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.
70
questions
2
votes
2
answers
313
views
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 ...
- 654
2
votes
0
answers
159
views
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 ...
- 21
1
vote
1
answer
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 ...
- 113
1
vote
2
answers
284
views
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 ...
- 9,146
0
votes
1
answer
144
views
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
3
answers
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 ...
- 282
2
votes
2
answers
824
views
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 ...
- 21
3
votes
1
answer
671
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 ...
- 133
9
votes
1
answer
1k
views
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 ...
3
votes
2
answers
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 ...
- 131
2
votes
0
answers
103
views
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 ...
- 21
1
vote
2
answers
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,...
- 3,439
2
votes
2
answers
252
views
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 ...
- 123
1
vote
2
answers
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....
- 113
1
vote
2
answers
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 ...
10
votes
8
answers
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 ...
- 418
0
votes
1
answer
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 ...
- 4,105
1
vote
1
answer
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 ...
- 223
15
votes
4
answers
1k
views
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 ...
- 151
3
votes
1
answer
425
views
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 ...
- 3,439
2
votes
1
answer
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 ...
- 23
4
votes
3
answers
1k
views
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 ...
- 41
1
vote
3
answers
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 ...
- 11
1
vote
2
answers
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 ...
- 13
5
votes
1
answer
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 ...
- 4,105
2
votes
1
answer
79
views
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-...
- 4,105
3
votes
2
answers
2k
views
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 ...
- 51
2
votes
1
answer
83
views
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 ...
- 21
5
votes
2
answers
2k
views
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 ...
- 187
1
vote
2
answers
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 ...
- 11
6
votes
2
answers
425
views
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 ...
5
votes
1
answer
68
views
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 ...
- 51
2
votes
0
answers
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
...
- 275
4
votes
3
answers
188
views
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 '...
- 151
13
votes
3
answers
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 ...
- 357
4
votes
2
answers
1k
views
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 ...
- 205
5
votes
3
answers
2k
views
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 ...
- 153
13
votes
4
answers
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 ...
- 291
5
votes
2
answers
2k
views
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-...
3
votes
1
answer
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) ...
- 4,756
1
vote
2
answers
2k
views
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 ...
- 11
3
votes
3
answers
1k
views
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 ...
- 41
3
votes
1
answer
946
views
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/...
10
votes
1
answer
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 ...
3
votes
0
answers
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 ...
- 131
6
votes
1
answer
1k
views
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 ...
- 163
3
votes
2
answers
2k
views
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 ...
- 31
3
votes
1
answer
802
views
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 ...
- 143
3
votes
3
answers
526
views
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' ...
- 382
3
votes
1
answer
3k
views
What's the probability of having a combo on the first turn in MTG?
I'm creating a combo deck, and I'm interested in the probability of having a certain combo on the first turn.
For this combo, I need 4 different cards. There are 4 copies of each of these cards in ...
- 157