The infamous coin toss • Hacker News Board

Re: The infamous coin toss

#91

Post by [deleted] » Thu, Aug 03, 2023, 10:27 AM UTC

n2d4 wrote: post #67

DarkNova6 wrote: post #63

Earlier quoted context omitted.

Confusing the equivalence of -50% and +50% is very common. In fact, many video games provide wrong bonuses based on this misunderstanding (Age of Empires 2 being a famous example). Even a simple calculation will show the truth: -40% = 0.6 +50% = 1.5 0.6 * 1.5 = 0.9 Conclusion: With every coin-toss you lose 10% of wealth on average.

While I agree, that conclusion is wrong because you forgot to look at the win-win and loss-loss cases. Even with two coin tosses, as in your example, you'll win on average: 1.5 * 1.5 = 2.25 0.6 * 1.5 = 0.9 1.5 * 0.6 = 0.9 0.6 * 0.6 = 0.36 => 1.1025x total It's counter-intuitive because even though you almost always lose, you still win (linear) wealth on average (but not median). The difference is that if you have unl…

[deleted]

Re: The infamous coin toss

#92

Post by Swenrekcah » Thu, Aug 03, 2023, 10:29 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…

>The obvious conclusion: increasing wealth concentration is an unavoidable consequence of capitalism that probably has very little to do with merit. The only solution: eat the rich.

This is exactly why we need progressive asset taxes. Income tax should be almost abolished, it can be something like 10% on all types of income and then nobody needs to bother with tax evasions on that.

5-15% VAT or sales tax to generate revenue for the places where people congregate and do their business, the rest of society should be funded by asset taxes.

Re: The infamous coin toss

#93

Post by rcxdude » Thu, Aug 03, 2023, 10:41 AM UTC

ActivePattern wrote: post #20

jstanley wrote: post #8

I think the part about the misalignment between the individual and the collective is basically wrong. In the given game, the collective loses money just as the individual does. The collective wealth is the summation of the individuals' wealths, and both the collective and individual wealths drop over time. Write a simulation and try it if you don't believe me. I did, because I couldn't work out how the collective wea…

No, your expected value is indeed positive over repeated iterations: (1.05^i)*w, where i is the number of iterations and w is the starting wealth. The intuition for why this happens is that the losses of the majority are made up by the big gains of a minority. You can even see that after two iterations: Case 1: two heads -- 225% wealth Case 2: heads, tails -- 90% wealth Case 3: tails, heads -- 90% wealth Case 4: two…

Yeah, which implies for any finite N eventually the average will collapse, once the lucky guy's luck runs out. The expected value prediction is only true over a long enough timescale for actually infinite N (I do wonder how this scales: I would intuitively expect that the time window scales with log(N), which implies even very large N will not last drastically longer, but I don't know if that's the case)

Re: The infamous coin toss

#94

Post by inopinatus » Thu, Aug 03, 2023, 10:47 AM UTC

PHYSICIST: I offer you the following gamble. I toss a fair coin, and if it comes up heads I’ll add 50% to your current wealth; if it c—

ROSENCRANTZ: (interrupting) Do it.

Re: The infamous coin toss

#95

Post by LeonB » Thu, Aug 03, 2023, 10:47 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…

Imagine if — on top of that - we let the undeserving rich invest their wealth in things such as:

- owning media - lobbying the government - owning the means of production

It could take that dire situation and make it drastically worse. I mean, in theory.

Re: The infamous coin toss

#96

Post by _0ffh » Thu, Aug 03, 2023, 10:50 AM UTC

AdamN wrote: post #86

drekipus wrote: post #76

Earlier quoted context omitted.

> increasing wealth concentration is an unavoidable consequence of capitalism My bad I thought you made a coin flip simulation, not a capitalism simulation. At what point do we stop wagging the finger at the ghost of capitalism and just say it's mathematics? You don't hear people crying for the upheaval of mathematics

People do say that. Usually the critique of (perfect) capitalism is that it (structurally and mathematically) skews towards increasing wealth for winners at the expense of the rest of the population and that this is inevitable. Then the response of advocates against this situation is to either commit to more structures to prevent that outcome towards diluted (non-perfect) capitalism or other social forms (socialism,…

I'd rather take my chances with the coin flips than with the politburo.

Re: The infamous coin toss

#97

Post by robertlagrant » Thu, Aug 03, 2023, 10:50 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…

> The only solution: eat the rich.

Don't look at history when people did this, though. Just do it based on this simulation.

Re: The infamous coin toss

#98

Post by LeonB » Thu, Aug 03, 2023, 10:52 AM UTC

Swenrekcah wrote: post #92

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…

>The obvious conclusion: increasing wealth concentration is an unavoidable consequence of capitalism that probably has very little to do with merit. The only solution: eat the rich. This is exactly why we need progressive asset taxes. Income tax should be almost abolished, it can be something like 10% on all types of income and then nobody needs to bother with tax evasions on that. 5-15% VAT or sales tax to generate…

Vat is irredeemably regressive. I suspect you know that.

Income tax fails in its progressive goals not because it is inherently bad (like VAT) but because the tax laws are written by the richest players. (Ask a poor person how much influence they’ve had on tax law, and then ask a top 5 accountancy firm. This isn’t a controversial statement.)

Re: The infamous coin toss

#99

Post by credit_guy » Thu, Aug 03, 2023, 10:53 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…

> The obvious conclusion: increasing wealth concentration is an unavoidable consequence of capitalism that probably has very little to do with merit.

Not really. P implies Q is not the same as Q implies P.

The fact that you can get a large gap between rich an poor with pure coin toss does not mean that when you have such a gap the gap resulted from pure randomness. It could have resulted from any combination of merit, hard work, inheritance, cheating, and luck. Your conclusion simply does not follow.

Re: The infamous coin toss

#100

Post by robertlagrant » Thu, Aug 03, 2023, 10:56 AM UTC

LeonB wrote: post #95

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…

Imagine if — on top of that - we let the undeserving rich invest their wealth in things such as: - owning media - lobbying the government - owning the means of production It could take that dire situation and make it drastically worse. I mean, in theory.

> owning media

Who should own media? Private people, or the state?

> lobbying the government

If lobbying the government is effective, it's either because the lobbying was correcting a wrong, or the government is allowing itself to be corrupted.

> owning the means of production

The "means of production" was barely relevant when Marx found out what a factory was from his factory-owning mate. A plumber owns "the means of production" when he owns his own tools. It's far too low resolution a phrase to be useful, except for anyone who finds it useful to teach people to hate another group of people.