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.
(a) It is a highly stylized example to illustrate game-theoretic concepts. In a sense I am asking the reader to imagine that THE GAME is about the runner getting to second or not holding all else about the game constant. That's not really baseball, but it is a baseball-like situation.
(b) The situation described is both vague (was the probability referenced by the color commentator for this runner? For this team? For this situation?) and specific (a specific runner/pitcher pair, there are zero outs not two).
(c) You are right about the goal of baseball. I had originally written it with the goal being scoring. But then it is a vastly more complex game.
A very good article. I'm just getting into games now, and seeing lots of small simplified examples like this is exactly what I need to improve my intuitional understanding.
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.