Sort of following on from Ron's 'AA' thread, two scenarios for you

[Dorkus Malorkus]

I'm making a separate thread for this so I can make a poll. Keep discussing the hand (if you must ) in that thread, this thread is just intended as a 'fun' little aside.

Scenario A

A man walks up to you, says he's feeling very generous today, and offers you a choice of two one-time only deals.

1) He gives you $1m, no questions asked, there and then.

2) He offers you the chance to flip a coin. If it comes up heads, he will give you $3m there and then, if it comes up tails, you get nothing.

You know this man is honest and the coin is completely unbiased (it's a hypothetical question, let's not go down that route). Do you take option 1 or 2?

Scenario B

A man walks up to you, says he's feeling very generous today, and offers you a choice of two one-time only deals.

1) He gives you $3m, no questions asked, there and then.

2) He offers you the chance to flip a coin. If it comes up heads, he will give you $2m there and then, if it comes up tails he will give you $5m.

Again, you know this man is honest and the coin is completely unbiased. Do you take option 1 or 2? Should we be more inclined to take option 1 or 2 than we are in Scenario A, and if so why? What's the practical 'difference' between the scenarios (note that in both scenarios the $EV difference between options 1 and 2 is exactly the same - $500k)?

 

[amygrantfan]

i would take the straight up cash and not do the coin toss in scenario A. I would toss the coin in scenario B. i know the EV is better for both if you flip the coin. however, i want to be guaranteed money. i would give up the higher EV for the guarantee.

 

[mrsnake3695]

In A I take the million and spend it on Hookers and drugs.

In B I flip the coin and spend it on even more hookers and drugs.

 

[extrachrisb]

Of course I'm going to pick Scenario A Option 1, Scenario B Option 2.

What about if you added a hard kick in the nuts? That might change the outcome

"He offers you the chance to flip a coin but first, he gets to kick you in the nuts first as hard as he can. If it comes up heads, he will give you $2m there and then, if it comes up tails he will give you $5m."

 

[brutus]

in scenario 1 id take the money and head straight to Vegas, i want the guaranteed money

in scenario 2 id flip the coin, either way im a millionaire. though knowing my luck the coin would land on its side and stay there and i would win nothing

 

[Goldog]

Looks like few of us are rich enough to worry about EV in senario 1.

Goldog

 

[Emperor IX]

I think that I'll go with EVERYONE here. A:1 B:2

 

[tenbob]

lol variance. Obv wealth depandant. Option B, flipament.

 

[KMC1828]

ill just take all the guaranteed money and invest most of it, thanks. make money off my money

 

[BillLeaf]

Well I am one who answered option 2 for both. I could walk away with the money sure, but I would always be doing the what if. I am a gambler, I will admit it. I have done this sort of thing with a lot less involved, but I don't think the amount would change the way I act.

I will let you know when it happens if I did it or not.

 

[dj11]

Scenario A - A bird in the hand is worth 2 in the bush. I take the 1 mil guaranteed.

Scenario B - Ah ha!, a little wiggle room, lets gamble!


I'm with snake......

 

[t1riel]

Scenario A: I'll take the million. You are guaranteed money in this situation. Why risk it for two million more?

Scenario B: I would do the coin flip. You are guaranteed 2 million if you lose. Which is 1 million less than what you get if you just take the cash. So, you are gambling 33% of what you would have gotten if you didn't take the coin flip to win 66% more.

 

[amygrantfan]

Well I am one who answered option 2 for both. I could walk away with the money sure, but I would always be doing the what if. I am a gambler, I will admit it. I have done this sort of thing with a lot less involved, but I don't think the amount would change the way I act.

I will let you know when it happens if I did it or not.

it is a gamble, but y'know, you are the only one making the right "pot odds" decision amongst all of us

 

[amygrantfan]

lol variance. Obv wealth depandant. Option B, flipament.

i iddn't even think about the wealth dependent aspect. but you are totally right. if i was a multi millionaire already, i'd prolly pick B in both cases because it's a better EV. so I guess i will have to worry about that scenario after I come back from vegas this weekend with my multi millions

 

[bw07507]

Lol, I think Im the first one to say this, but Id do option one for both of the scenarios. In the second scenario I dont think I could risk that extra guaranteed million on a coin flip.

 

[skoldpadda]

Knock him on the noggin and take all his loot.

 

[Emperor IX]

Well I am one who answered option 2 for both. I could walk away with the money sure, but I would always be doing the what if. I am a gambler, I will admit it. I have done this sort of thing with a lot less involved, but I don't think the amount would change the way I act.

I will let you know when it happens if I did it or not.

And while all of us in scenario one sit there with our million you'll be sitting in the observer box saying "SOMEONE GIVE ME TEN BUCKS"

 

[BillLeaf]

OK, here's a question or everybody who wants to take the guaranteed money. How much does it have to be with the same odds for you to take the guaranteed money. Where is your line that makes the guaranty the way to go. $50, $100, $1000, ...

The odds don't change so why should your decision? If it does.

 

[BillLeaf]

And while all of us in scenario one sit there with our million you'll be sitting in the observer box saying "SOMEONE GIVE ME TEN BUCKS"

More likely continuing doing what I am doing now. Enjoying the life that I already have.

 

[Emperor IX]

OK, here's a question or everybody who wants to take the guaranteed money. How much does it have to be with the same odds for you to take the guaranteed money. Where is your line that makes the guaranty the way to go. $50, $100, $1000, ...

The odds don't change so why should your decision? If it does.

Um, because $1m is life changing and $10 is day changing. Anything $100 or up I'd take the guaruntee.

 

[dj11]

In the original post (OP), there is no down side to scenario 2, so obviously we all choose that.

In scenario 1, there is a serious gamble, with a devastating downside, it would be just like that munificent stranger never made the offer. But since the offer is made at those odds I prefer to profit with a 100 % win decision.

 

[shinedown.45]

In scenario 1 I would take the coin flip, sure the guaranteed 1 mil is very enticing but the thought of winning 3 mil on a coin flip is even better and if I lose the coin flip all I have really lost here is the time it took to flip the coin.
Scenario 2 is really a no-brainer, guaranteed money no matter the out come.

 

[Afterlife000]

I would take the money in scenario 1, and flip the coin in scenario 2.

 

[Dorkus Malorkus]

I was hoping someone who voted fold in the AA thread said A1B2 here so I could yell at them.

In the original post (OP), there is no down side to scenario 2, so obviously we all choose that.
In scenario 1, there is a serious gamble, with a devastating downside, it would be just like that munificent stranger never made the offer. But since the offer is made at those odds I prefer to profit with a 100 % win decision.

Yeah, this summarises everything pretty well. As I briefly mentioned in the thread but intentionally avoided going into any detail over, it's utility theory.

It's actually not all that different from the principles governing fluctuating chip values in tournaments. Invariably, the more of something you have, the less satisfying any additions of that particular something are, just as in a tournament the more chips you have, the less true value additional chips have.

Imagine a big box of chocolates. Compare the satisfaction you get from the first chocolate to the satisfaction you get from the 30th chocolate, and then try and plot a graph of 'satisfaction' for all the chocolates you eat in between (you fat bastard). You should get a downward-sloping curve - the gradient of which will level out close to (or at) zero after a certain point, depending on your tolerance for chocolates.

The same can be said of money. The inherent 'difference' between the two examples is the outcome should one take the coinflip and lose. Instead of thinking in terms of chocolates, now think in terms of millions of pounds. You gain a huge amount of satisfation from your first million pounds, but that diminishes for every consecutive million, so much so even only after a couple of million that in the examples given most people who want the guaranteed money in Scenario 1 are willing to take the 'gamble' in Scenario 2. For what it's worth, I agree. Although taking the guaranteed money in Scenario 1 is a -EV decision, the utility one gains from the first million is so far in excess of the utility one gains from the extra $500k in EV (this is, incidentally, assuming we're not very wealthy to start with), that taking the money is the most practical option.

As the utility curve mentioned above (except in terms of $m, not chocolates ^^) goes down and levels out, the EV of the decision becomes more important, so again, people will take the 'gamble' in Scenario 2.

The whole of Ron's AA thread hinges on the steepness of each person's specific $m utility curve. Some people will find a second million much more/less satisfying than others. The more satisfying one finds the second million, the more one should be inclined to fold, despite it being -EV. I'd argue that from my perspective the second million is worth nowhere near as much as the first million in terms of utility, and so EV should be the overriding concern in my decision-making at this point. That said, and despite what I've said and/or implied in the thread, I've come to the conclusion that there isn't really a 'wrong' answer to Ron's question, because ultimately it can be boiled down to a scenario not unlike the two in the OP. I'm too lazy to do the maths in order to do this, but it lies somewhere between the two above cases.

 

[CaptnDaveCoulthard]

If You Pick To Gamble In Scenario One And Lose, You Kick The Guy In The Nuts And Take His Coin! Everyones A Winner! In Scenario Two You Gamble And Even If You Win Big Kick Him In The Nuts And Take His Coin! You Can Never Have Too Much Money!