You sit down with a well mixed deck containing A cards marked "+" and B cards marked "—". You may draw cards from this deck as long as you want, i.e., you can stop playing at any point. Each time you draw a + card you are given $1 and each time you draw a — card you have to pay $1. Cards are not
replaced after having been drawn.
What would be a fair amount to pay for the right to play (i.e., what is the expected payoff) and under what circumstance should a player cease drawing?
(In reply to re(3): What's the catch? - it's not that simple
What do you mean by the "general case" and what is still unresolved? You agreed (in your 15:52 posting) that one should not even start if B$ + entry fee > A$.
If you do punt, I would think you should ALWAYS stop if the remaining B exceed the remaining A (assuming a fair shuffle, etc.) . Hence that is the GENERAL case, nicht wahr? (If you have exhausted all the A cards, a fort. you should stop since B > zero.
Anything else would be what the good Dr J. would call "the triumph of hope over experience" in a different context. I don't see what all the separate probabilities have to do with "solving" this one: if your expectation on the next play is positive, continue; otherwise quit. (That's why I gave it a low rating -- which I might change if convinced there is more to this).
Of course if everyone reasoned this way, then the carny would find his practice unprofitable. But "a new one born every day."
Is the fog rolling in over Newfoundland, or where is this site based (to judge by the time stamps) ?