What Would You Pay? A Thought Experiment

[PAllen]

I see a qualitative distinction between
- performing activities that one need to do accomplish things in one's daily life, knowing those activities carry a risk of failure, and
- taking a risk purely for the thrill of the possible win.

Strictly using the term gambling, I would apply it to the latter but not the former.

Where would you put investing in a mutual fund? Starting your own business? Objectively, the latter has a relatively low probability of success, but a favorable expectation (or so you judge).

 

[nonequilibrium]

I have an objection to the reasoning that the expected gain is infinite.

Rather, the expectation value $E(X)$ is infinite. However, one must ask "how does $E(X)$ acquire its usual meaning of the expected gain?". The answer is: "due to some limit theorem". These limit theorems (e.g. law of large numbers) requires that E(X) is finite. Consequently, the math doesn't seem to tell us anything about the expected gain.

 

[moejoe15]

I'd bet 4$. You have a 50/50 chance of losing 2$ on the first toss. If you don't lose you have a 50/50 chance of winning 4$ (8-4=4) on the next. You also will keep doubling up for every consecutive tails you throw after the first one. If you throw 3 tails in a row you have 16$ and a 50/50 chance to double it on the next toss, as well as after every additional tails thrown.