DRW Interview Question: I have \$1M on hands. You're i... | Glassdoor

# I have \$1M on hands. You're invited to a gangling game

. Tails: Payoff: twice you bet (if you bet \$1, you will get \$2+ your bet). Heads= you lose your bet. How much would you bet (it's a one-off gamble, no second chance).
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1

You have to say that the expectation is positive.

Interview Candidate on Dec 3, 2011
2

I actually think that the right answer is to not place a bet. You should only bet when you have an edge (probability of winning is greater than 50%).

Matt on Dec 13, 2011
1

to put this in trader language - you are risking 1 unit to make 2 units. While this is enough to put the statistics (positive expectation bet) in your favor requiring a trader to engage (bet), as a trader i prefer to put on trades that have a minimum risk 1 to make 3 units risk vs reward profile. As such, I would not risk more than 1/3 of my gambling money on this bet as this is a one time only bet. So, I would bet 1/3 to 1/4 of the money.

rob on Mar 25, 2012
1

I haven't interviewed with them, they hadn't replied to my application. Never the less I found this question interesting so I'm posting.

Rob is correct, I think the key is to realize that while we have positive expectancy, that exists only after many many repeated trials. For a one off scenario, we have to look for the best risk reward payoff, which is really a function of our capital constraints and risk tolerance. The spectrum goes from risk adverse to highly risk seeking.

1/3 or 1/4 is a rule of thumb used a lot in retail trading but there are plenty of opportunities where 1/5 and even 1/10 can be achieved. For example if it's your first trade, you'd probably have a choice of moving your money into buying a firm below its NAV, creating a convex trade where you have upside and downside buffer. Money management has to be factored in too: if you lose 1/2 your money you have less money in the bank to make up for the losses. Unless the trade was too good to resist versus what I can earn elsewhere, I won't bother with it.

Will Fan on May 26, 2012
4

25%. It is actually well defined nice problem. I'm not a trader but i believe every trader should be familiar with it. Here is the solution:
1M is irrelevant (at least mathematically) so suppose you invest x fraction of your wealth. Odds of winning or losing is = 0.5. Easy to check that win-lose leaves you with same money as lose-win sequence. So let's calculate how much you are left with after win-lose or lose-win, it is: 1M*(1+x-2*x^2). It is maximum at x=25%.

xeesus on Aug 5, 2012
0

Simply apply the Kelly's formula.

Amount to bet = (p*(b+1)-1)/b with p = probability of winning (50%) and b=2 (odds of this game 2:1).

Then: (50%*(3)-1)/2 = 25%

Tommy on Nov 21, 2016