SIG is well known for asking probability questions to filter trainees. This is not surprising. They view option theory as a pillar of decision-making in general. Thinking in probabilities takes practice which is why they like to look for talent amongst gamers who make many probabilistic decisions and need to interpret feedback in the context of uncertainty. They require many hours of poker during “class”. In this 3 month period, junior traders live and breathe options in lovely suburban Philly after apprenticing (“clerking”) on a trading desk for about a year.

Here’s some of the questions I remember from my interviews in 1999.

- You flip a single die and will paid $1 times the number that comes up. How much would you pay to play?
- Suppose I let you take a mulligan on the roll. Now how much would you pay (you are pricing an option now btw)?

- My batting avg is higher than yours for the first half of the season. It’s also higher than your for the second half of the season.
Is it possible your avg for the full season is higher than mine?

(Hint: Simpsons paradox)

- You are mid game that you have a wager on. Opponent offers to double the stakes or you automatically lose. (Like the doubling cube in backgammon)
What’s the min probability of winning you need to continue playing?

- You’re down by 2 with seconds left in regulation basketball game and have a 50/50 chance of winning a game if it goes to overtime. You have a 50% 2-pt shooter and a 33% 3-pt shooter.
Who do you give the ball to?

(simple EV question)

- You are given $1,000,000 for free but there’s a catch. You must put all of it into play on roulette.
What do you do?

- There’s a 30% chance of raining Saturday. 30% chance of raining Sunday.
What’s the probability it rains at least one day?

To encourage you to try before looking up the answers, I’ll make it annoying…the answers are somewhere in this thread.

I wrapped that thread with a short post on* Trading And Aptitude* (Link)

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