Consider the following simple model of gambling in the presence of bad odds. At the beginning, your net profit is 0. You play for a sequence of n rounds; and in each round, your net profit increases by 1 with probability 1/3, and decreases by 1 with probability 2/3.
Show that the expected number of steps in which your net profit is positive can be upper-bounded by an absolute constant, independent of the value of n.
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