Actual interview brainteaser at a top flight shop

SJFan, this is my strategy. I have not come up with a way it loses, perhaps you can.
First 2 flips:

37.50 37.50

If you won or lost BOTH of those 2 flips, you bet 25, 50, 100 UNTIL you are broke or have won game. Then you bet 0.

If you won 1 of first 2 flips, you are even ($100 bankroll),needing 2 of last 3 flips to be heads. So bet 50, 50, 100 UNTIL you have won game or game is over. You bet 0 once you have won game.

 

There are 9 possible ways to get 3 tails in 5 roles. 5/9 require a 1 on the first flip, 4/9 have a 0 on the first flip and 1/9 starts with '00' requiring you to get 111 on the next three rolls. How to use that to make a betting strategy I'm working on

 

I agree with KarateChop, but I'm not sure of the exact sequence.

It does make sense if you look backwards - if you have 1 flip left, you need at least $100 - 2 flips left, you need $50, 3 flips, you need $25 minimum to catch up. If the flips that are left at that point don't come through as heads you don't win and it doesn't matter.

So, you bet how much you are able to while still making sure you will have enough money left to hit $200 after the remaining flips if the early flips are losers. The other thing then would be to make sure if the early flips are winners, you bet enough to get up to $200 and then quit betting.

 

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

 

Bah I got the same solution and I only read the original post. $37.50 is the right first bet, and I also solved it by building a tree. I solved it in about 25 minutes. I wonder how much time people were given to solve it in the interview ??

 

I think any amount ranges from 33.5 to 37.5 works as well.

 

Bet nothing until the outcome depends on the final filp.

So it could be 1100, 0011, 1010, 0101, 0110 or 1001. On the final flip bet 100. If you win the game, you will get 200.

 

i think the point is to bet when you have a positive expected value... not gamble

 

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.

 

we should be roulette buddies