How much would you pay for this game?

[magithighs]

I appolgize if this has already been asked.

Here's the game based on flipping a coin. You get $2 if the coin comes up heads on the first flip. You get $4 if the coing comes up head on the second flip. You get $2^N if it comes up heads on the N'th flip.

What do you pay to play this game?

Why do I ask? Again, I'm not sure about my point, but it revolves around bankroll requirements to play poker.

Cheers
Magi

[jdl22]

How much money do you (or whoever I'm playing with) have?

The St. Petersburg paradox seems to have more to do with probability than psychology, although it could be relevant I suppose given how far off most people's intuition is.

Most people I've asked say around $10 bucks. Before I saw this in a stats class I said about 20.

[bigpooch]

Even more interesting is this: some wealthy billionaire
offers this game to one person; unfortunately, people submit
bids to play this game and it's only played exactly once!
How much would you bid?

I think I would bid $63 because I might just win a buck and
because I used to read a Soviet publication! [img]/images/graemlins/smile.gif[/img]

Just this week I gave this question to some of my friends,
all of whom play poker online:

Suppose you are given a 50-50 proposition but get a small
overlay: say you pick a color and an online holdem table
and take the majority color on the flop (where you're not
seated or know anyone's hole cards!). If you guess wrong,
you pay off $100 but if you guess right, you get $100 + $x.
The value of x is nonnegotiable and it's only a one time
shot.

What's the lowest value of x you would take this bet right
now?

I asked a few people who happened to be both chess players
and poker players (including myself) and surprisingly my
first two answers were x = $0.01 and x = $20 ! If I were
to answer it myself, I would take x=$6 but that's because I
am such a nit! Someone else said kind of vaguely around
two bucks only. Anyone else?

[jdl22]

This is also an interesting question. My answer would be $10 at present because losing $100 would tough for me but not catastrophic.

You could ask the same question slightly differently. An urn has x red balls and 100-x blue balls (hehe). We'll draw one ball. If it is red I pay you $100, if it is blue you pay me $100. What is the smallest value of x for which you will play this game?

It's more interesting what happens when you up the stakes. I'm curious how much positive expectation would be necesary for the excellent players here for them to be willing to wager something like their mortgage.

[Paul2432]

I guess I don't understand the question. Does the game end if the coin comes up tails?

Paul

[magithighs]

Yes the game ends if it comes up tails.

[daryn]

but do you lose your previous winnings? is it like millionaire? you can keep flipping if you want, but you can quit anytime? or if when i first flip heads, and win my $2 , do i keep that and then i'm freerolling?

[jake]

I understand the rules to be that you pay once to play the game. And you keep flipping until you hit a tail. Then you get paid out once, depending on the how many times you flipped. Once - $2 (2^1), twice $4 (2^2), three times $8 (2^3) etc... (2^n)

So. What would I pay? Lets start with boundaries.

Minimum $2 obviously - that's the minimum return.
Maximum? hmmmm. I'd have to consider what is the maximum payout I could rationally expect/value. Yes, theoretically the payout is infinite - but being pragmatic I have little utility for $ beyond 2^25 or so. And little expectation that any entity could book this game much past 2^28.

So given that - my maximum boundary would be $25 (fair odds for my maximum utility I think).

So between $2 and $25.

Having said that... and thinking I'm gonna have to flip 10 heads in a row to even get into the $thousands, if you give me one shot I'm not real inclined to spend more than, say $12 on this. (But hey - if you'll sell multi-chances at this price - I'll take a few thousand).

So tell me again how this helps with bankroll requirements? [img]/images/graemlins/confused.gif[/img]

Jake

[jdl22]

You pay $m to play the game. The question he is posing is what is the maximum m you are willing to pay.

You flip a coin until heads comes up then the game ends. Let n be the toss that ends the game (ie the first toss where heads comes up). You get paid $2^n. Your profit is then 2^n - m.

I'm assuming based on his statement about bankroll that you can play multiple times but if you do that the game must start over again with you paying $m.

[flopdanutz]

EV
= 1/2 x $2
+ 1/4 x $4
+ 1/8 x $8
...
EV = infinity

theoritically we should put in all our money to play this game. but realistically I would pay at most about $8