Help me settle this dispute (Simple EV problem)

[Brons]

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I suspect that if someone offered you the same deal but the bet was your next 5 years income you would very rapidly come around to your friend's way of thinking.

[/ QUOTE ]Bankroll is the only valid reason there is to let this offer down. So the next 5 years income isn't really a fair proposition and most people will in fact turn it down, and not because they don't like the odds on the flip but because it's not within their bankroll.

[qpw]

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I suspect that if someone offered you the same deal but the bet was your next 5 years income you would very rapidly come around to your friend's way of thinking.

[/ QUOTE ]Bankroll is the only valid reason there is to let this offer down. So the next 5 years income isn't really a fair proposition and most people will in fact turn it down, and not because they don't like the odds on the flip but because it's not within their bankroll.

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I disagree. The most valid reason for turning the bet down is that you are not a gambler and see no reason to risk losing $10.

It's as simple as that.

If she were offered a guaranteed, unlimited, series of similar wagers, and had the BR to handle the unlikely possibility of a run of very bad luck, then the position would be quite different.

As it is, it seems perfectly sensible to say that you can make better use of $10 100% of the time than $21 50% of the time and $0 50% of the time.

The important point is, of course, that it is pointless to talk about +EV when she's only being offered one flip of the coin.

If you are not in the habit of gambling, it really makes little difference how good the odds are (until it becomes a near certainty that you'll win). For a one off event you still risk losing your money and you may well prefer the certainty of having $10 to a 50% chance of having $21 but with a 50% chance of having sweet FA.

[DrVanNostrin]

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...you may well prefer the certainty of having $10 to a 50% chance of having $21...

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We already figured this out. This is exactly what a utility function accounts for.

[qpw]

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We already figured this out.

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Oh, Really?

I think I might have missed that in amongst all the sarccy comments suggesting that the non-gambler must be a couple of sandwiches short of a picnic.

[DrVanNostrin]

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Oh, Really?

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Yes, really. This was the first response to the OP:

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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.

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Try reading the thread again.

If you have $1000 bankroll the question isn't "would you prefer $10 or a 50% chance at $21 and a 50% chance at nothing?" The question is "would you prefer $1000 or a 50% chance at $990 and a 50% chance at $1011?" There's a big difference between these two questions.

[qpw]

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Yes, really. This was the first response to the OP:


If you have $1000 bankroll the question isn't "would you prefer $10 or a 50% chance at $21 and a 50% chance at nothing?" The question is "would you prefer $1000 or a 50% chance at $990 and a 50% chance at $1011?" There's a big difference between these two questions.

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Hey, chill!

You're agreeing with me.

I just saw more posts slagging off the friend so I posted in support.

No need to make a federal case about it [img]/images/graemlins/cool.gif[/img]

[SumZero]

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Her argument was based arround the fact that she is not willing to risk any amount of money on a +10% wager, when the coin is only going to be flipped once. It was this element that prolonged the argument, because she valued risk aversion much higher than the EV of a single coin flip. Not necessarily because she doesn't know the concept of +EV, but because there was no guarantee of outcome on a single flip. I asked her what +% would she need in order to take the flip, but she wasn't able to answer. For the same reason I'm sure - it would still be a single flip. She did however say that she would flip the coin 100 times. But definitely not once. As was said already, beyond bankroll issues there really is no way to justify this.

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This is just stupid if what you've stated is true. If she'd accept the 100 flip game then she certainly should accept a 1 flip version where she wins more than 1 / 2^100 times (I.e., the chance that she'd lose all 100 flips). And she should likely accept much more than that. No matter how you define +10%, her chances of being negative after 100 flips are pretty high. If you define +10% as risking 10 to win 11 then there is a greater than 27% chance she is negative after 100 flips (and often times negative by a lot). If you define +10% as a 55% chance to win each flip then there is a greater than 13% chance she's negative after 100 flips. Even at 60% likely to win any individual flip she's more than one and two thirds percent likely to be negative.

[qpw]

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This is just stupid if what you've stated is true. If she'd accept the 100 flip game then she certainly should accept a 1 flip version where she wins more than 1 / 2^100 times (I.e., the chance that she'd lose all 100 flips). And she should likely accept much more than that. No matter how you define +10%, her chances of being negative after 100 flips are pretty high. If you define +10% as risking 10 to win 11 then there is a greater than 27% chance she is negative after 100 flips (and often times negative by a lot). If you define +10% as a 55% chance to win each flip then there is a greater than 13% chance she's negative after 100 flips. Even at 60% likely to win any individual flip she's more than one and two thirds percent likely to be negative.

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I still disagree that she's being stupid.

There's a great deal of difference between a 13% chance of losing and a 50% chance of losing.

The risk/benefit ratio is much smaller for 100 tosses than for one so her position seems eminantly sensible.

[wtfsvi]

As a non gambler, your friend will probably feel a lot worse if she loses X than she will feel good if she wins X*1.1. So her stance is perfectly reasonable.

[Hielko]

I always wonder what people like your friend will do when they make a lot of money. Savings account?.....