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## What would you pay...?

Quote by Moonbear 					 				 				I know I'm risk aversive when it comes to gambling.  I'd pay $2. I can't really see any reason to pay more if you can win all the higher prizes regardless of how much you spent on the game. Perhaps you meant the question to be, "How much could someone ask to pay to play and you'd still be willing to try?" I probably still wouldn't play for more than$2, but you might get more people to play if charged $4 or$8 considering they play lottery tickets for that much.
You could interpret 'willing to pay' as if there were an auction on the right to play once.

What is amusing is that the same theory that correctly says all casino gambling and all lottery games (unless the winning amount rolls unclaimed a number times) are foolish, claims that you should be willing to bid any amount to play this game once.

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Quote by DaveC426913 					 				 				Uh. Isn't that what I just said?
Sorry, data transmission error. The message I "received" was something like "why is the OP asking how much you would pay on a rational basis, when there is no mathematically correct answer?". Which is not what you wrote!

The game host should pay me at least 51 cents to play his game, of course! (Since 1+1+1+...=-1/2) lol ;) kidding...

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Quote by nucl34rgg 					 				 				The game host should pay me at least 51 cents to play his game, of course! (Since 1+1+1+...=-1/2) lol ;) kidding...
50 cents. Be fair!

I was tempted to post this answer myself some time ago.

This is discussed here:  http://www.physics.harvard.edu/acade.../problems.html  If anyone is interested. It's toward the bottom, Week 6.

I think the answer is that you should play the game if you have to pay 4 dollars or less. (If you pay 2 dollars, you are guaranteed to always at least break even. If you pay $4, you have a 50-50 shot at at least getting your money back or making more. If you pay anything over$4, you have less than a 50% chance to win, so you shouldn't play.

Since the question is what I would pay, I would pay zero, so that any winnings would be pure profit.  Frankly, I think the question (and the game rules) are both poorly worded.

Recognitions:      Gold Member  I would pay \$1.99. Guaranteed to win, baby!

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Quote by larrybud 					 				 				Since the question is what I would pay, I would pay zero, so that any winnings would be pure profit.
And what if the person running the game said "No thanks" to that offer? What is the top amount you would be willing to pay to play? Keep in mind that the expected value is infinite. Also keep in mind that the only way to obtain this expected value is to flip an infinite number of tails in a row, which is something you will not be able to do in a finite amount of time. (And you will presumably die in a finite amount of time.)

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Quote by D H 					 				 				And what if the person running the game said "No thanks" to that offer? What is the top amount you would be willing to pay to play? Keep in mind that the expected value is infinite. Also keep in mind that the only way to obtain this expected value is to flip an infinite number of tails in a row, which is something you will not be able to do in a finite amount of time. (And you will presumably die in a finite amount of time.)
Most forms of gambling (and lottery) are just taxes on stupid people. If you're not literally enjoying the act of gambling, then the value of the game might be negligible to some.

In my opinion, this is a boring game... I would elect to low-ball.

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Quote by FlexGunship 					 				 				Most forms of gambling (and lottery) are just taxes on stupid people.
Everyone gambles many times a day. They just don't know it. Hopping into the car to drive to work, run errands, or go out on the town is a gamble. You might be killed or injured by someone with failed brakes or by some fool on a cell phone. Every election of how to allocate one's retirement account is a gamble. It doesn't matter whether its the riskiest REIT that can be found or a supposedly safe money market account.

Quote by D H 					 				 				Everyone gambles many times a day. They just don't know it. Hopping into the car to drive to work, run errands, or go out on the town is a gamble. You might be killed or injured by someone with failed brakes or by some fool on a cell phone. Every election of how to allocate one's retirement account is a gamble. It doesn't matter whether its the riskiest REIT that can be found or a supposedly safe money market account.
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.

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Quote by DaveC426913 					 				 				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).

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.

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.

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