The infamous coin toss • Hacker News Board

Re: The infamous coin toss

#251

Post by Etherlord87 » Fri, Aug 04, 2023, 11:24 AM UTC

rerdavies wrote: post #64

Huh. So I wrote the code, and ran the simulation. Now I get it. Investors: 100,000 Iterations: 100 Average worth after 100 iterations: $83.923 Average net worth increases. However the distribution of wealth is skewed dramatically. Winners: 13,704 (net worth of more than $1 at the end) Investors worth What That Guy was worth (the investor who made the most money): $1,171,830.00 He flipped 71 heads and 29 tails. Median…

Why make it about the rich. Your statistic doesn't magically change if you change the starting $1 to something else.

And to put the phenomena in much simpler words: flipping a coin once is good, having $100 bucks you either lose $40 or get $60, on average you get $10, and you win half of the time. The problem is if you have to flip a coin at least twice, because then the accumulated multiplier of your value, rather than .6 / 1.5 becomes:

.6 / .9 / .9 / 2.25

So while on average you gain 16.25% of value, you are a winner only ¼ of the time, and it gets better/worse depending on average gain / chance to gain.

…And apparently, what I learned just now, since your chance to gain approaches 0, for a finite population and infinite time, the chance approaches 0, therefore rendering the average gain to also be 0.

Re: The infamous coin toss

#252

Post by kevinwang » Fri, Aug 04, 2023, 3:00 PM UTC

jacknews wrote: post #250

kevinwang wrote: post #214

Earlier quoted context omitted.

> If the loser got 0.6666c instead of 0.6c, and the winner got $1.50, then over time you'd break even, on average. For what definition of "average"? Yes, the most likely outcome would be to break even. But if we mean "expected value" when we say average, then on average, that repeated wager would be massively profitable for us (in terms of wealth). Maybe a better way to view it is that it would be massively unprofita…

I think the conclusion is that 'expected value' calculated this way is a bogus metric, even for a single toss (what is the 'average' of a single toss, it already makes no sense). You can't simply take the mean average of summed probability-outcome products, or at least, it does not mean 'expected value', it means the 'probable limit' of the total. In the $60/$150 bet the 'expected value' is $105, but no-one is gettin…

Hm... Do you agree, though, that the bet is a good one if you can wager a size of your choice instead of your entire bankroll?

Re: The infamous coin toss

#253

Post by kgwgk » Fri, Aug 04, 2023, 8:27 PM UTC

jacknews wrote: post #250

kevinwang wrote: post #214

Earlier quoted context omitted.

> If the loser got 0.6666c instead of 0.6c, and the winner got $1.50, then over time you'd break even, on average. For what definition of "average"? Yes, the most likely outcome would be to break even. But if we mean "expected value" when we say average, then on average, that repeated wager would be massively profitable for us (in terms of wealth). Maybe a better way to view it is that it would be massively unprofita…

I think the conclusion is that 'expected value' calculated this way is a bogus metric, even for a single toss (what is the 'average' of a single toss, it already makes no sense). You can't simply take the mean average of summed probability-outcome products, or at least, it does not mean 'expected value', it means the 'probable limit' of the total. In the $60/$150 bet the 'expected value' is $105, but no-one is gettin…

> You can't simply take the mean average of summed probability-outcome products, or at least, it does not mean 'expected value'

Howver, that's what 'expected value' means: https://en.wikipedia.org/wiki/Expected_value

Re: The infamous coin toss

#254

Post by Fredkin » Fri, Aug 04, 2023, 9:22 PM UTC

jncfhnb wrote: post #223

Fredkin wrote: post #212

Earlier quoted context omitted.

In a "normal" environment, it doesn't make sense to me that wealth begets more wealth passively without doing anything: A) If your wealth is in cash in the bank, you are providing the bank with deposits. The bank can now make cheaper loans which helps others. But if these loans default, your bank fails and you get bailed-in. Assuming no government intervention comes to save you. B) If your wealth is in stocks or corp…

While it is problematic that bail outs happen to such a scale, the risk of things going south isn’t really a strong counter effect. You “can” lose. But you generally will not. Especially in the long run. And even if you do in particular, lose your investments, most wealth will beget more wealth. It’ll be a wealth transfer in dollars or real assets from you to a different wealthy party rather than society at large. Th…

To quote Keynes, ironically, "in the long run, we are all dead", and even wealth that gets passed on to children is frequently frittered away. There is no guarantee of unending passive growth if society at large does not make productive investments. Plenty of countries have learned that the hard way. I think this is a bias of modern westernized countries for the last century.

"The economy improves and so assets do become more valuable, inevitably." More pricey, no guarantees about more valuable though. Some assets may be entirely Ponzi-like and have little value, but a high price.

And anyway, if the economy is improving, homeownership / rent would be more affordable, families would only need one parent to work, the number of hours worked to buy S&P500 would be more reasonable, things like healthcare and education would be getting relatively cheaper. But artificially cheap margin debt, speculation, and financial chicanery backstopped by the central bank have lead to a lack of productive investment. Unusually high immigration and population growth without a corresponding increase in productivity causes higher prices too. Everything is getting harder from the point of view of Mr & Ms NoAssets 20-somethings who earn a wage.

The fixation of the tax-happy is on making the rich poorer in a dollar-net-worth sense. But there is no focus on making the poor richer in a purchasing power sense (what you can buy).

This requires a gradual deflation, higher reserve requirements, saving and careful investment. All currently very unpopular with the asset-rich, banker class, and thoroughly captured mainstream economics profession, who want you drowning in debt buying ever more expensive stuff, and not deferring consumption to the future.

Re: The infamous coin toss

#255

Post by rerdavies » Sat, Aug 05, 2023, 4:36 AM UTC

sobriquet9 wrote: post #224

coryfklein wrote: post #221

Earlier quoted context omitted.

Uh do you mean "bet 0% of your wealth every time"? Or does betting some number greater than 0% lead to net positive expected gains for an individual?

Kelly criterion defines the optimum ratio.

The Kelly Criterion, in this case, suggests that the optimum bet size is ~25% of your wealth.

Making 4 separate bets in each round with 25% of your wealth produces the following results:

Investors: 100,000 Iterations: 100 Portfolio size: 4

Avg wealth: $130.041 Median wealth: $11.6259

Winners: 85,902 Investestors worth Max wealth: $86,177.5 heads: 241 tails: 159

Re: The infamous coin toss

#256

Post by sobriquet9 » Sat, Aug 05, 2023, 10:50 AM UTC

Timon3 wrote: post #248

sobriquet9 wrote: post #203

Earlier quoted context omitted.

If you have nothing in your checking account, it does not mean your wealth is zero. In real life you can earn more money, in the given example you can't.

In real life you can also have negative money. In real life you can live paycheck to paycheck. In real life you can have costs higher than your earnings.

If you have no money to bet, the example is not applicable.

Re: The infamous coin toss

#257

Post by svnt » Sat, Aug 05, 2023, 4:57 PM UTC

credit_guy wrote: post #239

svnt wrote: post #118

Earlier quoted context omitted.

If you change the equation slightly and place a fixed resource consumption requirement (take 1-10% of the initial amount to pay to flip a coin) on each person’s continuation, and then unevenly distribute the initial balance, it will become apparent that your ability to become “that guy” is dominantly determined by your initial balance. In this version people do not end up at some small fraction of the initial balance…

With the wrong analogy you can prove anything. In this analogy the coin flip results in 150% your net worth or 60%. In real life, we make thousands of decision per day, but very few people make a single decision like that in their entire life. And this analogy goes for 1000 such decisions. In the real world, most of our decisions are not like a coin toss actually: if I do this homework, I might become a bit smarter a…

Your first sentence is correct.

The idea that the choice of homework vs TikTok is the choice of wealth vs destitution is a valid concept for relatively low values of income, generally within the realm of working for other people. This is because performance on homework is not necessary and not sufficient for actual wealth, only for a relatively safe employment outcome.

What we are talking about is making major bets on all the wealth you have accrued to date. To the point where a single major bet moves the global average wealth.

If your homework told you how to build the next Amazon/Tesla/Facebook after having enough money to start it, then it is relevant to this wealth discussion. Otherwise it is just a myth that got you to a relatively healthy, stable income.

Re: The infamous coin toss

#258

Post by jncfhnb » Sun, Aug 06, 2023, 11:37 AM UTC

Fredkin wrote: post #254

jncfhnb wrote: post #223

Earlier quoted context omitted.

While it is problematic that bail outs happen to such a scale, the risk of things going south isn’t really a strong counter effect. You “can” lose. But you generally will not. Especially in the long run. And even if you do in particular, lose your investments, most wealth will beget more wealth. It’ll be a wealth transfer in dollars or real assets from you to a different wealthy party rather than society at large. Th…

To quote Keynes, ironically, "in the long run, we are all dead", and even wealth that gets passed on to children is frequently frittered away. There is no guarantee of unending passive growth if society at large does not make productive investments. Plenty of countries have learned that the hard way. I think this is a bias of modern westernized countries for the last century. "The economy improves and so assets do be…

There is no guarantee of unending passive growth, but it nearly always happens. There is no guarantee of gradual wealth accumulation but it nearly always happens.