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40 members have voted
But considering pure EV can be a bad choice: would you pay all your current wealth to push the green button ?
Deal or No Deal is largely based on this type of question. When large amounts of money are involved (in the six figures) and few cases left, the banker offer will be much less than fair value, based on the shows I have watched.
You have to compare the 50% chance of being a suicidal assh*le who blew his peace of hind and his release with a 100% chance of getting on "moderate" easy street. Get the $1M.
Now, if it were $1 and a $100 bill, then the green.
Hey - 1000 posts! I'm hoping I get an exclusive members only jacket or something.
Quote: WizardAccording to the economic theory that happiness is proportional to the log of your wealth, you should be indifferent with wealth of $20,833.33. With more, go for the 50 million, with less take the sure one million.
Deal or No Deal is largely based on this type of question. When large amounts of money are involved (in the six figures) and few cases left, the banker offer will be much less than fair value, based on the shows I have watched.
Not quite sure how that log thing works? It seems a bit low to say I'm indifferent at $20k though. I'd have to have at least $1 million before I didn't take another million without risk.
Quote: thecesspitNot quite sure how that log thing works
You maximize the expected logarithm of your total wealth.
If W is your current total wealth, then the expected logaritmic wealth for the red button is log(W + $1M).
For the green button it is 0.5 * log(W) + 0.5 * log(W + $100M).
Hence the Threshold is at log(W + $1M) = 0.5 * log(W) + 0.5 * log(W + $100M), which resolves to W = $1M/98 ~ $10k.
Edit: missed the colors
I chose the Red button. I think about all the things I could do with the $1 million dollars. If I make the right choices I could turn the $1 million into $100 million on my own!
Quote: WizardAccording to the economic theory that happiness is proportional to the log of your wealth, you should be indifferent with wealth of $20,833.33. With more, go for the 50 million, with less take the sure one million.
Deal or No Deal is largely based on this type of question. When large amounts of money are involved (in the six figures) and few cases left, the banker offer will be much less than fair value, based on the shows I have watched.
Well according to your first sentence that means I should've picked the green button. But, alas, I believe in making money with money so even if I could never turn $1 million into $100 million I sure could multiply it a whole lot. What a risk to push the green button, too scary for me!
But the funny thing is, before I saw you comment on the Deal or No Deal, when originally thinking about how to answer the question, I thought in this case I would choose the $1 million but if I were on Deal or No Deal I would play all the way to the end. That would be my game plan on the show but don't know if while I was on the show and in the middle of it all if m emotions would give in and I'd take the Banker's offer without hanging on till the very end!
They give me $25M, and I press the green button. If I win I pay them $75M.
They get very generous 3.0 odds on an even shot, and I get $25M to settly my families lifes and a $25M shot.
A million would pay off my mortgage and I'd have no problems paying for my kids college expenses.
Quote: FinsRuleHey - 1000 posts! I'm hoping I get an exclusive members only jacket or something.
It will be sent to you as long as you don't post a 1001st entry. Please reply to this post with your jacket size.... :)
It's only a factor of 100 to get from $1 million to $100 million. It's divine intervention to turn nothing into $1 million.Quote: Nareed...it's easier to turn $1 million into $100 million, than to turn $0 into $1 million.
But if you had $10,000 to turn into $1 million, would it be more difficult? Potentially, seven hands of no limit Baccarat would be all that would be needed in either case.
Quote: AyecarumbaIt's only a factor of 100 to get from $1 million to $100 million. It's divine intervention to turn nothing into $1 million.
You begin to see the problem.
Quote:But if you had $10,000 to turn into $1 million, would it be more difficult? Potentially, seven hands of no limit Baccarat would be all that would be needed in either case.
I wouldn't try it gambling.
But I think it's easier to turn $1 million into $100 million than $10,000 into $1 million. Suppose you start with a small business. It's far easier to capitalize that business if you have $1 million, and easier to obtain some kind of credit, too.
If the payouts were identical, but the probabilities were 90% and 45%, and you had to buy in for $10K, then which button would you push?
an open briefcase on the left with a million dollars in it.
On the right there's 100 open briefcases with a million
dollars in each. Now which button do you push.
Quote: MangoJYou maximize the expected logarithm of your total wealth.
If W is your current total wealth, then the expected logaritmic wealth for the red button is log(W + $1M).
For the green button it is 0.5 * log(W) + 0.5 * log(W + $100M).
Hence the Threshold is at log(W + $1M) = 0.5 * log(W) + 0.5 * log(W + $100M), which resolves to W = $1M/98 ~ $10k.
Edit: missed the colors
Thanks. I'd suggest log-base-10 might not be correct... $10k = 4 Happy, $1M = 6 Happy. I'm not going to be only 1.5 times as comfortable and hence happy with a 100-fold increase, but the difference between 1M and 100M is lesser (though still a 100-fold increase). I'd suggest there needs to be a fudge factor in there.
Quote: WizardI would argue that it resolves to $1M/48.
I just took the answer from WolframAlpha which I usually trust (W in millions $).
Quote: thecesspitI'd suggest log-base-10 might not be correct..
The base of the logarithm is irrelevant, as it cancels on both sides: log_a(x) = log(x) / log(a). You can choose the base to whatever is convenient for you (it's just a common prefactor of the *log*, not of the wealth).
Quote: thecesspitThanks, yes, you are right. Playing with this on wolfram alpha points out the error of my ways.
If you assume there's a base amount of money I need to have any happiness say $10,000 :
log(W + 1) - log(0.01) = (0.5 * (log(W)-log(0.01)) + 0.5 * (log(W + 100)-log(0.01))
(calculating W in millions)
=> W = 0.137 or $137,000 before I should gamble.
If my base line is $100k, then W = $546,000
These seem more 'real' to me. Granted I may have screwed up again. (Used Wolfram Alpha)
If you wan't a "level of happiness" (say you have a 10k dept) you should substract 10k from W. Then you obviously would need 20k (10k more) more before you push the green button.
There is still debate whether W is your absolute total wealth (including your paid house, college savings) or just the amount you're comfortable spending.
In my humble interpreation of Kelly W *is* your total wealth (i.e. the amount you would be able to spend in a life-threatening event without any help of others) for the simple reason that log(W) diverges at W<=0. In this interpretation you should intrinsically never ever do a bet which has a non-zero probability where you need to spend more than you could possibly afford (which kind of seems a reasonable result).
But when it comes to Kelly betting, there is actually no convincing mandatory reason to stick to Kelly.
The amount does make a difference, though. If there were a $500 slot machine, and I only had $500 to my name, but you could spin it with a 50/50 chance of turning it into $50,000, I'd take that chance in a heartbeat. I tend to look at it from the standpoint of actually owning everything I own vs. its opposite. With either the $1,000,000 or 100 million, I now own everything that I own.
I believe that Deal or No Deal takes the mean amount of the cases and subtracts 15-30% situationally. I've noticed that they occasionally go with the straight mean (and sometimes a little better) on the last two cases, but I think that's because they think the player is going to take the shot. The mean - 15-30% is attractive for DoND because it is less than the fair value, but is also attractive to the player because (with the way the cases are graduated) it still usually ends up being a greater amount than the median case, or average of the two median cases on an even number.
Then I thought about taxes. 600k sounds a lot worse than 1 million. I still think I'd go red though, I'm just less certain.
Sir, you grossly overestimate my net worth !
Quote: pacomartinIt is not that difficult to understand that "even money" has the same probability as insurance on any other bet, but people will still take it despite understanding the concept.
Here's an interesting quiz: See how many dealers (outside of Vegas... eh, leave Vegas in the mix) would be able to tell you that the concept of taking "even money" is the same as taking insurance. I've gotten into many an argument with a dealer otherwise. In Illinois (or Missouri), it is classified as a separate bet, but other than the occasional dealer who actually halfway understand Spanish, I'd place the odds that less than 30% of dealers get the concept of even money = insurance.
As for the original question, for a million dollars, there is 0% chance I would ever consider pressing the green button. While a million dollars wouldn't change my life drastically, it would help it enough that I could pursue having a house, a car, etc.
If it were between 1000 and 100,000, I'd consider pressing the green button, if I knew it were truly a 50/50 chance to win 100,000.
I have always had a problem with buying LIFE insurance.
They want to bet I will life to a ripe old age and I want to bet they are wrong ?
Once while playing in Biloxi,I forgot to take even money but put up the insurance bet,when the dealer turned over her Blackjack she didn`t know what to do.
She tried to take my main bet but I insisted it was a push. She then had to call the floor who refused to pay the insurance bet.The pit boss came and she had to call the shift boss.The shift said he would have to call surveillance.It took 20 minutes to resolve such a simple thing. They then said "don`t do it again or we won`t pay you next time".
Would an older person, say over 60, be more willing to take the higher-risk choice? Or do younger people traditionally go for high-risk/high-reward?
Quote: rudeboyoiso many pessimists here, your life isnt going to be that much different with $1mil but vastly different with $100mil. go for green!
I disagree strongly. If I end up with 600k, then I would still pay off my mortgage, pay off the car that I do not own outright (I own an older one outright), pay off my personal loan, pay off my student loans, pay off my wife's student loans, and still have $481,000 left to invest. I'd be kicking ass, guaranteed! I would keep my job (and have a ton of extra money) and use the ROI to put my kids through college as well as buy new vehicles, as needed.
It would be awesome!!!
If I had the 100 million (or whatever it is after taxes), then I'd basically have to quit my job, trust other people to manage my money, I'd probably have to move, and I really love where I live right now because I am near all of my family. People would be hounding me for cash, they would treat me differently, I'd have this-or-that charity up my ass constantly when I prefer to decide...without solicitation...where my donations will go.
It would just be a mess. I can't even say for sure whether or not I would even want the 100 million. It would be a tremendous headache, but there are obviously great positives that go along with it. I think with the 600k, though, I could take care of everything, never have to take out a loan for anything again, and my life would remain otherwise unaffected.
Quote: SOOPOOA million is a lot of money, but not enough to never work a day.... 100 million is enough to never think about money again, and enough to always be in position to help others. My guess is that anyone who would select the easy million would likely use it, not grow it.
I would grow that which was not used to pay off any outstanding loans. I'd also donate a good percentage of my ROI, for what it's worth. I donate pretty kindly now, in my opinion, when you compare my donations to my earnings.
Quote: Mission146I disagree strongly. If I end up with 600k, then I would still pay off my mortgage, pay off the car that I do not own outright (I own an older one outright), pay off my personal loan, pay off my student loans, pay off my wife's student loans, and still have $481,000 left to invest. I'd be kicking ass, guaranteed! I would keep my job (and have a ton of extra money) and use the ROI to put my kids through college as well as buy new vehicles, as needed.
It would be awesome!!!
If I had the 100 million (or whatever it is after taxes), then I'd basically have to quit my job, trust other people to manage my money, I'd probably have to move, and I really love where I live right now because I am near all of my family. People would be hounding me for cash, they would treat me differently, I'd have this-or-that charity up my ass constantly when I prefer to decide...without solicitation...where my donations will go.
It would just be a mess. I can't even say for sure whether or not I would even want the 100 million. It would be a tremendous headache, but there are obviously great positives that go along with it. I think with the 600k, though, I could take care of everything, never have to take out a loan for anything again, and my life would remain otherwise unaffected.
youre still living the same life though. whether youre in debt now or have your debts paid off youre still utilizing the same things. whether you live in a house that has a mortgage or doesnt have a mortgage youre still living in that house!
Quote: Mission146If I had the 100 million (or whatever it is after taxes), then I'd basically have to quit my job, trust other people to manage my money, I'd probably have to move, and I really love where I live right now because I am near all of my family. People would be hounding me for cash, they would treat me differently, I'd have this-or-that charity up my ass constantly when I prefer to decide...without solicitation...where my donations will go.
If you ever win $100 million and face such a dire situation, I solemly pledge to relieve you of as much as your burden as you care to lay on me ;)
Quote: rudeboyoiyoure still living the same life though. whether youre in debt now or have your debts paid off youre still utilizing the same things. whether you live in a house that has a mortgage or doesnt have a mortgage youre still living in that house!
I understand exactly what you are saying, but I rather like my house. I have a nice four-bedroom, two-bath, two-story with an eat-in kitchen and a mud room. It sits on about an acre of land. I have an attached garage and a detached garage. The upstairs has two of the bedrooms as well as the largest bathroomm with a walk-in closet and walk-in shower. I have a large front porch. I have a garden, apple trees, a pear tree and some grape vines. In the rearmost part of the property I have a really cool brick burn pit that I built, so we have fires out there every now and again.
It's everything my wife and I want in a house, and it's doubtful that we would move if we had the opportunity. I was actually recruited for a hotel management job in Omaha, and I could have sold my house at an anticipated profit of 20k, and I would have made more at the other job...even adjusting the increased income against the cost-of-living index, but I declined.
Quote: NareedIf you ever win $100 million and face such a dire situation, I solemly pledge to relieve you of as much as your burden as you care to lay on me ;)
Your generosity knows no bounds. ;)
Quote: rudeboyoiyoure still living the same life though. whether youre in debt now or have your debts paid off youre still utilizing the same things. whether you live in a house that has a mortgage or doesnt have a mortgage youre still living in that house!
I don't technically have a house, the bank owns my truck, and the ex wife has pretty much everything else. I'd still take the million. The joy of a million subtracted by the sadness of no 100mil is greater number than the joy of a possible 100mil subtracted by the furious rage of blowing it and having nothing.