Jane Street Interview Question: You are going to see a sports... | Glassdoor.co.uk

## Interview Question

Summer Trading Analyst Interview London, England

# You are going to see a sports tournament between two teams

. Best of 7. Can only have win/loss outcomes. Devise the optimum betting strategy such that at the end of the tournament you are either up 100 or down 100. Was initially confused about starting money but he told me that you can bet any amount.

0

Right, so you were told you can bet any amount of money........surely you can just bet 100 on the first game then you'll either be up or down by 100 (as required) whatever the outcome, then for the rest of the games just bet 0 and nothing will change......

Anonymous on 13 Jan 2013
1

It is Best of 7, meaning you should win 100 dollar if your home team won the tournament and lose 100 dollars otherwise.

Just think through all possible cases.... BACKWARDS, like in pirates and golds problem.

Step 1:
How much you should bet on last game? Well if you team has won 4, 5 or 6 games so far, you are already up 100 dollars and therefore bet 0 dollars. If you team has won 0, 1 or 2 games you are already down 100 dollars and bet 0 dollars as well. So the only case left is you team has tied with score 3 : 3. If now you are up X dollars from initial amount and bet Y dollars, you will be up X+Y if your team won or up X - Y if your team lose. now X+Y=100 and X-Y = -100 by condition; meaning X=0 and Y=100.

Step 2: apply the same reasoning.

Carry this one until you reach step 7, which should tell you how much to bet in game 1. I am too lazy to carry it out though.

Anonymous on 21 Feb 2013