The question is a variation of the 'American Game Show' problem. You may remember the character played by Kevin Spacey in the film '21' deals with this in a lecture to his students at the start of the film (before they go to rip off Las Vegas). As Dan Murray has posted it, he had no risk, i.e. he is not gambling as he is not putting any money up. An expected return is the price up to which you would pay to play a game. Dan Murray says "there would be a point where the attractiveness of option (a) would be compelling." That point is the expected return. If you pay more, you will always lose. So, how much would you pay to play this game?
He's not paying, so it's not gambling: it's more like a game show. He has three options (a) to pick definite win of EUR 10; or (b) a chance of winning EUR 21 or (c) a chance on losing, having in the last two options rejected a definite win. In effect, he has three envelopes before him. One has a mark that confirms it has 10 euro in it; the other two have no marks but one has 21 euro and the other does not. If you are not paying to play, which do you choose? That is to say, if you have a definite win of 10 euro, is it to your advantage to select one of the other envelopes?