Risk aversion

2 articles

Combinatorics & Discrete Math LicenceAnalyse12 min

Two Seats, a Dollar Each, and Only One Worth Taking

Both seats in the marble game average a dollar a play, and that arithmetic stays true to the last line. Seat A carries variance 3/2 against seat B's 1, and seat A's law turns out to be seat B's law with one prize smeared outward, so every concave utility prefers B without variance ever being mentioned. Once both players stop flipping coins, seat B is ahead on the average too, at 1 against 3/4.

Probability & Statistics LicenceExplication9 min

The Same Three and a Half Million, with a Thousandth of the Spread

Both games pay 3.5 million dollars on average, so "they match" is true and the inference that it is a wash is not. Shrinking the ticket by a million divides the spread by a million while adding a million independent rolls multiplies it back by only a thousand, so the ratio of standard deviations is exactly root of a million: 1,707,825 against 1,707.83. The whole argument rests on independence, and at a correlation of 1 the diversified game becomes the single roll exactly.