Make a market questions with a twist

1 + 2 , Yes you're right. I suppose it depends on what type of market making exercise it is and how confident you are of the right valuation at each stage.

E.g. 1: Make me a market on the total number of pips (dots) on 5 randomly rolled dice. Before any dice is rolled, the expected value is 17.5. You should be confident making a 15-20 market (or even tighter). Say you get lifted at 20. Your mid here is still 17.5 but you would rather make a 17-24 market. Even if there are only 2 people in the market, you would not buy at more than 17.5 here. First dice comes. It's a 6. Now your mid market is really 20. You reprice accordingly.

This was more the situation I was thinking about but come to think of it, I did not make my assumptions clear. This game assumes that the interviewer is simply a price taker. Everyone knows the expected value of a dice (like people know where mid market is IRL) but they are paying you a premium to take on the other side of the trade. You are the house and they are the punter.

E.g. 2: Make me a market on the number of tables (I'm creative like that!) on this floor. Now in this case you could never really know the right answer. The guy knows the answer (I mean at least he already thought of a number that is supposed to be the right answer). I guess this is more the situation you were thinking about.

In this scenario, you are sure to lose money (unless you guess bang on but what's the fun in that?). The aim of the game is therefore to get to the right price with the smallest loss possible. An obvious strategy would be as you describe i.e. selling at progressively higher prices. To minimise the loss, minimise your initial size and make super wide market. The key here is to keep track of your inventories and they average price you buys/sell it for. This helps you make the right price.

Now you see the right strategy is different in each scenario and even in the same scenario, I would argue that there is more than 1 right strategy. So your first step really should be gather as much information about the rules of the game and the information the other guy has. He may laugh and not offer any but if you don't ask, you don't get.

3, Say, mid is X. The price out there is X-2, X+2. However, you're already short some so you are willing to buy it back at X-1 or even at mid. You quote a X-1, X+2 market even though mid is X. This means you're a better buyer.