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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Deriving statistics from original card games [duplicate]

I have drafted a game that uses a French Deck with 52 cards, 4 suites (diamonds, clubs, hearts, spades), and no jokers. I'm interested in profiling game play along a few axes: How many turns are ...
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1answer
76 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 ...
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2answers
80 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 ...
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6answers
7k views

How can I estimate my chances to win a Risk battle?

I'm looking for an way to estimate the percent chance of winning a specific Risk battle. Assume the maximum number of dice will be used. It doesn't need to be a perfect calculation, just an ...
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3answers
124 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' ...
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1answer
465 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 ...
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1answer
169 views

King of Tokyo: Complete Destruction

What is the expected number of turns required to get the required roll for Complete Destruction, given no evolutions or other cards?
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1answer
985 views

Risk (revised edition 2008): Is it better to roll 1 or 2 Defense dice with the Bonus Defense die Major Reward?

The Risk revised edition rules have a Major Reward that grants the defender a bonus defense die. This die will replace the lowest defender's die rolled (unless the bonus die is the lowest). What are ...
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1answer
374 views

Use exactly 36 combinations instead of two dice

I like playing Settlers of Catan with one extension: "Catan: Event Cards" The deck consists of 36 dice cards to represent the 36 different combinations that can be rolled with 2 dice. This means that ...
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1answer
293 views

What are the odds of being dealt particular melds in Double Deck Pinochle?

This is a followup to another question: What are the odds of getting a double run in four-handed pinochle? I'd love to know the odds of being dealt particular melds in Double Deck Pinochle. I found a ...
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2answers
270 views

A Couple of Hearts Probabilities

Here's what I don't get. I've played a lot of Hearts for many years - thousands of games I'm sure. The number of times I've played a low heart, and the trick has gone 2H, 3H, 4H, 5H seems way out of ...
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4answers
856 views

In backgammon, can you resign, and how can you tell when you should?

In backgammon, there comes a time when all pieces have passed each other; there is no more interaction, you are simply rolling it out until you can bear off all of your pieces. If one player is well ...
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1answer
469 views

How do cards like Brainstorm affect the probability of drawing an out?

I posted this on a Magic forum and got zero responses. I'm playing a High Tide combo deck. Let's say I am Brainstorming with 50 cards in my deck, 23 of which are outs that make me win. I think the ...
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3answers
1k views

What are the chances of going out on the first hand in Rummy?

What are the chances of any particular player being able to go out in the first round of rummy? For two players the hand size is 7. For all other numbers the hand size is 5. Going out requires a ...
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3answers
11k views

Which Faction Power will result in the greatest bonus troops and/or fewest troop losses?

Without taking into account any other packets that might be opened over the course of a game (no spoilers please, only use the starting rules, starting scars, starting stickers). 1) What is the best ...
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1answer
138 views

Does Avis or Iago have a better chance of winning a match?

In my quest to find the answer to this question, I have decided to start smaller. The rules of Button Men are here, and the characters are listed below. Avis: d4, d4, d10, d12, dX (where X is d4, ...
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3answers
28k views

How do you calculate the likelihood of drawing certain cards in your opening hand?

In Magic, at the start of the game, you draw 7 cards. How would you calculate the likelihood of drawing a specific card in your opening hand? For example, let's say I have a 60 card deck, and I'm ...
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3answers
3k views

What are the odds of drawing a given card after discarding my initial hand?

Let's say that I have 4 of a card in my 60 card deck. What are my odds of drawing at least 1 of that card in my initial 7 card hand? If I discard those 7, what are the odds of drawing 1 of the 4 in ...
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1answer
3k views

Risk Legacy: Is it better to roll 1 or 2 defense dice when defending a bunkered location?

In Risk Legacy, there is a Bunker that always adds (+1 to the highest defense die, except when the high die is a 6). Is it better to roll 1 or 2 defense dice when defending a bunkered location.
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5answers
677 views

How many spins does it take to complete a game of Hi Ho! Cherry-O?

I recently picked up this game for my 2-year-old daughter, who is learning how to count. I find this game fairly infuriating to play by the actual rules. It contains a spinner with the 7 following ...
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2answers
4k views

What are the odds of getting the following hands in euchre?

I really like euchre, but I stink at statistics. Last time we were playing euchre, people would get some crazy hands, and we kept saying, "What are the odds?" So now I ask you all, what are the ...
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3answers
374 views

How many submarines do I need to take down an aircraft carrier?

In Axis and Allies, how many submarines do I need to have a greater than 60% chance to take down a lone aircraft carrier?
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4answers
375 views

If I put a copper and add 4 more random cards into my hand from my starting deck, does it change the odds of getting the 5:2 split?

I was thinking about a situation where someone accidentally reveals a copper from their starting hand while shuffling their deck or discovers that they only have 9 cards in their starting deck (and ...
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1answer
377 views

Are there statistic/probabilty applications specifically made for card game designers?

I am developing a card game that involves building out sequences of matching symbol pairs and also has a lose state for a (different set) of symbols that is hidden to the player. Trying to create an ...