1/n After the additive vs multiplicative statistics exercise yesterday, today we are going to look at the example I learned from @ole_b_peters -> You play a game where each rounds is a coin flip. If you bet X and win you end the round with 1.6X and if you lose you end with 0.6X

2/n Let's say the game starts with you getting $1 million to play with. If you split that money into 10,000 piles of $100 and play the game with $100 a round 10,000 times your expected outcome looks really good - on average you win $100,000 and you basically never lose money

3/n Having seen those results, you think this is a positive expected value game and instead will bet the full $1 million at the beginning and then whatever your entire bankroll is each time.

4/n If 10,000 people do this, you will see the average wealth of the group grow. This is a log chart of average wealth. Since everyone starts with $1 million, the log (base 10) average wealth graph starts at 6

5/n So everyone wins, right?? Let's look at the median wealth of our 10,000 players over time. Surprise!! It falls over time

6/n Also the wealth becomes concentrated - here's the max wealth of any of the 10,000 players divided by the total wealth - eventually the player with the most money has a huge share of the total money

7/7 So this result is quite a surprise when you see it for the first time. Is this a positive expected value game or a game where your wealth will go to zero almost surely? The difference between additive and multiplicative approaches to this game is pretty wild!