![]() ![]() The payout for a given n round is then 2^n. If there is a head in the second round you win four rubles in that round. If you have a head in the first round you win two rubles for that round. The probability of n heads in a row is then (1/2)^n The probability of two heads in a row is (1/2)² = 1/4. The probability of the first heads is 1/2. Each coin toss is an independent event and so we multiply probabilities possibly with the use of a tree diagram. The probability that a fair coin lands heads up is 1/2. The expected value is calculated by multiplying each of the possible outcomes (payout) by the likelihood (probability) each outcome will occur and then summing all of those values.įirst, let’s begin by discovering the probabilities. The standard framework used in that kind of situation, where you need to anticipate value for a given investment, is expected value. The coin is tossed again, and for each tossing, I’ll double the amount of the previous round, but at the first tail, the game is over.“ Question is: how much would you pay to play this game? If it lands tails up, then you lose, and the game is over. If it lands heads up, you win two rubles, and the game continues. She explains: “I will flip a coin (mine or yours, it’s your choice). You’re visiting the mighty city of Saint Petersburg, and an old woman offers you to play “a game worth playing“. ![]() ![]() How Should You Deal With Randomness? Photo by Jonathan Petersson on Unsplash ![]()
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