Market Making Card Bet Game
Mathematically, the problem is a bit ill-defined.
We're not certain of your goal: Do you care about your strategy's expected value of winnings only? Or do you want to end up above $2000 at the end of the interview but are very averse to busting? Etcetera.
We're also not certain what sorts of prices you're going to be given in the future.
That said, it makes sense to bet more when the price is very high or very low, as you're more certain to win in those cases, so your risk is lower, and furthermore your expected return is higher.
How to go about this in a coherent manner? I think there are several ways. One I'll mention is to have some sense of "acceptable risk." For example, you could decide that on any given round, you don't want more than an $X\%$ chance of losing more than $Y\%$ of your holdings, i.e. use a value at risk metric for deciding how much to wager on any given round.
From a pure expectation point of view, you just buy/sell as much as you can each round.