Actual interview brainteaser at a top flight shop

sjfan · Dec 22, 2009

The question ask for an exact answer. There is an exact strategy of sizing your bets so that you will always win $100 when you win the game (getting three heads before 3 tails show up). Under this strategy, you will get this result 100% of the time (not that you will win the game 100% of time, but you will get your desired pay off 100% of the time)

Quote from OTCkrak:

betting zero, waiting for the first two heads will win 50% of the time

sjfan · Dec 22, 2009

Also, your probabilities are wrong. Just because the next flip after getting two heads is a tail doesn't mean you lose the game. This is a win: 1101.

Quote from OTCkrak:

betting zero, waiting for the first two heads then going all in wins 50% of the time, the flip will have a EV of 0

OTCkrak · Dec 22, 2009

Quote from sjfan:

The question ask for an exact answer. There is an exact strategy of sizing your bets so that you will always win $100 when you win the game (getting three heads before 3 tails show up). Under this strategy, you will get this result 100% of the time (not that you will win the game 100% of time, but you will get your desired pay off 100% of the time)

my career in IB was limited to back office accounting for 15.25/hr

FreeMarkets · Dec 22, 2009

I'm not smart enough to know if it's something off the wall like $37.50 so I'll go with 50 bucks a toss.

tman · Dec 22, 2009

$14.29

sjfan · Dec 22, 2009

What to tell me (and everyone here) how you got the answer?

Much like in a real life interview (or a college exam), no credit will be given for an answer without showing work

Quote from tman:

$14.29

sjfan · Dec 22, 2009

Nope. Remember my hint: you will need figure out the entire bet sizing strategy to arrive at the right answer;

Quote from FreeMarkets:

I'm not smart enough to know if it's something off the wall like $37.50 so I'll go with 50 bucks a toss.

tman · Dec 22, 2009

1st win $14.29 + 2nd win 2 x $14.29= $28.58 + 3rd win 2 x $28.58= $57.16

$14.29 + $28.58 + $57.16 = $100.03

FreeMarkets · Dec 22, 2009

So would the wager amount change depending on circumstance?

Quote from sjfan:

Nope. Remember my hint: you will need figure out the entire bet sizing strategy to arrive at the right answer;

AyeYo · Dec 22, 2009

Quote from sjfan:

You are playing this coin game: a fair coin will be flipped five times in a row. You will win on the 3rd head. You will lose on the 2nd head. (ie, if 1 is head and 0 is tail, if the flip comes out 111, you win. if it comes out 1011, you win. if it comes ou t 1000 you lose).

Did you mean you'll lose on the second TAILS?