Skiing
Three quick games to help you understand the concept of ergodicity.
Game 1: Single Player
You're a skier. You can race up to 10 times. Each race has a 20% chance to win and a 20% chance to get injured. Once injured, you cannot race anymore.
Game 2: Alice vs Bob
Alice and Bob are both skiers. They can participate, together with other skiers, in a championship consisting of 10 races.
Alice takes more risks, so she has a 20% chance of winning each race, but also a 10% chance of getting injured.
Bob takes fewer risks, so he has a 15% chance of winning each race, but also a 1% chance of getting injured.
Who do you think will win more races?
Game 3: Population of Skiers
Now we have 100 skiers: 50 Alices and 50 Bobs.
Each Alice has a 20% chance of winning and a 10% chance of injury per race, and each Bob has a 15% chance of winning and a 1% chance of injury per race.
Play the game for at least 20, noticing how Alices are likely to win more races at the beginning but fewer as the game progresses. So, it would be a mistake to think that Alice's strategy is better just because it grows faster at the beginning.
Alices
Wins: 0 (average per skier: 0.00)
Injury status: (0% injured)
Bobs
Wins: 0 (average per skier: 0.00)
Injury status: (0% injured)
Learn more about Ergodicity
Ergodicity
How irreversible outcomes affect long-term performance in work, investing, relationships, sport, and beyond
