1827: "Survivorship Bias"

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Jorpho
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1827: "Survivorship Bias"

Title Text: They say you can't argue with results, but what kind of defeatest attitude is that? If you stick with it, you can argue with ANYTHING.

Firefox says "deafeatest" is spelled wrong. Think it'll get fixed? [EDIT: It was.]

This echoes a lovely bit of advice from Bo Burnham that has been circulating of late.
Spoiler:
Last edited by Jorpho on Tue May 02, 2017 8:52 pm UTC, edited 1 time in total.

rhomboidal
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Re: 1827: "Survivorship Bias"

He's convinced me: I will never stop trying to steal money bags from lecturing lottery winners.

Soupspoon
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Re: 1827: "Survivorship Bias"

I always play winning numbers in lotteries.

Ok, so they were previously winning numbers, but they've got just as much chance of (re-)winning next time round as any other set, the people who once won with them probably aren't going to be continuing (to split the jackpot) and how many other new people will willingly jump onto the exact same bandwagon, eh?

da Doctah
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Re: 1827: "Survivorship Bias"

I once put my math degree to work and figured out what you'd have to do to guarantee winning at least some prize in every drawing. At the time, my state's lottery paid off for four, five, or six matching numbers. I was able to determine that you could have every possible four-number combination covered with no more than about 500 tickets, sold at a buck apiece (and it was still possible that you'd have more than four, but four was guaranteed).

Thus, for an investment of \$500 per week, you were assured of being a winner every time and pocketing a prize that averaged about \$40.

(Math is hard; let's go shopping.)

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Re: 1827: "Survivorship Bias"

Znirk
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Re: 1827: "Survivorship Bias"

Soupspoon wrote:I always play winning numbers in lotteries.

Ok, so they were previously winning numbers, but they've got just as much chance of (re-)winning next time round as any other set, the people who once won with them probably aren't going to be continuing (to split the jackpot) and how many other new people will willingly jump onto the exact same bandwagon, eh?

Wait. Are you saying that previous winners will move on to different numbers because they will expect people to jump on the same bandwagon as you, but you yourself are convinced there won't actually be much of a bandwagon so you are safe to jump on it all by yourself?

Anyway, that reminds me of a half-remembered, possibly-urban-legend, almost-certainly-exaggerated story about that one time the German jackpot was split so many ways that getting all 6 numbers right ended up paying out less per winner than having only 5 correct guesses. After some confused investigation 'they' noticed that most of the winners were concentrated in the northwest, and then they discovered the exact same numbers had won in the Dutch lottery the previous week.

Old Bruce
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Re: 1827: "Survivorship Bias"

Znirk wrote:... that reminds me of a half-remembered, possibly-urban-legend, almost-certainly-exaggerated story about that one time the German jackpot was split so many ways that getting all 6 numbers right ended up paying out less per winner than having only 5 correct guesses. After some confused investigation 'they' noticed that most of the winners were concentrated in the northwest, and then they discovered the exact same numbers had won in the Dutch lottery the previous week.

Sounds too good to be true, so I'll believe it.

drazen
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Re: 1827: "Survivorship Bias"

The lottery makes money because average people are frequently not consciously rational have an odd bias towards skewed payoff distributions (huge payoffs with low odds tend to overwhelm modest ones with better odds). I do wonder if there was some evolutionary point to this a million years ago.

speising
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Re: 1827: "Survivorship Bias"

drazen wrote:The lottery makes money because average people are frequently not consciously rational have an odd bias towards skewed payoff distributions (huge payoffs with low odds tend to overwhelm modest ones with better odds). I do wonder if there was some evolutionary point to this a million years ago.

The point is in the comic title, isn't it?
The ones that braved the mammoth and got trampled didn't propagate their genes, but the few lucky ones who got a nice meal out of the beast did.

The Moomin
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Re: 1827: "Survivorship Bias"

Znirk wrote:
Soupspoon wrote:I always play winning numbers in lotteries.

Ok, so they were previously winning numbers, but they've got just as much chance of (re-)winning next time round as any other set, the people who once won with them probably aren't going to be continuing (to split the jackpot) and how many other new people will willingly jump onto the exact same bandwagon, eh?

Wait. Are you saying that previous winners will move on to different numbers because they will expect people to jump on the same bandwagon as you, but you yourself are convinced there won't actually be much of a bandwagon so you are safe to jump on it all by yourself?

Anyway, that reminds me of a half-remembered, possibly-urban-legend, almost-certainly-exaggerated story about that one time the German jackpot was split so many ways that getting all 6 numbers right ended up paying out less per winner than having only 5 correct guesses. After some confused investigation 'they' noticed that most of the winners were concentrated in the northwest, and then they discovered the exact same numbers had won in the Dutch lottery the previous week.

In the UK something similar did actually happen in 2014.

If you match three numbers now, you're guaranteed a pay-out of £25.
If you match more than three numbers, you get a split of the total money allocated for that prize bracket.
So many people matched four numbers, the prize was £15 each. Much complaining ensued.
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speising
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Re: 1827: "Survivorship Bias"

Also part of "Bruce Almighty"'s plot.

Steve the Pocket
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Re: 1827: "Survivorship Bias"

I remember Thas K. Dye of Newshounds fame had a good rant about this, how people in showbiz practically make a religion out of the reckless abandon it takes to even try to make it in the entertainment industry. Meanwhile he never quit his day job and continues to treat his successful webcomic as a hobby that he can sometimes make money from, and that's probably the only reason he hasn't starved to death.

Or something to that effect. It was years ago and on who-knows-what platform.
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cellocgw
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Re: 1827: "Survivorship Bias"

Old Bruce wrote:
Znirk wrote:... that reminds me of a half-remembered, possibly-urban-legend, almost-certainly-exaggerated story about that one time the German jackpot was split so many ways that getting all 6 numbers right ended up paying out less per winner than having only 5 correct guesses. After some confused investigation 'they' noticed that most of the winners were concentrated in the northwest, and then they discovered the exact same numbers had won in the Dutch lottery the previous week.

Sounds too good to be true, so I'll believe it.

It definitely did happen once in one of the Massachusetts lotteries. I forget what they did to try to correct that situation, but I think they gave everyone the equivalent of the second-place payout.

Meanwhile, I think I'll send this comic to every jackass who quotes Edison's 10 000 non-failures .
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Re: 1827: "Survivorship Bias"

Don't forget a prayer to Cthulhu, the god of lottery scratchers.

Soupspoon
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Re: 1827: "Survivorship Bias"

Znirk wrote:Wait. Are you saying that previous winners will move on to different numbers because they will expect people to jump on the same bandwagon as you, but you yourself are convinced there won't actually be much of a bandwagon so you are safe to jump on it all by yourself?

Actually, I was saying as how the winners (of the whole jackpot all-numbers-match, or the next tier down even) have... won! So why would they want to continue to play the lottery with numbers that have already won, so are unlikely (sic!) to turn up again. (Yes, I'm assumng people playing the lottery don't have the understanding of the odds1. That's why they play the lottery...)

Actually, when I participated in a lottery syndicate in a past job (the personal rationale being that if I was the only non-winner in the department, it would have been aawwkkwwaarrdd...) I chose my own contributive numbers by taking all past results (there hadn't been that many, but enough to do this without huge gaps of "not appeared yet" numbers) and discarding the most frequent ones (as likely to be chosen by those who analysed for "lucky numbers", and the least frequent ones (as likely to be chosen by those who thought that "their time would come") and left myself with the most median-performing set.

I suppose I could have looked at the 1st/3rd quartiles, or 2nd/3rd quintiles (probably from the least frequent side, because of "reversion to the mean", right? But the aim was not to beat the Lottery Machine, but to avoid landing on guesses by the average punter (I also saw that the numbers concerned were already fairly statistically skewed against "those that could be derived from birthdays"2, as it happened, so I didn't end up doing any further adjustment to remove that factor) and if we happened to share the jackpot with several groups of similarly-inclined (and probably liable-to-be-defrocked!) statisticians, then it'd make a good paper for combined submission to a journal, eh?

It all comes down to the whole "lost in a park" thing? If you're a (rational) lost child, do you run all over, hoping to bump into your parent, or do you stand somewhere hoping that the searching parent (who you don't anticipate will also stand and wait, obviously) will happen across you. (Not a perfect analogy. Unlike lotteries, parents have memories, but that's why the most rational/pre-agreed party should stand still, the moving party excluding pre-searched space in whatever manner. If both move then the search space cannot be excluded. Although landscape features to search around, repeatedly, might come to the fore. I'm sure there's studies on this.)

These days, there's a Lucky Dip option, on the UK lottery (one of them, probably also the other, I don't know much about that one), so asking the PRNG to pick numbers that might win in the RNG sounds like what I should do these days (with no 'park memory', it's actually just more against picking the same numbers as others, although I now get no power to veer away from birthday numbers, as per footnote 2), with the additional psychological effect of not being 'attached' to a set of numbers, howsoever one personally chose them, then saw them come up a week or two after the brief (mad!) experimemt was over. Play for the day, and let it go!

And good luck to everybody who plays the lottery! (Everybody. Thus keeping things even. Why should I play favourites? If it's not me that is favoured, that is.)

1 Or, just from first principles, if half the money paid in comes out as prizes (the rest to "good causes" and the company running costs and profits) then the ROI of an average play is -50%3... It's almost a pyramid scheme.
2 Every birthday has a 1 in 12 chance of having a particular number from 1 to 12 from the month, then there's the overlapping 1 to 28 (all the months), trailing off to 1 to 31 (half the months), that get days picked, per birthday tried. I ignored the years. Couldn't begrudge the old people who could choose 1..49 directly from personal or perhaps parental birthdays, and the rest is stuff like house numbers (Benford's Law rules there), but I didn't bother with that, or I might have been accused of overthinking the problem!
3 In a quick (unscientific) analysis of the lottery results since it converted to 1..59, over here, and a new prize structure, pitting my rand() function against what actually happened I get roughly 25% of the stakes I put in back as prizes (counting "lucky dips" rewards as if the cash equivalent, which I then use in place of investing new cash next time round, and never once getting a valuable variable prize to worry about how that skewed things), but then there seems to be an auxiliary 'thing' now with Millionaire Raffle Numbers given out for every number-line chosen, so that'd be giving me the other 25% (in a PRNG vs PRNG competition?) of the half-the-money-back-as-prizes (smeered out, that is, rather than "millionare or nuthin'...").

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Re: 1827: "Survivorship Bias"

How much money is in those five small bags compared to the total sum that he "poured into tickets"?

Vorticity
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Re: 1827: "Survivorship Bias"

speising wrote:The ones that braved the mammoth and got trampled didn't propagate their genes, but the few lucky ones who got a nice meal out of the beast did.

Also, the Puppeteers have been breeding us for luck.

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Re: 1827: "Survivorship Bias"

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Re: 1827: "Survivorship Bias"

Vorticity wrote:
speising wrote:The ones that braved the mammoth and got trampled didn't propagate their genes, but the few lucky ones who got a nice meal out of the beast did.

Also, the Puppeteers have been breeding us for luck.

Never thought I'd see a Ringworld reference on this comic. Winning.
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Re: 1827: "Survivorship Bias"

cellocgw wrote: I think I'll send this comic to every jackass who quotes Edison's 10 000 non-failures .
I think either you (or the jackass quoting it) is missing the point.

Inventing something is a progressive act, and the odds change with each attempt. Also, on entering this task the inventor has already decided that 700 attempts is a worthwhile cost for success.

The lottery player (by contrast), is obviously not calculating (or caring about) the fact that the lottery ticket has a -60% RoI.
Soupspoon wrote:the personal rationale being that if I was the only non-winner in the department, it would have been aawwkkwwaarrdd..
Or, on the other hand, you would have gotten a great story and a promotion to acting head of department (you have to quit your job after winning the lottery, that's (like) a law or something).
And good luck to everybody who plays the lottery! (Everybody. Thus keeping things even. Why should I play favorites? If it's not me that is favoured, that is.)
Well, the house can lose through freak probabilities, so that kind of make sense.
speising wrote:
drazen wrote:The lottery makes money because average people are frequently not consciously rational have an odd bias towards skewed payoff distributions (huge payoffs with low odds tend to overwhelm modest ones with better odds). I do wonder if there was some evolutionary point to this a million years ago.

The point is in the comic title, isn't it?
The ones that braved the mammoth and got trampled didn't propagate their genes, but the few lucky ones who got a nice meal out of the beast did.
I think a big part of it is just that our instincts are not mathematically precise. Great thing * small chance = good thing

Or rather, because of Fechner's law:
ln (Great thing) + ln(small chance) = ln (good thing)
With the error margin being logarithmic.
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orthogon
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Re: 1827: "Survivorship Bias"

I think there's partly a problem of intuitive perception, but I make an argument that playing the lottery isn't so irrational after all. The expected ROI might be -60%, but the probability of winning the jackpot is so low that this expectation isn't really meaningful for an individual. Playing fruit machines is a mug's game, since for practical purposes you're definitely going to lose more or less the expected amount. But on the lottery you're either going to win the big prize once in your life or (probably) never. If you do win, you've beaten the house. Who cares what you'd win if you lived for a million years?
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1827: "Survivorship Bias"

Soupspoon
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Re: 1827: "Survivorship Bias"

orthogon wrote:If you do win [the lottery], you've beaten the house.

You don't beat the house in a (competantly planned) lottery. You can beat the casino by getting red or black (or green(s)) guessed correctly more than you statistically should, but prize funds in a lottery will be suitably defined fractions of the income of a lottery and the house knows that will be paying out half (or notably less, it seems, for other quoted lotteries) of the income in prizes, give or take some no-claims for lost and forgotten entries.

And it doesn't even (except for PR reasons) bother the company if you win the top prize of however many millions, week after week after week, Someone has to win that, or else take a share with others.

Spoiler:
What might cause concern (aside from the suspicion that you've got the equivalent of the Sports Almanac from the future, if you're not clever enough to employ surrogate claimants, on commission, to keep it on the down-low) is getting too many of the fixed-prize 'lower tier' prizes. There are.. *hmmm*... ?twenty? different ways to 'accidentally' choose any three numbers from the six you happen to know will win. Pay £40 and get back £500, in the lottery that I know most (barely) about. Arrange to do that 2000 times in a single draw, probably strategically through those proxies you might instead have lined up for grabbing successive jackpots, and you've extracted a million. Which I think just lowers the funds now allocated to the fraction-of-the-draw, but what happens when the fixed-prize demands more out of the variable-prize pot than there ever was some in? They probably have a clause about that, too, but it'd definitely kick up a stink by the time that happens.

Anyway, horses for courses. But I think lotteries are safe enough to run, and could survive even bald-faced Time Crime with care. Which is what makes them a less than optimal place to invest your belief of transient luck. Though temporal foresight allows all kinds of tricking of all kinds of systems (including those horses on those courses), if you really have the ability to do that.

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Re: 1827: "Survivorship Bias"

There's a bunch of people out there saying loudly that they survived cancer by eating the right thing and exercising. Well I'm here to say I survived by undergoing chemotherapy as recommended by my oncologist.
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Re: 1827: "Survivorship Bias"

Eternal Density wrote:Is this one about cancer?

There's a bunch of people out there saying loudly that they survived cancer by eating the right thing and exercising. Well I'm here to say I survived by undergoing chemotherapy as recommended by my oncologist.

No, I'm pretty sure it's about the 'how to succeed' seminars and speeches, since it pretty much is one (just with a ridiculous suggestion)

But the behavior applies to a lot of things, indeed including recovering from any illness (miracle cures aren't just for cancer; You can have a 'family cure' for anything from the flu to broken bones).
You even get some Sovereign Citizen 'teachers' (so, people who teach others how to be SCs, I doubt they're actually SCs themselves; It's hard to tell a believable lie if you're not aware it's false) using 'survivors' who have somehow won a case while using their techniques (generally because the case was already going to get tossed out because sometimes that happens to cases, and the SC didn't self-sabotage enough to change anything) as examples of why their techniques totally do work.
Or people who've lived for ages in good health having some secret to longevity, from eating specific food to specifically not bothering with diets and staying generally active.

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Re: 1827: "Survivorship Bias"

Soupspoon wrote:
orthogon wrote:If you do win [the lottery], you've beaten the house.

You don't beat the house in a (competantly planned) lottery. You can beat the casino by getting red or black (or green(s)) guessed correctly more than you statistically should, but prize funds in a lottery will be suitably defined fractions of the income of a lottery and the house knows that will be paying out half (or notably less, it seems, for other quoted lotteries) of the income in prizes, give or take some no-claims for lost and forgotten entries.

Perhaps my wording about beating the house was wrong, but what I meant was that you, personally, have come out ahead over a lifetime, which is something you won't do playing roulette. The house also comes out ahead overall every week, of course. It's all the other punters who lose out.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1827: "Survivorship Bias"

Yeah, under most circumstances, treating probability fractionally can be at least a guide, but I don't think this is one of those situations. If you make a bomb with half a critical mass of uranium, it doesn't kill half as many people. = .
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

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Re: 1827: "Survivorship Bias"

orthogon wrote:but what I meant was that you, personally, have come out ahead over a lifetime, which is something you won't do playing roulette.

The first time I ever played roulette for 'money' was at a company function, where there was a hired casino and play-money tickets. I waited a while (investigated the other stuff, as well, like the Sumo Suit Wrestling thing and outside to the archery) then decided to plonk my wad of tokens down on the green zero. (European, no double-zero of the cheatier US casinos, or I'd have done that instead as the same matter of principle.)

I won. Had I stopped there, I would (in play-money world) have come out ahead. But you just know that I let it ride. For my second (and last ever) go at a proper game of roulette.

(You can guess how that went. But I had more fun than I would have had at the Blackjack tables where I could make a mistake, beyond just the mistake of trying to beat the odds. This way I knew I was not to blame for diverting from my prior plan, or anything, nor was I depriving other players of their poker-stakes.)

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Re: 1827: "Survivorship Bias"

First time I ever played roulette at a real casino in Vegas I was gonna try the double-up strategy where you keep betting on one color, or odd or even, high low, any of the bets with (nearly) even odds. If you lose, you double your next bet and just stay with your choice. Eventually, after many doublings, you get a hit and your net for the excursion is a single chip. Then you start over.

I went through around 10 of those cycles, one lasting for 6 doublings. After a point I just got bored with the slow (but positive) progress and moved to the poker tables. Interesting though ... the croupier at the roulette wheel (I was the only player) gave me a look like "Oh great ... another double-up attempt." No house rule against playing that strategy. They just rely on the mathematical certainty that eventually you'll have such a long streak of doubles that you won't be able to cover the next bet.

By the time I got to my sixth doubling I was playing \$64 on red. I had enough cash on hand to go maybe 3 more doublings but was already getting paranoid about whether this strategy would work. I knew the odds of 9 even-odds losses were 0.5^9 = 2/1000 (ignoring the zero & double zero) but really wanted to walk away with some spending money left over. So I wimped out and walked away.

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Re: 1827: "Survivorship Bias"

aerion111 wrote:No, I'm pretty sure it's about the 'how to succeed' seminars and speeches, since it pretty much is one (just with a ridiculous suggestion)
I know one of those guys. He strikes me as a smug git.

I came across a definition of "privileged" a while ago, along the lines of "believing that because something is not a problem for you personally, it isn't a problem". It seems to me an effective way to dismiss such people.

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Re: 1827: "Survivorship Bias"

Soupspoon wrote:The first time I ever played roulette for 'money' was at a company function, where there was a hired casino and play-money tickets...

I went to one of those once. I too looked around the room, and noticed to my surprise that one of the games was broken. There was a strategy whereby you were guaranteed to win money across a long play. (No, it wasn't an ordinary casino game - real casinos aren't that stupid.) I told the croupier that his game was broken; he laughed, and said that people had been telling him that for years, and they were always wrong. I shrugged and sat down to play. I didn't like anyone at the company, so I didn't care about socialising. I cared more about proving that I was right. I know, typical xkcd reader.

An hour later, when I had a big stack of fake money in front of me, he asked me what I did at the company. "I'm a statistician," I told him. "I analyse probabilities for a living." Suddenly he believed me about his game being broken, and asked me how I'd done it, so I told him. He phoned his boss, who didn't care because it wasn't real money being wagered for once, but he said they were going to withdraw the game in future. The croupier was a good guy though, I liked him better than my colleagues, so I sat and played his game all night: we had a great time, and I ended the night with something like half a million in fake money.

Anyway, funniest part is that the company gave out a cash prize to whoever won the most money that night - and despite having beaten the casino, I only came second. First place went to a girl who'd put all her starting money on a single roulette number, won, put it on the same roulette number again, won again, and decided to stop. She made two and a half million (in fake money).

Which all goes to prove that you're better off being lucky than good.

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Re: 1827: "Survivorship Bias"

chrisjwmartin wrote:Which all goes to prove that you're better off being lucky than good.
A simple rule that every great man knows by heart: It's smarter to be lucky than it's lucky to be smart.

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Re: 1827: "Survivorship Bias"

I'm curious if anyone ever did any large-scale analysis of self-help / motivational media like this. There are of course some obvious correlations, such as luck, confidence, perseverance, making up a system at sticking to it, and a propensity for writing books telling other people how they should live, as well as all the other common sense things most people say louder than they do themselves (consume in moderation and what-not).

But maybe there's a less obvious and more tangible thing that might pop out if one were to rigorously scrutinize a large sample of self-help guff.
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Re: 1827: "Survivorship Bias"

eviloatmeal wrote:I'm curious if anyone ever did any large-scale analysis of self-help / motivational media like this. There are of course some obvious correlations, such as luck, confidence, perseverance, making up a system at sticking to it, and a propensity for writing books telling other people how they should live, as well as all the other common sense things most people say louder than they do themselves (consume in moderation and what-not).

But maybe there's a less obvious and more tangible thing that might pop out if one were to rigorously scrutinize a large sample of self-help guff.

I've thought about this, and I've yet to come up with a way around the massive missing data problem - put simply, people who fail (and don't eventually succeed) don't tend to write self-help guff about it. It's hard to do a rigorous analysis when your dataset as a whole is so horribly biased towards success. You'd really need to do a large scale prospective cohort study comparing different self-help strategies. But that's expensive, and doesn't sell books nearly so well as inspirational anecdotes.

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Re: 1827: "Survivorship Bias"

What we need is a long term study of a random sampling of (initially) babies, large enough such that a statistically studyable population of motivational speakers will be statistically likely to be included in the set.
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Re: 1827: "Survivorship Bias"

a.k.a. we need to study ALL THE BABIES!!!.

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Re: 1827: "Survivorship Bias"

Heimhenge wrote:First time I ever played roulette at a real casino in Vegas I was gonna try the double-up strategy where you keep betting on one color, or odd or even, high low, any of the bets with (nearly) even odds. If you lose, you double your next bet and just stay with your choice. Eventually, after many doublings, you get a hit and your net for the excursion is a single chip. Then you start over.

I went through around 10 of those cycles, one lasting for 6 doublings. After a point I just got bored with the slow (but positive) progress and moved to the poker tables. Interesting though ... the croupier at the roulette wheel (I was the only player) gave me a look like "Oh great ... another double-up attempt." No house rule against playing that strategy. They just rely on the mathematical certainty that eventually you'll have such a long streak of doubles that you won't be able to cover the next bet.

By the time I got to my sixth doubling I was playing \$64 on red. I had enough cash on hand to go maybe 3 more doublings but was already getting paranoid about whether this strategy would work. I knew the odds of 9 even-odds losses were 0.5^9 = 2/1000 (ignoring the zero & double zero) but really wanted to walk away with some spending money left over. So I wimped out and walked away.
Given that the house effectively has infinite money compared to you, this "strategy" ends with you losing everything with probability 1. (It doesn't even require zero or double zero. Martingale betting doesn't work for coin flips, either.)

Edit: Also, while the chances of the next 9 spins being consecutive losses are 1/512, the chance that the next three spins will be losses is 1/8, regardless of what the last six were. And the chances of getting 9 consecutive losses at some point in, say, 100 spins, is more like 9%.
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rmsgrey
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Re: 1827: "Survivorship Bias"

Yeah, the Martingale is, in many ways, the reverse of a lottery: rather than a steady stream of small losses, punctuated by the occasional big win, it's a steady stream of small wins punctuated by the occasional huge loss. Of course, the symmetry is imperfect - the losses always outweigh the wins if you play for long enough because the games are biased in the house's favour...

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Re: 1827: "Survivorship Bias"

Soupspoon wrote:I always play winning numbers in lotteries.

Ok, so they were previously winning numbers, but they've got just as much chance of (re-)winning next time round as any other set, the people who once won with them probably aren't going to be continuing (to split the jackpot) and how many other new people will willingly jump onto the exact same bandwagon, eh?

As lottery strategies go, this isn't bad. While you only *assume* that any number you play can actually come up, prior winners are *proven* to be possible, at least once.

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Re: 1827: "Survivorship Bias"

rmsgrey wrote:Yeah, the Martingale is, in many ways, the reverse of a lottery: rather than a steady stream of small losses, punctuated by the occasional big win, it's a steady stream of small wins punctuated by the occasional huge loss. Of course, the symmetry is imperfect - the losses always outweigh the wins if you play for long enough because the games are biased in the house's favour...
When evaluating betting strategies, it's often more useful to do things like calculating the likelihood of doubling your money before you lose it all. A positive long-term expected value is useless if you'll probably lose everything before you benefit.

If you're betting on coin flips, there's more than a 60% chance that you'll see a string of 10 losses in the first 2048 tosses. So if you start with \$1024 and your first bet is a dollar, you'll most likely lose everything you started with before you can expect to have won 1024 times, which is what it takes to double your money.

There's also the general technique of considering utility rather than absolute monetary value. Losing all your money generally has more of a negative impact than doubling your money has a positive impact. Thus a game with zero or slightly positive expected value might have negative expected utility.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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