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Interview Question

Quantitative Analyst Interview New York, NY

How much would you pay to play this game? You have a fair

  coin. You get heads you win $1 and can continue to play. You get tails, you collect your winnings ans stop the game. Second question. Now what if the winnings double each time you get heads.
Answer

Interview Answer

4 Answers

0

simple expectation formula. For example, for 4 trows . E(Reward) = 0.5*0 + (0.5*1 + 0.5* ( 0.5 *2 + 0.5*(0.5*3 + 0.5 * 4)))) = ... The sum converges if you continue the formula, for example to 10 trows

Interview Candidate on Jul 20, 2012
8

1) $1
2) infinity (well, expectation is infinity)

xeesus on Aug 13, 2012
0

The fair amount to be paid for this game is the expected winnings from it. Let x be the expected winnings. Now, to calculate x, consider the first toss - With probability 1/2, we get a tail thus earning $0. With probability 1/2, we get a head to get $1 and make another $x in expectation from further tosses.
x = 1/2 * 0 + 1/2 * (x + 1) => x = 1

In the second scenario, if winnings double with every toss:
y = 1/2 * 0 + 1/2 *( 2 * y + 1) => y = infinity (ie expectation diverges)
where y is the expected winning.

Anonymous on Jan 6, 2016
0

After simulating the second scenario a bunch of times on Python (each averaging 1,000,000 iterations), there was an average payoff roughly in the range of 4-12. Obviously, the expectation is infinite, but in practice it is reasonable to use monte carlo estimations for a more realistic answer. Indeed sometimes you can win massively, sometimes you can win nothing.

Anonymous on Oct 11, 2018

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