You are long 10 contracts on the number of sixes in 30 dice, bought at an average of 5.2 at Rs 100 a point, when the interviewer reveals that none of the first 12 dice shows a six. Reprice, mark your P&L and decide whether to cut.

Fair value is now 3, down from 5, and the position is marked at a loss of Rs 2,200: 10 lots times Rs 100 times 5.2 less 3. That loss is already real whether you sell or not. Against a market of 2.8 at 3.2, selling at 2.8 gives away Rs 200 of expected value and buying at 3.2 does the same, so the expectation says hold; cut only if the position's remaining swing, about Rs 1,581 one standard deviation, breaches a limit you set before the game.

Reprice before you look at your position. Before any dice, 30 dice at one sixth each gave an expectation of 5 sixes with a standard deviation of 2.04. Twelve dice have been rolled and contributed nothing, and they cannot be rerolled, so the contract now settles at the number of sixes in 18 dice: expectation 18 divided by 6, which is 3, with standard deviation 1.58. The intuition that the dice are now due a run of sixes is the gambler's fallacy; the intuition that nothing has changed because dice have no memory is the same fallacy from the other side. Twelve chances are gone, and the mean falls by exactly their share, 2. Think of a cricket chase: if the first twelve overs produce no boundaries, the team is not owed boundaries later, and the expected total has simply fallen by what those overs were expected to give.

Say how surprising the news was, because it bears on whether to trust the dice. Twelve fair dice with no six happens with probability five sixths to the twelfth power, about 11%. That is unusual but not extraordinary, one game in nine, so it is weak evidence of anything wrong with the dice. If the interviewer's dice were loaded against sixes the fair value would be lower still, and that is a reason to be more careful about buying, not a reason to hold on hoping.

Mark to the new fair value. Ten lots at Rs 100 a point bought at 5.2 and worth 3.0 is 10 times 100 times minus 2.2, a loss of Rs 2,200. That loss exists now, in expectation, whatever you do next; selling does not create it and holding does not avoid it. Before the roll the same position was marked at minus Rs 200, the small price you paid for buying above fair, with a one standard deviation swing of about Rs 2,041. The roll was a one standard deviation bad outcome for you, which is what holding a long position through a reveal means. The remaining swing is smaller, about Rs 1,581 for one standard deviation, because fewer dice are left.

The decision compares the market with fair value and ignores where you bought. Selling 10 lots at 2.8 realises 2.8 for something worth 3.0, which gives away 0.2 a lot, Rs 200; buying more at 3.2 pays 0.2 over fair for the same reason; holding has zero expected cost. So on expectation you hold, and you quote your own market around 3 if the game allows it, say 2.9 at 3.1, to earn the spread rather than pay it. The only reasons to sell below fair are about risk, not price: a loss limit for the game that another bad roll would breach, or a belief that the dice are biased. Those reasons are legitimate, and if you had set a stop before the game at, say, Rs 2,000 of marked loss, you honour it now and pay the Rs 200 as the price of discipline. What you never do is hold because 5.2 was your price and you want it back: the probability of settling at 6 or more is now about 7%, and about 40% of the time the count ends at 2 or fewer.

Close with what the interviewer is grading: the speed of the reprice to 3, the mark stated as a loss without flinching, and a decision argued from the market against fair value with your entry price left out of it. Volunteering that you would not have bought 10 lots above fair in the first place, and that you would quote rather than take, earns the rest.