VSauce2's Infinite Money Paradox Reaction

[Andrew WCY]

Originally Posted by TheSaxRunner05

Despite the expected value going off to infinity, could you make an argument for the Median result being something modest like $4? Since half of all games end after the first flip, would it be safe to say the median value is either 2 or 4, without even running a sample size, or does the median require a list of results to exist?

The Infinite Money game in the video can be viewed as a discrete probability distribution. From https://en.wikipedia.org/wiki/Median..._distributions, the median (M) can be found where the probability of having a value equal to or less than the median AND the probability of having a value equal to or more than the median is at least 0.5.

Winning $2 has a 50% chance, winning $4 has a 25% chance and so on. Notice the gap between $2 and $4: This implies we don't have a value for the median; rather, the median is in the range of $2 <= M <= $4. It's a bit hard to interpret this.

Originally Posted by TheSaxRunner05

Wouldn't an expected median value be more telling? It seems more practical and less theoretical than an expected value.

I think it really depends on the context in which the median or expected value is used. For lotteries (discrete probability distributions), medians are reliant on the range of winnings you can earn, the number of possible winnings and the probabilities of which they occur; the expected value depends on the values of the winnings and their associated probabilities.

The above factors influence the choice of an appropriate statistical measure. Since I'm not familiar with the application of statistics in these fields, maybe someone with relevant experience could discuss about this.