Getting the highest amount of positives on one set with a 50% random chance

Question

If you had 2 sets of numbers, that both start at 0 (each set can only go up from 0, but never lower than 0), and you run a 50 percent coin flip computer program and if it is heads, you add +1 to a chosen set, and tails -1 from a chosen set, and you have to choose which set of numbers to add/subtract. What would be the best way to alternate between the two sets so you can get the highest number in the first set?

Answer 1

Let's call the 2 numbers A and B.

Initially, A starts at 0 and B starts at 0.

Let us consider possible stratergies:

1) All coin flip results go to either A or B. This is not optimal because it models a random walk with expected value being 0.

2) Alternate coin flip results between A and B. So first coin flip result affect A, the second result affects B, the third result affect A, etc. This is not optimal because we cannot prevent either number from decreasing thereby reducing long term average value.

3) If the coins flip is head only apply the result to A otherwise apply the result to B. This ensure A keeps growing and B can't get any lower than 0 anways.

Conclusion:

3) is the most optimal way.