The poll results of the probability puzzle in Twitter on October 11, 2020, showed that risk of ruin is often underestimated. In this article, we discuss how this puzzle is related to trading and risk. Access to article requires Premium Insights subscription.
Below is the post of the probability puzzle with the poll results in Twitter.
Sunday probability puzzle
Three fair coins tossed. Heads gets +1, tails -1, pay-offs are added and net pay-off added to equity. The 3 tosses are repeated 1000 times. Initial equity is $10. What is the probability of total ruin (within +/- 0.05 error)? Please do not post answers.
— Michael Harris (@mikeharrisNY) October 11, 2020
The correct answer is about 0.83 but only 23.6% of the votes got it right. Several people confirmed the correct result by coding simulations. The 34.3% who voted for probability of 1 were correct assuming sufficient samples but in the puzzle the number of trials was limited to 1000. Note that 18.1% of the votes for 0 probability is a puzzling result when it should be obvious that three consecutive tosses of three tails would cause ruin.
Below is additional analysis with a few charts and also a discussion about the relation of this puzzle to trading and risk.
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