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re: 20k guaranteed or coin flip for 100k?
Posted on 7/1/16 at 9:45 am to shel311
Posted on 7/1/16 at 9:45 am to shel311
quote:
quote:If your goal is to do anything other than maximize EV, you're making the poorer choice out of possible outcomes
That's silly. It's only so based on math, math is obviously not the only factor here
What's silly is that people are debating this from two different rationales... If talking strictly just math, then yes, all people who say flip are correct. If we are talking based on current life situation, then you end up with a bunch of outcomes.
1
Posted on 7/1/16 at 9:45 am to TigerstuckinMS
That's the thing, it wouldn't be illogical. It would be smart.
Posted on 7/1/16 at 9:55 am to DrownEmTide
I'd take the $20k and spend it all to have a pleasant Korean woman call the coin flip losers every day to remind them they could have had $20k
Posted on 7/1/16 at 9:56 am to TigerstuckinMS
quote:
Once again, emotion and personal situation, feelings, etc. does NOT change the fundamental underlying math that tells you the flip is the best move.
I think a lot of you are missing the point. Just because you say "but, but, but, that's a lot of money and people have to factor that in!" doesn't mean squat. The mathematics say what the mathematics say. If your goal is to do anything other than maximize EV, you're making the poorer choice out of possible outcomes. Making the poorer choice is fine, but that's where you start bringing in risk aversion, emotion, etc., and that is not rational. A rational actor would flip every time because that's what math tells us is the optimal choice.
Let me introduce you to the St. Petersburg paradox...
quote:
A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, 8 dollars if a head appears on the first two tosses and a tail on the third, 16 dollars if a head appears on the first three tosses and a tail on the fourth, and so on. In short, the player wins 2^k dollars, where k equals number of tosses (k must be a whole number and greater than zero). What would be a fair price to pay the casino for entering the game?
Assuming the game can continue as long as the coin toss results in heads and in particular that the casino has unlimited resources, this sum grows without bound and so the expected win for repeated play is an infinite amount of money. Considering nothing but the expected value of the net change in one's monetary wealth, one should therefore play the game at any price if offered the opportunity.
This is what you're arguing, but you cannot simply ignore the real world application of the problem. In the real world you must consider the expected utility of money. That isn't emotional and it isn't some hocus pocus shite. The rational actor has to consider their own circumstances - you sort of conceded that point later in your post.
For the record, in the St. Petersburg paradox, the suggested values someone should pay based on their situation is as follows:
quote:
This formula gives an implicit relationship between the gambler's wealth and how much he should be willing to pay to play (specifically, any c that gives a positive change in expected utility). For example, with natural log utility, a millionaire ($1,000,000) should be willing to pay up to $20.88, a person with $1,000 should pay up to $10.95, a person with $2 should borrow $1.35 and pay up to $3.35.
Risk aversion or emotion is another issue altogether.
This post was edited on 7/1/16 at 10:19 am
Posted on 7/1/16 at 9:57 am to TigerstuckinMS
quote:
Just because I freely admit I'd act against logic and reason in that situation doesn't make the choice to take the money the logical or rational choice.
Of course it's the rational choice if you're talking about 20 million
Posted on 7/1/16 at 9:59 am to TigerstuckinMS
If someone said here's $20, but you can flip a coin for $100, everyone would say flip it. If someone said here's $20B, but you can flip a coin for $100B, everyone would take the money. This scenario has everything to do with the amount of money, and your financial situation, and very little to do with math and odds.
I personally would take the $20k. Would i take $20k out of my savings to win a $100k in a coin flip? Not at this moment in my life. Would i when i have more in savings, say somethign like $400k, yes.
I personally would take the $20k. Would i take $20k out of my savings to win a $100k in a coin flip? Not at this moment in my life. Would i when i have more in savings, say somethign like $400k, yes.
Posted on 7/1/16 at 9:59 am to Steadyhands
quote:
What's silly is that people are debating this from two different rationales... If talking strictly just math, then yes, all people who say flip are correct. If we are talking based on current life situation, then you end up with a bunch of outcomes.
And as noted as the numbers increase it is more rational to opt out and take the guaranteed money.
Just put it to the most extreme you can get. Let's say it's 2 trillion vs 10 trillion
Anyone that doesn't take the 2 trillion guaranteed is the biggest moron alive
Posted on 7/1/16 at 10:00 am to slackster
quote:
2k dollars
Hmmmmm....
Or did the format here get rid of the power
Posted on 7/1/16 at 10:19 am to StringedInstruments
Expected value is calculated by taking the probability of success and the number of trials. Given this scenario the probability of success in a coin flip is 1/2. The number of trials is 1, thus a 50% probability of success. the "expected value of this activity" would then be $50,000.
Given that the expected value of this activity is higher than the other ($20,000) you should always take the flip, because the expected value is higher.
Given that the expected value of this activity is higher than the other ($20,000) you should always take the flip, because the expected value is higher.
Posted on 7/1/16 at 10:19 am to castorinho
quote:
Hmmmmm....
Or did the format here get rid of the power
Yeah, it did. Nice catch. Thanks.
Posted on 7/1/16 at 10:25 am to LSU-MNCBABY
quote:
Expected value is calculated by taking the probability of success and the number of trials. Given this scenario the probability of success in a coin flip is 1/2. The number of trials is 1, thus a 50% probability of success. the "expected value of this activity" would then be $50,000.
Given that the expected value of this activity is higher than the other ($20,000) you should always take the flip, because the expected value is higher.
Well... now that we've cleared that up...
Posted on 7/1/16 at 10:32 am to Emiliooo
quote:
Law of probability:
$20,000 x 100% = $20,000
($100,000 x 50%) + ($0 x 50%) = $50,000
Therefore, $20,000 < $50,000
Accept the $100k scenario.
Are you saying that getting $50k is an option?
You either get 20k, 0 or 100k. Those are the only possible results. If 0 and 20 don't bear much separation in your world, take the coin flip. If 20k would solve financial issues for you (which is most people) then take the 20k. But don't be fooled into thinking that winning or losing the coin flip would both be better than 20k. Because only winning the coin flip is better. Losing the coin flip doesn't get you 50k, it gets you zero.
Posted on 7/1/16 at 10:34 am to DrownEmTide
You have a 50% chance at 5 to 1 odds. You're supposed to take that action.
Posted on 7/1/16 at 10:34 am to LSU-MNCBABY
quote:
Given that the expected value of this activity is higher than the other ($20,000) you should always take the flip, because the expected value is higher.
What if you owed the KGB 15k due tomorrow and you were flat broke?
Posted on 7/1/16 at 10:36 am to jacquespene8
quote:
You either get 20k, 0 or 100k. Those are the only possible results. If 0 and 20 don't bear much separation in your world, take the coin flip. If 20k would solve financial issues for you (which is most people) then take the 20k. But don't be fooled into thinking that winning or losing the coin flip would both be better than 20k. Because only winning the coin flip is better. Losing the coin flip doesn't get you 50k, it gets you zero.
Yeah, people are overthinking this.
Posted on 7/1/16 at 10:48 am to jacquespene8
quote:No. He's saying $50k is the expected value of the coin toss.
Are you saying that getting $50k is an option?
quote:Who implied that?
But don't be fooled into thinking that winning or losing the coin flip would both be better than 20k.
This post was edited on 7/1/16 at 10:49 am
Posted on 7/1/16 at 10:54 am to Powerman
quote:
Just put it to the most extreme you can get. Let's say it's 2 trillion vs 10 trillion
Anyone that doesn't take the 2 trillion guaranteed is the biggest moron alive
I dunno, $2Trillion is more than the GDP of all but the 8 or 9 most economically powerful countries... but $10Trillion and you would only be behind China and the USofA.
Posted on 7/1/16 at 11:06 am to shel311
quote:
quote:
Are you saying that getting $50k is an option?
No. He's saying $50k is the expected value of the coin toss.
quote:
But don't be fooled into thinking that winning or losing the coin flip would both be better than 20k.
Who implied that?
He said that since 50k is greater than 20k, then you should take the coin toss. He compared an average to a pile of cash.
Look, I got an A in statistics at LSU too. I can understand how incensed one would be that the almighty being responsible for making this head scratching offer had the gall to offer a guarantee that is lower than the "expected value" according to the law of probability. But the truth is that most people would be more wise to compare the guaranteed offer against the worst case scenario, not some average of possible outcomes.
I'm not in bad shape financially, but if I was walking down the street and somebody said, " I'll give you 20k or.....," I would probably just stop them and take the 20k right then and there.
Posted on 7/1/16 at 11:08 am to LSUBoo
quote:
I dunno, $2Trillion is more than the GDP of all but the 8 or 9 most economically powerful countries... but $10Trillion and you would only be behind China and the USofA.
Right.
Make the number as absurd as you want.
The larger the number, the dumber you'd have to be to flip the coin.
Posted on 7/1/16 at 11:11 am to jacquespene8
quote:
He said that since 50k is greater than 20k, then you should take the coin toss. He compared an average to a pile of cash.
Look, I got an A in statistics at LSU too. I can understand how incensed one would be that the almighty being responsible for making this head scratching offer had the gall to offer a guarantee that is lower than the "expected value" according to the law of probability. But the truth is that most people would be more wise to compare the guaranteed offer against the worst case scenario, not some average of possible outcomes.
Right. I'd imagine even a probability professor would consider taking the 20K. Because they're probably not that wealthy to begin with and the guarantee would be tempting.
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