I tried to solve it with (dp[i] = sum_j(max(dp[j - 1], dp[i - j])) + 10) formula, but the way of getting the math expectation as max(dp[A], dp[B]) isn't right. Ho to do it? What is the formula..?

please, help me... :(

Add one more dimension to your DP

oough, I still cant get it. What is the 2nd dimension? I divide the current line(C) to A and B... I really cant understand what else should I know or do to calc C.

What else? You should actually know what is max you're trying to find expectation of!