Answer

An admission that you robbed will not be accepted in order to convict you as a robber. They will obligate you to give him the money based on the rule that a litigant’s admission is equivalent to a hundred witnesses. A litigant’s admission is accepted regarding the money, but the implications regarding the person himself (his being deemed wicked) are not accepted, because he is a litigant and is disqualified from testimony.
There are several explanations for the difference between this and a litigant’s admission. First, some claim that even a litigant’s admission is not a matter of credibility at all, but a kind of gift. In any case, even if it is credibility, it is clearly not the same as witnesses. In monetary matters, a litigant’s admission is effective because proof other than witnesses can help, but for convicting a person or disqualifying him from testimony, proofs do not help, no matter how good they are; only witnesses do. See Maimonides, Laws of the Sanhedrin, beginning of chapter 20 and beginning of chapter 24.