This site has been invaluable for me during recruiting so I thought I would pay it forward now that I have graduated and am gainfully employed. Specifically I wanted to address thefinal round interview for a full time position, which I had last year and could not find exactly what I was looking for on this site in terms of what to expect.
Before the interview I went through five(!) phone interviews before they invited me down, and I think they would have kept going except that I had an exploding offer coming up so I told them its final round or nothing. Every time I thought I had finally messed up the interview to the point where they wouldn't invite me back, but every time hr contacted me with the next date. When they say 'we aren't looking for the right answer so much as how you think about a problem', they mean it.
Before the final round they send you a sheet outlining the basics ofterminology. What bid and ask mean, as well as how to properly phrase that you would like to make a trade and at what price. My first pearl of wisdom is to study the shit out of this sheet. If you have had experience before, great, but most applicants to are, like me, math or other STEM majors so have not seen these terms or if they have certainly have not used them in a real time environment. As a note: I had taken finance courses and knew what these definitions actually meant, but there is a HUGE difference between being able to pass an econ exam and being able to rattle off a trade without thinking about it. The last thing you want is to be committing mental capacity to figuring out if you want to give your bid or your ask price first when you should be fully committed to doing three digit fraction multiplication. Even worse, if you get confused and phrase the trade incorrectly the interviewer will not be afraid to crush you and take a highly unfavorable trade (for example by selling to you at the price you meant to give as your ask price). You should have a couple days between getting this sheet and the final round, use that time and don't wait until you were sitting around in the hotel the night before like me.
At the final round itself you are given 100 poker chips at the start of the day. Over the course of the next 4-6 hour long interviews (I only had four, but I think that's because I got cut after four - there were still people interviewing as I left) you have to use the chips to make bets on scenarios given to you. Some sources claim these scenarios can be as simple as 'make a market on the temperature in the room', I didn't get these questions and I'm guessing that they are reserved for internship interviews. I got much more difficult ones, that require a decent amount of math. You will need to use theterms to bet on the results you get. There is probability involved (for example a deck of cards or non-six sided die), so the more astute of you will notice that a better candidate may end up with fewer chips than one who bet and got lucky - don't worry is fully aware of this and you based on what you bet and why, not how much you win. Therefore the actual number of chips you end up with is irrelevant (to a degree -see below), so if you have 20 chips after getting very unlucky on reasonable bets, don't try to win it all back thinking you are below some magic cutoff, there really isn't one. It is best to just ignore the existence of the chips to the extend you can, and think about each problem as just an isolated probability/brain teaser problem.
The biggest single thing to remember about your chips is to never go all in. They tell you at the start of their interview that in their job they make positive expected value bets, but to never do so if there is a chance of being wiped out. Therefore keep in mind: if you are 99% sure of something it means that you are willing to bet 99 of your chips just to get one chip, and even if what you're betting on is a coin flip with only heads, its not acceptable to take that bet (extreme example, the in-interview examples are much more subtle). This means that if you end up with single digit chips you will almost certainly not get an offer, since you bet in a way that 'wiped you out' (note I ended up with 87 and still didn't get an offer).
Not every interview depends on the chips - some are straight math questions. All the more reason to just ignore the chips since you don't want to be thinking "shit I only have 43 chips" during an interview that doesn't concern the chips at all - always stay focused.
In terms of specific questions they ask: I would recommend going on glassdoor and looking up interview questions forand maybe some other prop shops (ex. SIG). I actually encountered some very similar to the ones I had seen there, but they have enough new material that you will not be able to memorize your way through the interview.
Finally they do ask an unsolvable question (or rather, one that you need a PhD in probability to answer), so yeah those rumors are true. Not gonna tell you what it is (where's the fun in that?), but I had seen it online before my interview. The point of the questions is not to get it right, but to bet chips on how long you think it will take you to answer it (the prompt is deceptively easy). Now remember, if you bet on a 99% confidence interval, it means you are technically saying you would bet 99 chips that you will be able to solve it for the chance to win one chip.
So yeah I didn't get the job, but it was by far the most difficult yet most interesting/rewarding interview I've ever had. I wrote this from the point of view of what I would have liked to know, so it may not be exactly what you are looking for, in that case ask questions and I will answer them as best I can - though I'm gonna abstain from actually giving away what the questions were (hint, hint: glassdoor!). Also I tried not to give out specifics on the interview that would give someone a big unfair advantage - just more what to expect so as too calm the nerves of people who are nervous enough to be searching for advice on WSO!