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In game theory, "guess 2 / 3 of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to 2 / 3 of the average of numbers chosen by all players.
The misdirection in this riddle is in the second half of the description, where unrelated amounts are added together and the person to whom the riddle is posed assumes those amounts should add up to 30, and is then surprised when they do not — there is, in fact, no reason why the (10 − 1) × 3 + 2 = 29 sum should add up to 30.
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
What Is a 2-for-1 Stock Split? A forward 2-for-1 stock split — sometimes expressed as 2:1 — occurs when a company doubles the number of outstanding shares and cuts the value of each share in half.
Williams-Sonoma stock split in two in July after gaining 136% in one year. However, it disappointed investors with its earnings update right after, and its stock trades down about 10% since the split.
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A normal play game starting with a single heap of 8 is a win for the first player provided they start by splitting the heap into heaps of 7 and 1: player 1: 8 → 7+1 Player 2 now has three choices: splitting the 7-heap into 6 + 1, 5 + 2, or 4 + 3.
The company has split its stock twice in the last five years: a 4-for-1 split in 2021 followed by a 10-for-1 split in June of this year, bringing its share price to a more affordable $118.