment football teams based on their playing style using multiple features. I want to see which football teams have similar playing styles using cluster algorithms. For each team I ...
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1 vote
1 answer
182 views

Does the Elo K-factor affect winning probabilities?

Per the Wikipedia article on Elo ratings: The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each ...
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1 vote
0 answers
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How do you define the portion of a game's result that is accounted for by chance?

I'm not sure if there's an established way of defining the concept I'm describing, but every game that can be played involving a random component — dice, coins, or otherwise — has a certain amount of ...
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1 vote
1 answer
39 views

How do I derive the generala formula? Does anyone know a way of thinking ot apply this to other problems? [closed]

The textbook said that it would be easy to derive the general formula. Is there a certain way of thinking that I am not seeing? I understand that the equation is doing (whole - piece) / whole. The ...
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1 vote
1 answer
122 views

Poker hand: probability of a straight or a straight flush

I have seen this and this, but my setup is a little different so I'm not sure how to proceed. Setup: We are using a single standard deck of 52 cards. Suppose I have been dealt two cards, and one of ...
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4 votes
2 answers
78 views

How to find the probability of winning this game?

Here's a very simple "game": Standard 52 card deck, shuffled. You deal cards face up, one at a time, while counting up towards 13, starting back at 1 once you reach 13. If the number you count out is ...
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2 votes
0 answers
23 views

Leveling the field for a race competition

I'm not sure if this is really a statistics question, but I can't think of a more fitting Stack Exchange for it. My friends and I at work are having a competition to see who can decrease their one-...
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4 votes
2 answers
592 views

What should be statistically significant game score in football and basketball to say that one team stronger?

4 teams play 2 games: football and basketball. (2 games just to better understand theory) Final result of a football game is 2:1 Final result of basketball game is 101:96 What should be the result ...
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1 vote
1 answer
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Multi stage neural net

I'm going to use my specific use case here, but I'm curious about this AI structure in general. I want to create an AI to play Rocket League (a video game). For context, in Rocket League you control ...
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2 votes
2 answers
113 views

Paradox game for life and death

This is probably not new to any student of statistics - yet I can't find the name of that "paradox" to search for. Imagine the richest person on earth holds a game: A participant is invited to roll ...
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1 vote
2 answers
55 views

Useful measure to quantify how competitive a sports match is

I'm trying to put together a summary of data from a recreational sports league's most recent season. There are significant disparities in skill level between teams, so a large portion of the games ...
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14 votes
3 answers
386 views

Where is the bomb: How to estimate the probability, given row and column totals?

This question is inspired by a mini-game from Pokemon Soulsilver: Imagine there are 15 bombs hidden on this 5x6 area (EDIT: maximum 1 bomb/cell): Now, how would you estimate the probability to find ...
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How to model game theory of poker-like card game

I'd like to get a general understanding of the optimal strategy from a game called Team Fight Tactics. To reduce this problem into a simpler form I'd like to analyze a simpler card game problem I've ...
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