Science collection
Patterns and surprising results
Consecutive labels, balanced categories and repeated combinations make more sense when the outcome space is visible.
Start with Is 1-2-3-4-5-6 as Likely as Any Other Lottery Combination?, then follow the questions below. Each guide includes a worked explanation, a figure and routes to an experiment or calculator.
Patterns and surprising results
Is 1-2-3-4-5-6 as Likely as Any Other Lottery Combination?
Yes under a uniform 6/49 model. Understand why a specific ordered-looking line differs from the broad category of all consecutive sets.
3 min read · Formula & figurePatterns and surprising results
Are Balanced Lottery Numbers Better? Odd and Even Categories Explained
Compute odd/even category probabilities while showing why a three-odd three-even line has no individual advantage over an all-odd line.
3 min read · Formula & figurePatterns and surprising results
How Likely Are Consecutive Lottery Numbers? An Exact Formula
Derive the probability of at least one consecutive pair in a k-of-n draw and see why it is nearly half for a 6/49 lottery.
3 min read · Formula & figurePatterns and surprising results
How Often Do Lottery Numbers Repeat Between Draws?
Use the hypergeometric distribution to calculate shared labels between independent draws, including zero overlap and four repeated numbers.
3 min read · Formula & figurePatterns and surprising results
Lottery Number Sums: Why Middle Totals Are Common
Derive the expected sum and variance of a uniform lottery draw, and explain why selecting a common sum does not improve a ticket’s odds.
3 min read · Formula & figurePatterns and surprising results
The Birthday Paradox in Lottery Draws: Any Repeat vs One Repeat
Why any repeated combination becomes plausible much sooner than a chosen combination returning, with exact and approximate collision formulas.
3 min read · Formula & figurePatterns and surprising results
Three Consecutive Lottery Numbers: Why Pair Counting Is Not Enough
Calculate a specified triple, distinguish expected triple counts from occurrence probability, and avoid double-counting overlapping runs.
3 min read · Formula & figure