Actual interview brainteaser at a top flight shop

[Kovacs]

Yeah, always betting $37.50 to start and going from there is what I arrived at as well.

I came to the solution through this reasoning--What's the minimum amount I need to guarantee $200 if there's a winning sequence from these scenarios:

two heads and one flip left $100
two heads and two flips left $150
two heads and three flips left $175

One head and two flips left $50
One head and three flips left $100
One head and four flips left $137.50

Took me two hours

 

[SomeYoungGuy]

gaak this is the worst worded teaser question I have ever seen. 14 pages and I'm still clueless.

What happens if four or five heads come up? The OP says "a fair coin will be flipped five times in a row" not "up to 5 times".. Are those wins or losses? Or does the game automatically end after 3 heads?

Are there any positive or negative ramifications of only partially fulfilling your goal vs. failing completely?
There are 4 outcomes:
a) lost game & did not double money
b) lost game & doubled money
c) won game & did not double money
d) won game & doubled money

Is d the only outcome that matters? Are all of the other outcomes equally bad?

 

[jem]

Quote from sjfan:

Since once in a (short) while there's a question about what the interviews are like at an actual investment shop (ie, IB, hedge fund, asset manager, not "prop"), I figured I'd share one in the spirit of the holiday. This is an actual interview brain teaser used by one of the top 5 trading shop in the world in an interview for a strategist (5y+ experience, 300k+/yr):

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).

You start out with $100. You can bet any amount, but no more than what you have on hand at the time, before each flip. If head, you double what you bet. If tail, you lose what you bet.

You want to double your initial $100 stake if you win the game (3 heads).

Question: what is the size of the first bet that you should make?

Hint: there is ONE right answer. It will require you coming up with the full betting strategy.

My answer would be to learn from the largest banks and bet it all every time to get a big bonus. (and have the tax payer as a backstop.)

However if I had to play by the rules regular traders do --- why bet prior to the second head. You preserve you captial until you have the best chance earning the highest return.

Hence no bet until I see the second head.

 

[tradethis]

Almost had it.............missed the 100 (tails,heads,heads) scenario



Bet 50 on flip 1.

If heads. Bet 50 on flip 2.
If tails. Bet 25 on flip 2.

if 00- you now have 200...make NO more bets, you've already doubled if you win the game.
if 10-you now have 75
if 11-you now have 25
if 01- you have 100

for 10-bet 25: 101 will leave 50....100 will leave 100

for 11-bet 25: 111 will make it game over....110 will leave 50

for 01-bet 50: 011 will leave 50....010 will leave 150

if 101- bet 50. if tails, the game is over. if 1010, you're back to 100

if 100- bet

if 110-bet 50. if 1101, the game is over. if 1100, you're back to 100

if 011-bet 50. if 0111 the game is over. if 0110 you're back to even.

if 010-bet 50. 0100 will give you 200 and the win. 0101 will leave you with 100

in all scenarios, go all in. heads will give you 200 and tails will lose the game.

 

[m22au]

What about

100

37.5 W 137.5
-37.5 L 100
37.5 W 137.5
37.5 W 175 and game over

you've only made it to 175 and not the goal of 200

Quote from Pension_Admin:

KarateChop, I am backing up your answer with the following analysis:

FLIP OUTCOME CAPITAL
100
L -37.5 62.5
L -37.5 25
W 25 50
W 50 100
W 100 200


100
W 37.5 137.5
W 37.5 175
L -37.5 137.5
L -37.5 100
W 100 200


100
W 37.5 137.5
L -37.5 100
L -37.5 62.5
W 37.5 100
W 100 200

100
W 37.5 137.5
W 37.5 175
W 37.5 212.5
L 0 212.5
L 0 212.5

100
W 37.5 137.5
L -37.5 100
W 37.5 137.5
L -37.5 100
W 100 200

 

[MustPlayOptions]

Format is Result of first 2 flips and then bet for each flip

<pre>
Bet 1 2 3 4 5
WW 37.5 37.5 25 50 100
11001 137.5 175 150 100 200
1101 137.5 175 150 200
111 137.5 175 200


WL 37.5 37.5 50 50 100
10101 137.5 100 150 100 200
1011 137.5 100 150 200
10011 137.5 100 50 100 200



LW 37.5 37.5 50 50 100
0111 62.5 100 150 200
01101 62.5 100 150 100 200
01011 62.5 100 50 100 200

LL 37.5 37.5 25 50 100
00111 62.5 25 50 100 200

</pre>

 

[run_forex_run]

Quote from Pension_Admin:

In that case, if 11110 came up, then we would have more than 3 heads (winning criteria) and yet we would still lose the $100.

In any other scenarios (other than the six options I've mentioned earlier), inluding 11110, don't do a thing. You don't care if it was a winner or loser. Your aim is to double the pot when you win.

 

[m22au]

I think KarateChop and MustPlayOptions have it.

The first two bets are $37.50.

Then the strategy for bets three, four and five depend on the result of the first two coin tosses.

 

[Pension_Admin]

Quote from m22au:

What about

100

37.5 W 137.5
-37.5 L 100
37.5 W 137.5
37.5 W 175 and game over

you've only made it to 175 and not the goal of 200

That's a good point. Back to the drawing board for me!

 

[my7tvette]

bet 1/3 of your initial bankroll each of the first 4 flips. If you complete four flips w/out winning or losing, then you should be at $100, having won twice and lost twice. Bet $100 on the fifth flip.