It is not true at all that your odds of getting to second base are the same whether you steal or do not steal. Consider a situation with two outs. Stealing percentage is usually around 70%, so if you steal you are likely to get to second. But on-base percentage is generally less than 50%, so if you do not steal you are not likely to get to second.

In general this is not the right way to use game theory to analyze baseball. The relevant goal isn't getting to second base, it's winning the game, with a good proxy of scoring runs. If you successfully steal with no outs you are much more likely to score a run than you are if you advance later when there are two outs. So getting to second is a bad proxy for scoring runs.