Can you beat the probability puzzle loved by HFT traders and data scientists?
If you're interviewing for a role in electronic trading or quantitative finance, you'll often be asked a number of questions themed around dice and coin flips. Kris Abdelmessih, founder of volatility analytics firm Moontower and a former-HFT trader with Susquehanna, recently unveiled one that you might just find in an interview.
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The question, asked initially by University of Toronto professor Daniel Litt, is:
"Flip 100 coins, labelled 1 to 100. Alice checks the coins in order (1, 2, 3, ...) while Bob checks all the odd labelled coins, then all the even labelled (1, 3, 5... 99, 2, 4 ...). Who is more likely to see two heads first?"
Note: Alice and Bob both check coins at the same speed and at the same time, without taking turns.
Leave your answer in the comments below, and don't cheat by reading the answer! 😑
According to Abdelmessih, the answer is Bob. His reasoning is actually quite simple.
"The first coin is irrelevant," and on the second coin they each have an equal probability of landing on heads or tails. On the third flip, however, Alice will be looking at a coin that Bob had already checked. If we know it hasn't stopped the game, it is a "wasted look," while Bob gets to see a fresh new coin.
Garrett Peterson, a data scientist with crypto firm Openblock Labs, notes that by turn 50, the odds will reverse, as Bob is now checking coins that Alice has already checked. However, given the low barrier to victory of seeing only two heads, chances are the game won't get that far and Bob is more likely to win.
Abdelmessih says the riddle "works the same muscles as pricing an option." Their value is computed "at the next time step," and requires a backward induction process to figure out when the price will be optimal.
If you prefer a more bizarre brainteaser, check out this one asked by Goldman Sachs, which has puzzled over 3.5 million people on our official TikTok.
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