Help me settle this dispute (Simple EV problem)

[cianosheehan]

My friend and I were having an argument over this basic scenario.

Someone is offering you +10% on a coin flip. So, for example they are willing to give you $11 if they lose, and you give them $10 if you lose.

Given that you only ever get to flip the coin once, are you losing by declining the bet?

Her argument was (she may want to adjust this later in case I dont have it the exact way she wants), was that she wont flip the coin. She doesnt lose money by not flipping the coin since she preserves the money that she does have. So, since there is nothing put at risk, there is no loss. She is not losing anything by not flipping the coin, therefore she would prefer not to take the risk.

My argument to her was;
It is an indisputable +EV proposition for you. Seeing as though you are being propositioned, you have to make one of two choices. Flip the coin or not. One of these choices is the +EV choice, the other is -EV choice. By NOT flipping the coin and knowingly turning down a +EV proposition, you are losing expected profit, which is the same as losing money. Whether you preserve what you have or not, you are still essentially losing money because you made the -EV choice. And in being given the choice, that is how you lose money by declining the bet.

She still refuses to accept that she is 'losing' money by declining. She says that yes, she is turning down possible expected profit, but with only one flip she does not lose anything by declining the bet. The argument then continued to go around in circles. I tried explaining it as clearly as I could but it still couldn't convince her. Then again maybe I'm wrong! Anyone help?!

[DrVanNostrin]

It depends on what you define an EV of 0 to be an one's utility function and bankroll.

I would define an EV of 0 to be not accepting the bet. So by my definition not accepting the bet is not -EV. But it is -EV relative to accepting the bet. So accepting the bet is better.

There are cases where this bet should be declined. For example, if one's bankroll was $10 and a logarithmic utility function was being used this bet should not be excepted.

[iveyleague24]

Well explain it like this. Let's say you won a ticket that gave you a 39.53% shot of claiming a $1,250,343.74 prize [img]/images/graemlins/spade.gif[/img]. The ticket isn't worth anything tangible other than the plastic/ink it's made from. However, you have nearly a 4/10 chance of winning over a million dollars thanks to this ticket. If you throw away the ticket, you're throwing away your chance at being semi-rich. Even though you aren't losing money you have, you are losing money that you should have. One more thing, most people understand this crap by the time they turn 10, so this girl just might {this section omitted by Güd Jüd Jamént}...no offense.





[img]/images/graemlins/spade.gif[/img] Hopefully, the complicated numbers will remove any %%%%%% that my hypothetical scenario is associated with that wonderful logic intensive masterpiece of a game show "Deal or No Deal"

[cianosheehan]

Thanks for the replies.

My argument was that in being forced to make a choice of flipping the coin and not flipping the coin, you are forced to make a choice between one that is +EV, or the other being to decline a +EV proposition. You can only make one of two decisions, a yes or a no. The 'yes' is +EV, and knowingly turning down the yes is -EV.

In this instance, is it necessary to define what EV of 0 is? Can you really call declining a known +EV opportunity as zero EV? True you aren't risking anything, but since you only have one of two choices (to flip or not to flip the coin), and knowing that flipping is +EV, can you not say that refusing a +EV proposition is -EV as opposed to zero EV?

As DrVanNostrin said, there are of course instances where you shouldn't take the bet, ie I wouldn't bet everything I own on a coin flip even if I was getting +10%, because starting from a financial 0 is more -EV than declining a +10% EV.

[DrVanNostrin]

[ QUOTE ]
In this instance, is it necessary to define what EV of 0 is? Can you really call declining a known +EV opportunity as zero EV? True you aren't risking anything, but since you only have one of two choices (to flip or not to flip the coin), and knowing that flipping is +EV, can you not say that refusing a +EV proposition is -EV as opposed to zero EV?

[/ QUOTE ]
EV is relative. You can say going to work is earning you XXX relative to staying home. Or staying home is costing you XXX relative to working. Both would be correct. In poker, folding always has an EV of 0; other EVs are calculated using that defintion.

[cianosheehan]

[ QUOTE ]
[ QUOTE ]
In this instance, is it necessary to define what EV of 0 is? Can you really call declining a known +EV opportunity as zero EV? True you aren't risking anything, but since you only have one of two choices (to flip or not to flip the coin), and knowing that flipping is +EV, can you not say that refusing a +EV proposition is -EV as opposed to zero EV?

[/ QUOTE ]
EV is relative. You can say going to work is earning you XXX relative to staying home. Or staying home is costing you XXX relative to working. Both would be correct. In poker, folding always has an EV of 0; other EVs are calculated using that defintion.

[/ QUOTE ]

So you can say that NOT taking the bet is costing you x?

[DrVanNostrin]

[ QUOTE ]
So you can say that NOT taking the bet is costing you x?

[/ QUOTE ]
Yes. But failing to take the bet isn't necessarily -EV. You could say that limping aces on the button after several bad players have limped is costing you money. However, by definition limping the aces would still be +EV.

[JennEric Screen Name]

I think this is clearer if you actually calculate the EV's instead of just asking whether the EV is positive or negative.

For a $10 bet, the EV of betting is:
50%*$11 + 50%*(-$10) = $0.50.

If we don't take the bet, the EV is:
100%*$0 = $0.

If there is no possible change in your wealth, the EV is 0.

I think the argument is really about what you consider to be yours before you choose whether or not to take the coin flip. If you see a $20 bill on the sidewalk, you can choose to pick it up or leave it. If you mentally take possession of it as soon as you see it, then choosing not to pick it up will seem like a –EV choice. I’d argue that it wasn’t yours in the first place, so the choices are +$20 or $0 in EV. In your example, you seem to be asserting that, having been presented with the coin flip proposition, your wealth already increased by $0.50.

So it comes down to answering this: How much wealth do you have before deciding whether to take the flip, $10 or $10.50?

[RarocASP]

[ QUOTE ]

Whether you preserve what you have or not, you are still essentially losing money because you made the -EV choice. And in being given the choice, that is how you lose money by declining the bet.

[/ QUOTE ]

I think this is where the two of you are missing eachother. It's a difference between value and losing money. You lose value, but not money, by declining to play the game.

[T50_Omaha8]

[ QUOTE ]
I tried explaining it as clearly as I could but it still couldn't convince her.

[/ QUOTE ] Maybe you should have used as evidence that anybody who buys insurance on anything is an idiot because insurance is the -EV choice. Oh wait...

If you understood this useful concept you'd see what your friend is talking about:

http://en.wikipedia.org/wiki/Risk_aversion

Anybody who turns down any wager could be making their best EV decision depending on their money utility function. Even a 50/50 flip at 100:1 odds.