Dice Probability Quiz: Paradoxes and Surprising Odds
A gambler's puzzle about dice led Blaise Pascal and Pierre de Fermat to found probability theory in 1654, and this dice probability quiz walks through it and other surprises. Play an interactive set of 10 questions on sums of two dice, snake eyes, expected value, the gambler's fallacy, nontransitive dice and the strange Sicherman dice.
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🎯 Daily Trivia Challenge • 🧠 10 Questions • ⏱️ 150 Seconds
Seven
Which sum is most likely when rolling two fair dice?
Snake
What is the probability of rolling snake eyes, two ones?
Méré
Which bet is slightly better than even?
Founders
Which mathematicians discussed the gambler's problem in 1654 letters?
Average
What is the expected value of one roll of a fair six-sided die?
Fallacy
After five sixes in a row, what is the chance the next roll is a six?
Doubles
What is the probability of rolling any double with two dice?
Ends
Which is more likely with two dice, a sum of 2 or a sum of 12?
Nontransitive
What is strange about nontransitive dice such as Efron's dice?
Sicherman
What is special about Sicherman dice?
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Scroll down to see the explanation for each question.
Explanations: answer key for all 10 questions
- Q1: Which sum is most likely when rolling two fair dice?
Answer: 7
Six of the 36 combinations add to 7, a probability of 1/6.
- Q2: What is the probability of rolling snake eyes, two ones?
Answer: 1 in 36
Each die has a 1/6 chance, and 1/6 times 1/6 is 1/36.
- Q3: Which bet is slightly better than even?
Answer: At least one six in four rolls of one die
The first wins about 51.8 percent of the time, the second about 49.1 percent.
- Q4: Which mathematicians discussed the gambler's problem in 1654 letters?
Answer: Pascal and Fermat
Their correspondence laid the foundations of probability theory.
- Q5: What is the expected value of one roll of a fair six-sided die?
Answer: 3.5
The average of 1 through 6 is 21 divided by 6.
- Q6: After five sixes in a row, what is the chance the next roll is a six?
Answer: 1 in 6
Dice have no memory; believing otherwise is the gambler's fallacy.
- Q7: What is the probability of rolling any double with two dice?
Answer: 1 in 6
There are 6 doubles among 36 outcomes.
- Q8: Which is more likely with two dice, a sum of 2 or a sum of 12?
Answer: They are equally likely
Each can only happen one way: 1-1 or 6-6.
- Q9: What is strange about nontransitive dice such as Efron's dice?
Answer: Each die beats another, but in a circle
A beats B, B beats C and C beats A, like rock paper scissors.
- Q10: What is special about Sicherman dice?
Answer: Different numbers but the same sum odds as normal dice
One die reads 1,2,2,3,3,4 and the other 1,3,4,5,6,8.
Dice Probability Quiz – The Surprising Math of Dice
Probability theory began with dice. In 1654 the gambler Chevalier de Méré asked why betting on at least one six in four rolls paid off, while betting on double six in 24 rolls of two dice did not. Blaise Pascal and Pierre de Fermat worked out the answer in letters.
With two dice there are 36 equally likely outcomes. A sum of 7 is most likely, snake eyes has a 1 in 36 chance and any double has a 1 in 6 chance. The expected value of one die roll is 3.5.
Dice have no memory, so believing a number is due is the gambler's fallacy. Curiosities include nontransitive dice, where each die beats another in a loop, and Sicherman dice, which relabel the faces but keep the same sum probabilities.
What This Quiz Teaches
Puzzle fans and math students will enjoy these questions.
- Which sums are likely
- How Pascal and Fermat solved a bet
- What expected value means
- Why streaks do not matter
- Which strange dice exist
Did You Know?
- Craps is built around the probabilities of two dice.
- Dice have been found in ancient Mesopotamia.
- Casino dice are made to very tight tolerances.
- Opposite faces of a standard die add to 7.
- Probability puzzles help teach fractions.
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