Interview Question for Investment and Trading Analyst at Citadel Investment:

4.25 - Work backward -- the expected value of the 2nd roll is 3.5, which means you would only choose to reroll the first dice if 1,2, or 3 came up. Thus, you get E[roll two] = 3.5 conditional on rolling 1,2,3 the first time (1/2 * 3.5 = 1.75), and you stop at 4,5,6 on the first roll, which each happens with equal probability of the time ((4+5+6)*1/6 = 15/6 = 2.5. 2.5 + 1.75 = 4.25.