Poker and games

A friend says picking 1, 2, 3, 4, 5, 6 in the lottery is wasteful, since that line never comes up.

Which draw is more likely, that line or a scattered set of six numbers?

Mental math practice

A crate holds 11 melons and each melon sells for 23 dollars.

11 × $23

What is the crate worth, in dollars?

Math questions

Algae covers a pond, doubling every day. On day 18 the pond is fully covered.

On which day is the pond half covered?

Trick questions

Each number in this list is smaller than the one before: 9, 3, 1, one third.

What number comes next?

Riddles for kids

You have 7 coins worth 50 cents in total, and every coin is 5 or 10 cents.

How many 10 cent coins do you have?

That's all of them for now.

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The question you opened

Playing 1, 2, 3, 4, 5, 6

A friend says picking 1, 2, 3, 4, 5, 6 in the lottery is wasteful, since that line never comes up.

Which draw is more likely, that line or a scattered set of six numbers?

Equally likely

Every specific set of six numbers has exactly the same chance. There are far more scattered sets than tidy ones, which answers a different question.

Every individual combination is equally likely, and the tidy line is one combination like any other. In a game drawing six numbers from 44 there are 7,059,052 possible tickets, and each has one chance in 7,059,052 of being drawn. The machine does not read the ticket. The confusion comes from swapping two questions.

Ask how likely it is that the draw looks scattered, and the answer is that scattered draws are overwhelmingly common, because almost every combination looks scattered. Ask how likely one specific scattered combination is, and it is exactly as unlikely as the tidy one. The first question is about a category with millions of members.

The second is about a single member. There is one practical reason to avoid the tidy line, and it has nothing to do with probability. Thousands of people play it, along with birthdays, arithmetic sequences, and the diagonal of the slip. If those numbers ever came up, the jackpot would be split many ways.

Since the chance of winning is fixed, the only thing a player controls is how much of the prize they would keep, which argues for unpopular numbers above 31, since birthdays occupy 1 through 31. That is also the reason a syndicate that buys every combination has to worry about company.

Covering all the tickets guarantees the jackpot and does not guarantee holding it alone. The wider habit this trains is separating the likelihood of an outcome from the likelihood of a description of outcomes. Patterns look meaningful because there are so few of them, and rarity of the description gets mistaken for rarity of the event.

Technique: One ticket against one ticket

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