# Questions tagged [probability]

Questions about probabilistic game mechanics and how to calculate and estimate random events, as well as how probability affects games and gameplay.

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### Does a maximally clumped deck or a mana woven deck require require more shuffling to sufficiently randomize?

I've been under the impression that a mana woven deck (i.e., nonland nonland land nonland nonland land...) reaches a state of randomization after fewer riffle shuffles than the same deck with all ...
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### Hypothetically, if Exodia was unlimited (3 copies), what is the probability curve of summoning?

As many of us know, in the game Yu-gi-Oh! summoning all five pieces of Exodia results in an instant win. Currently, the five pieces of Exodia have a "Limited" status which means only one ...
1 vote
281 views

### Are engraved dice unbalanced or biased?

On a regular six sided die (d6) the face with six pips has more material removed than the face with one pip during the engraving process. Does this worsen the distribution of outcomes (make the die ...
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1 vote
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### How can I acquire dice which are as close to perfectly fair and unbiased?

I intend to get a bit closer to my goal of finding a perfectly fair die. What I mean by that is a die that has as little as possible imperfections that might cause it to favor any particular side, or ...
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### How do I calculate the odds of any one of several card combinations?

Note: I know what a multivariate hypergeometric calculator is. Game: Yugioh The deck size/ population is 44 cards. The hand size is 5. For both of these, I'd like to also calculate the odds for ...
1 vote
290 views

### Probability of drawing perfect starting hand

I have a Magic the Gathering deck where an ideal starting hand can potentially let me win on turn 3. What is the probability of drawing an ideal hand? How is this computed, and what is a general ...
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### How do I calculate Mulligan probability?

I am playing a game of Commander and I have a deck of 99 cards. In this deck are 37 lands. Using a hypergeometric calculator it returned a 29.12% chance of drawing exactly 3 Lands on a 7 card draw ...
670 views

### What is the optimal way to roll for a two pair in Yahtzee?

Let’s say I’m playing Yahtzee and my aim is to get any two pair, the actual numbers don’t matter. As usual, I can save any dice I want and re-roll the rest. Let’s say that my hand contains the ...
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### What are the odds of beating this obscure solitaire game?

I have a question about a weird, unknown (and possibly impossible) game a friend of mine has taught me. It is a solitaire game that's played with a regular deck of 52 cards but it is suspiciously ...
504 views

### What is the optimal strategy for deciding dice to reroll when trying to reach a target value?

Let's say that I have N dice (standard d6) and I'm trying to reach a value of x or higher. I roll all of the dice once and I don't get my target value. I can do one reroll and can freely choose ...
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### Mahjong Probability Graph Question [closed]

Picture from pierebean's post in In Mahjong , what is the chance to get a hand that allows a player to finish on their first turn? I was wondering what the graph on the right meant? How does the ...
1 vote
725 views

### How likely is Yusri to get me an omniscience effect, if I have Krark's Thumb out?

The new card Yusri, Fortune's Flame has the clause, that if you win 5 flips off it's attack trigger ability, you can cast any card in your hand, for free!. Whenever Yusri, Fortune’s Flame attacks,...
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### Mahjong board formation and drawing rules

In Mahjong basic rule (this one for example), the board is setup in a spiral formation and the tiles are drawn in order from the 4 draw piles. With all the tiles facing down and shuffled, the ...
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1 vote
159 views

### Probability of i event_A and j event_B on n dice

I am trying to figure out probability for a game using 6-sided dice. The basic idea is that the player rolls n dice and gets a success for each 6 rolled. So far, so simple; I'm using Python's scipy....
1 vote
761 views

### Odds of this happening in euchre

Last night in euchre, 4 times in a row around the table we all turned up the Jack of spades. All good shufflers and we had 2 splits and 2 no splits. I know there are many variances in determining the ...
754 views

### Is there a method that gets beneficial diminishing returns when adding more dice, yet stays random?

Short Story: I want to find a dice system where multiple dice are rolled and compared at once, but rolling more dice is only slightly more effective than rolling fewer dice, while still being fairly ...
609 views

### In Gin-Rummy, what are the chances to make Gin on the first turn?

What are the odds for a Gin on the first turn? That is, what are the odds for arranging 10 out of 11 random cards in melds. In Gin-Rummy, at the start of a round, players draw 10 random cards. On the ...
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1 vote
148 views

### How to generate numbers from a Pareto distribution? [closed]

I need to generate numbers from a Pareto distribution (https://en.wikipedia.org/wiki/Pareto_distribution) for a game I'm making. Ideally with xm=10, and alpha = 2, but approximately is good enough. Is ...
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### What are the odds in Scrabble of not being able to make a legal move on opening turn

I've been playing the game for 50 years and this happened to me recently: I had the following rack PBQZJDH And so I could not play a legal move. I've been trying to work out the odds of this (no ...
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### What's the expected damage from playing Terror of the Peaks, when I have Mirror March out?

If I play Terror of the Peaks while I control Mirror March, what is the expected damage? That is the average of winning 1, 2, 3, ... 'Infinity' flips? I'm sure it's a converging sum, but I'm not sure ...
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516 views

### Probability of drawing duplicates of a card in magic [duplicate]

Was trying to figure this out, and realized I don't know the exact math: In the card game magic you have a deck of 60 cards. You can have 4 copies of any individual card, and you are dealt a starting ...
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### Probability of being dealt a 7-card flush in Rummy

Playing 7-card rummy with 4 players, I was dealt a 7 card Spade flush (not straight) and on the first card picked from the deck pulled an 8th card spade and immediately won (it was 23456 8910). What ...
1 vote
327 views

### Can a Pit Card Game be Won if two players refuse to trade with another particular player?

My sister and I had an argument after I stated that I did not want to play Pit with them anymore because her husband and her son for some unknown reason refused to trade with me. Since she is always ...
1 vote
611 views

### How likely am I to have a key card in my starting hand in Brawl?

I'm playing the Brawl format (a 60-card singleton format), and I really want one specific card in my starting hand. I'm willing to take two mulligans (leaving me with a starting hand of 5 cards after ...
195 views

### In Spades, what is the probability a suit is distributed in a way, given I hold n cards from that suit?

In Spades, (or any other trick taking game), when I hold n cards of a certain suit, what is the distribution of the other 13-n cards in that suit? In particular, what is the probability that ♦'s are ...
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### Is the Hand pattern probabilities equal to suit pattern probabilities?

In Spades, I wish to know the probability a certain suit is distributed in a particular way. For example I wish to know what is the probability that the diamonds are distributed either 4-4-4-1 or 5-4-...
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### In Pinochle, what is the probability of a thousand aces and a double run in one hand?

What are the odds of getting a hand containing: A♣ A♦ A♥ A♠ A♣ A♦ A♥ A♠ Tx Kx Qx Jx Tx Kx Qx Jx for some suit x, and another four unspecified cards. Rules Background Double-deck Pinochle is a four ...
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### What is the value by percentage of Lindel's reroll special ability?

Here is an image of Lindel's card. After rolling dice ofr an attribute test, you may reroll one die; you must accept the second resul As you can see his stats are 6, 6, 6, 5. He needs to roll ...
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### If I really need a card on my start hand, how many mulligans make sense? [duplicate]

There is a funny modern deck where you play Treasure Hunt, but you really need to have it on the starting hand. How many mulligans should I take, if my deck contains 60 cards and contains 4 copies of ...
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1 vote
879 views

### How do you calculate the likelihood of getting at least one combo after drawing so many cards in a deck with more than one combo?

With a game like Magic the Gathering, I can use a hypergeometric calculator to determine the probability of getting a specific card after so many draws. What I would like to know is how you determine ...
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### How do you calculate hand probabilities for 10 cards per hand (8 suits); e.g.: Cripple Mr Onion?

Cripple Mr Onion is a card game that involves 8 suits (104 cards in toto), with 2-7 players being dealt 10 cards each (without replacement). I've tried several different websites for hypergeometric ...
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### How do I determine a character's probability to escape from combat in DungeonQuest (third edition)?

I have 4 cards with the following numbers on them: 1, 2, 3, 4. My opponent has 4 cards with the following numbers on them: 2, 3, 4, 6. We both randomly draw a card from our decks, if my number is ...
175 views

### Skat tool to determine the probability for a win [closed]

Does anyone know a skat tool with the following feature ? You can enter the three hands and the contract of the solo-player (grand,spades,hearts,diamonds,clubs,null). The program determines the ...
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### Token Drawing [All At Once (per player) vs Round Robin] -- Mathematician / Statistician needed for a question

In Paris Connection (PC), you go player by player drawing a starting number of trains, with each player drawing their entire complement all at once. One of our players conjectured this draw method is '...
2k views

### How do the Monopoly odds change when the board is played in reverse?

One semi-popular house rule is to play Monopoly as usual, but move the pieces counter-clockwise instead of the usual clockwise - that is, hit the higher-end properties first and move down toward the ...
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### Calculate Mind Funeral efficiency

I was wondering about the formula on how to calculate the average number of cards milled by Mind Funeral. Target opponent reveals cards from the top of his or her library until four land cards ...
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### Magic The Gathering: probability of casting a 3 drop on turn 3

So, I have a probability related question. In MTG, which is the probability of landing a 3-drop on turn 3, but using the correct combination. For example, I want to cast a Geist of Saint Traft on turn ...
2k views

### Fairness of Cowry Shells as Dice

I just learned about the use of cowry shells as binary dice and find the idea enchanting. However, I'm concerned about the apparent "fairness" of the dice. Obviously, because there are multiple ...
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### What is the average number of turns in a game of Monopoly?

I can't find any research or public information on this topic. Edit: It was requested that I clarify the specifics of my request (e.g. the number of players and rule specifics). Rather than pigeon-...
173 views

### What are my odds of drawing the rest of my deck

Do to the deterministic nature of the game, if I have a decent memory I can easily know what cards are left in my deck, if not their order. I have two cards in my hand that let me draw a card (1 each) ...
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1 vote
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### What is the probability that a player is dealt 3 kings in a single euchre hand?

In the game of euchre, the deck consists of the nine, ten, jack, queen, king and ace of each suit. Players are dealt a five card hand. What is the probability that a player is dealt 3 kings in that ...
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### Calculating the probability of NOT drawing a traitor card in Dead of Winter

If you're playing a 3 player game and hand out 1 card to each player, out of a deck of 3 ally and 1 traitor cards, how likely are the players all allies? I think the math is you have a (3/4)^3 or ...
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### What are the probabilities of getting any or all five cards of Exodia using a specified monster card effect

In Yu-Gi-Oh!, there exists a monster effect card called Morphing Jar, which has the following effect: FLIP: Both players discard their entire hands, then draw 5 cards. There are more (magic/trap/...
11k views

### How to calculate the probability to get all cards of Exodia, the Forbidden One by drawing them from my Deck during the Draw phase?

In Yu-Gi-Oh!, there are some cards that allow to the duelist to win a duel automatically. In this case, I'm focusing my question on Exodia, The Forbidden One. To win a duel using Exodia, you must ...
319 views

### name and rules of a numerical card game

I am looking for some information about a pokerlike game where 2 cards with numbers from 1 to 60 are dealt to each player and and bets are related to number representing an average number from of all ...
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### French Tarot (card game): Feasibility of playing a King on the first hand

I had a little debate with some friends about the feasibility of a certain type of play and wanted to get the communities opinion. The question is whether playing a King(Regent) on the first hand is ...
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### Calculating the probability of a combo hand [duplicate]

Before I ask the question, I should mention I already saw this and just don't get it. I have a 40 card deck with cards I'll label: A (3 copies) B (3 copies) C (3 copies) D (2 copies) E (1 copy) F (2 ...
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### Probabilities: Backgammon - final move

So I was playing a lot of backgammon lately, and I noticed something. It seemed like I was "going out" on doubles more often than not. And my initial reaction was "Shouldn't that be, at best, a 1 in 6 ...
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### Why is 'equity' much more commonly used than 'winning probability'? What is the mathematical formula that links 'equity" and 'winning probability'?

In backgammon, people always speak about 'equity', but never about 'winning probability'. To me, 'winning probability' seems much more simple and much more intuitive than 'equity'. So why is 'equity' ...
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