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Rolling doubles in dice games means both dice show the same number. With a pair of fair six-sided dice, there are specific combinations that result in doubles:

• (1,1)
• (2,2)
• (3,3)
• (4,4)
• (5,5)
• (6,6)

In total, there are 6 successful doubles outcomes out of 36 possible outcomes when rolling two dice. This gives us the probability of rolling doubles as \( \frac{6}{36} = \frac{1}{6} \).
To find the probability of rolling doubles, we only need to count how many pairs of numbers are the same out of all possible dice configurations. Each die has 6 sides, which directly aligns with the total outcomes for doubles.

Consecutive outcomes occur when the same event happens multiple times in a sequence. In the context of dice, rolling doubles consecutively means getting pairs of identical numbers on several rolls back-to-back.
To understand this concept, consider rolling dice three times in a row. Each roll is independent, meaning the result of one roll does not influence the others.
The challenge with consecutive outcomes like triple doubles lies in compounding probabilities. For example, rolling doubles thrice is not just about achieving doubles once but doing so three separate times in a sequence without interruption.

To calculate the probability of an event happening multiple times, like rolling doubles on three consecutive rolls, you must utilize the multiplication rule for independent events.
Given the probability of a single roll resulting in doubles is \( \frac{1}{6} \), the task is to find the probability of this event happening three times in a row.
According to probability rules, you multiply the probabilities of each individual event: \( \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) \times \left( \frac{1}{6} \right) \). Thus, the combined probability is \( \frac{1}{216} \).
Breaking it down further:

• First roll: \( \frac{1}{6} \)
• Second roll: \( \frac{1}{6} \)
• Third roll: \( \frac{1}{6} \)

Multiply these probabilities together to get the likelihood of rolling doubles all three times consecutively, which illustrates how probabilities interact in independent scenarios.