@albertng2412
Easier way to look at the first question: Is there a number that A can choose where the area he covers is greater than the areas B covers? 1 to 21 = 231 22 to 30 = 234 Optimal play means A should choose 22 and which will force B to always choose 21. The way he did it was correct but his equation was more work than needed and I got lost and confused listening. (He’s definitely smarter, so this is just to say there may be easier ways to solve this type of question)
@anustart1934
This dude looks like he won a national math competition in china
@OpenQuant
This was a great walkthrough video of a multistep interview question, thanks for the explanation!
@proudirani
I don't agree with the comment you need to "rely on your gut to make decisions." If you are ever in a situation where you need to rely on your gut to make a decision, then you have not thought through the trade.
@ulkigmeme2703
0:50 maybe I am stupid but my immediate thought was that it solely depended on the strategy the other player would pick. Unless the other player would always bet 15 (which assumes they are hundred percent rationale), I could maximise my profit by going second.
@manuelteres7583
I think the first answer might not be correct. The centre of a dice with numbers 1-30 is not 15 but 15.5. In other words player A chooses arbitrarily between 15 and 16 and player B chooses the remaining number. The range in which they both win now is 15 numbers for both so it actually makes no difference whether you go first or last.
@scorch34
working out the probability of each number of B rolls is a lot easier in terms of combinations imo, for example 1 combination with 1 as the highest being 1-1, 3 with 2 highest being 1-2 2-2 2-1, etc. and then for 5 for example you can just count if the first is 5 there’s 5 possible numbers for the second and same if the second is 5 then taking away 1 for double counting 5-5 allows you to do it a lot quicker, and then of course 36 total combinations
@the_real_cookiez
These questions are absolutely insane. Not for me, but awesome to watch.
@k-man132
Forgot to subtract 10*(1-(probability of A winning)) for the solution of the second problem, since A will have to pay $10 if they lose.
@billbill1235
Guys I am 18, Cambridge engineering student and I am interested in Quant. Can anyone tell me if this is considered an easy or a hard question. Probably an easy for such a job but idk I want to understand how hard it is. Thanks to everyone who answers
@head0fmob
I'm confused with first question, 1-30 if player A choose 15, player B choose 16, assuming die is fair, both cover exactly 50% of outcomes (A no better than B) But if player A use other number say 14, B just choose 15 which cover 16 outcome. So B is actually better. Let me know if my logic is flawed.
@2k10clarky
For the second one personally I'd just monte carlo the shit out of it until I got the percent chance of A winning over B then apply the kelly criterion to work out the optimal stake. This is what computer are good at right... and most real world data don't break down in to neat toy models like this.
@ericluo28
the losing player will pay the otehr but then they forgot this later on in part 2?
@SheaMarcellusHamilton
These questions seem rather simple for a company like Two Sigma, nonetheless great video!
@rickyliuna9376
No Coding, Programming question for Quant Trading position??
@krombopulosmichael6280
His answer to the first question is flat-out incorrect. It is better to be Player B. Irrespective of the number chosen by Player A, expected value is always going to be higher for Player B as you have more information and can simply choose A+1 or A-1 to cover whichever part of the range is more valuable. This is true for numbers in the middle of the range (14, 15, 16) and very obviously true if A is stupid enough to choose numbers at either end of the range (which they wouldn't do since that would unnecessarily increase Player B's EV). Anyway, don't understand why they think this is correct?
@Akash-vs1yh
my brain went numb after this
@ishtiaqurrahman3020
Since the players are playing optimally wouldnt the correct answer be that it really doesnt matter who goes first because both would just pick 15?
@jackbrown1206
Why the hell do you need to be able to do mental arithmetic, like under what realistic circumstance would you not be able to use a computer do do all these calculations?
@jamesflanagin3215