(I think. I can't actually say I fully understand this piece, but it seems to make a bit more sense with each reread.)
"Let's say you see me flipping a coin. It is not necessarily a fair coin. It's a biased coin, and you don't know the bias. I flip the coin nine times, and the coin comes up "heads" each time. I flip the coin a tenth time. What is the probability that it comes up heads?
If you answered "ten-elevenths, by Laplace's Rule of Succession", you are a fine scientist in ordinary environments, but you will lose money in finance."
Why is it 10/11? If we are to take the probability by induction (as the author points out shouldn't be done), it would be 9/9, no? For a non-biased coin case, taking the limit of [h/(n)] as n -> inf and where h = 0.5n would be 50%. If we have observed 9 heads in 9 flips, doesn't induction dictate the we should expect the next flip to be heads? I'm not saying I'm right... but I'd like to correct my gap in logic.
https://en.wikipedia.org/wiki/Rule_of_succession
I'll try my hand at explaining:
Let's say there is a coin you have never seen flipped. You know it might be an unfair coin, but you don't know which side it favors. All you know is that there are two possibilities: heads or tails. Intuitively, we know at this point that the best information we have is gives us a 1 in 2 chance of flipping heads.
Laplace represents this intuition by representing what we know without having ever flipped the coin as pseudexperiments. In other words, we have two implied experiments, one in which heads was flipped, and one in which tails was flipped.
You flip the coin once, and get heads. But it would be extremely premature to assume at this point that you have a coin with a probability 1 of getting heads just because that's the result you've seen. Even a completely fair coin might have this result. Knowing that a fair coin might have this result, you can still include your pseudo experiments, and treat it as if we have 3 experiments: 1 pseudo experiment with result heads, 1 pseudo experiment with result tails, and 1 real experiment with result heads. So we now say the chances of flipping heads again are 2 in 3.
After 2 heads, we have HTHH, so we say 3 in 4.
After 3 heads, we have HTHHH, so we way, 4 in 5.
After 5 heads we have HTHHHHH, so we say 6 in 7.
And so on until 9 heads we say 10 in 11.
> Why is it 10/11? If we are to take the probability by induction (as the author points out shouldn't be done), it would be 9/9, no?
No. With a completely fair coin, there's a 1 in 512 chance that you would get heads 9 times in a row, so you can't completely discount that possibility.
The derivation proving that Laplace's method is equivalent to the sum of all the probabilities of having all the possible coins and flipping 9 heads with them is complicated, and I don't think I can do a better job of explaining that than the Wikipedia article did.
If on the other hand you choose a different prior, for example "the coin may have two heads, and it's difficult to manufacture a biased coin with two different faces that still favors one side more than 90% of the time", then you might instead reach the conclusion that there's a 65% chance that the coin has two heads. But we don't usually deal with weird priors like that in intro stats.
If, as GP suggests, you know that the coin is somehow biased, you should seed your beta distribution with a non-uniform prior. That is Beta(.5, .5)[0] or something instead of Beta(1, 1). Then you'd be 84% sure, instead of 65% sure that the coin was biased at least 90% in favor of heads.
[0]: https://homepage.divms.uiowa.edu/~mbognar/applets/beta.html Play around with this, in the Beta distribution, a=success, b=failures, X is the mean of the underlying dataset, and P(X>x) is the propbality that the mean of the underlying dataset is greater than the provided value. Look at
- Beta(1,1): the uniform prior
- Beta(10, 1): Laplace's method
- Beta(.5, .5): A prior where you believe the coin is weighted, but aren't sure how much.
- Beta(.1, .1): A prior where you're very confident the coin is weighted, but unsure in which direction
- Beta(9.5, .5): The coin after 9 flips
- Beta(9.1, .1): The coin after 9 flips when you're really confident it's weighted
- Beta(8.1, 1.1): The coin after 9 flips when you're really confident it's weighted, but both sides aren't in fact the same.
Those will give you some intuition about the distribution itself.
Until you’ve internalised the contents of the linked article, you should refrain from investing any money. In anything.
Haha, but not everybody knows it and a lot of different opinions exist on how awful it is or what even classifies as awful.
I have never been able to wrap a good definition around my intuition of behavior once understood is no longer effective. "Anti-inductive" is very interesting crystallization of this concept. Thank you for sharing this.
Look all cryptos are extremely volatile because the real market liquidity is an order of magnitude less than most people think it is, and the way automated market makers work force all exchanges to keep their prices "in sync" to avoid arbitrage like we had in the early days when it was possible to buy for 50$ in one exchange and sell for 100$ in another..
On the plus side, atm BTC is up ~8% in the last year and about ~22% since the beginning of the month.
Source: me a blockchain dev, former CTO of a crypto exchange that raised 30M in an ICO.
The concept is: decentralized databases
When should you have that? Well, one example: whenever you need a database, and a centralized database is politically or socially impossible.
Fun fact: bitcoin is a better currency than any currency that is undergoing hyperinflation right now. Some of those places also can't have centralized databases.
Speaking from a financial standpoint I think ETH will be more of a career for you if that's what you pursue--you can charge well for smart contract architecture. I think BTC will be more of a store of value (and then transactional too later on) and ETH will be computational/contractual. Lots of people have strong opinions on this and other decentralized scripting languages; this is just my opinion as a random guy on the internet :)
Speaking from a code efficiency standpoint: Solidity will force you to be very economical about the code that you write, since you pay per opcode to execute code. I think that alone is worth writing some smart contracts, because it forces you (as long as you set cost as a constraint) to be efficient in your architecture so it's a good exercise.
There aren't a ton of real world applications where you can honestly say "that architecture is better than a centralized one" yet. But if you study the tech and grow with it over the next 20 years you will have a complete understanding of how it works and will be in a position to contribute as it gets to higher adoption levels (or help push it there), which I consider a good idea.
- It's an unregulated market, so there's nothing preventing wealthy actors from buying up tonnes and artificially increasing the price, e.g: "pump n dump".
- It's inherently speculative and has no real use besides investing and unregulated money exchange.
- It's a global market, people from all over the world have access to the market with little overhead, making it volatile.
How about sending cash? You can do that with a bank account. But what if you can't? 1.7 billion people are unbanked and some of them do have access to computers.
There are situations where cryptocurrencies are currently the only solution. Sure, not for you, or for me. But definitely for a large group in the world that we don't know much about, because we don't live their lives.
Edit: the more I reread my reply the more it fits "unregulated money exchange". But I'd like to argue that such a thing is a real use case. And by trivializing it you're not allowing yourself to understand it with minimal bias.
And absolutely none of them are or should be storing their limited assets into something they can't change into spendable cash in the local economy without access to a bank account [even without taking into account volatility etc]. Regulated money transfers already serve this population much better for sending money long distance because they get cash at the other end. No matter how hard newly-minted foreign millionaires try to enlist them in the dump phase of their money-printing scheme, people in the developing world don't have a need for computer based tokens with volatile notional value which are not only not accepted by people in their local economy but also completely unintelligible to them
The real demand for unregulated money exchange is of course unlawful transactions, and serious crime like extortion undoubtedly represents several orders of magnitude more volume in the BTC economy than serving the unbanked.
Thanks for giving your opinion. Well, we clearly strongly disagree. The only issue I see in my argument is that I don't know well enough to what extent the unbanked can exchange bitcoin in their local economy for goods/services or their own currency. One can say they can't, but the real answer is: they probably can't, but I don't know and maybe they could. If they couldn't then my position is not holdable. If they can, then I'd say I strongly disagree.
In any case, you said the following.
> demand for unregulated money exchange is of course unlawful transactions, and serious crime like extortion undoubtedly represents several orders of magnitude more volume in the BTC economy
The way I made this quote is slightly out of context, but with this I agree (i.e. I deleted "the real" and "than serving the unbanked").
But what about playfulness? This is a completely different inquiry than my comment above that (i.e. the western world). I wonder how big that demand is. I'd venture to guess the following: at least 21 million people are willing to play with bitcoin by now for at least $1. If this number is 210 million people, then this lowerbound goes to $10 per bitcoin. Yep, handwavy, I know. I'm assuming by the way that in such a secnario everyone would then play around with 0.1 bitcoin.
The reason those values are sustainable is because $1 is within everyone's budget of being playful.
I'm simply wondering what you think as your views are very different from mine.
WRT crypto appealing to some people's playfulness, I entirely agree with you: it's well established fact that a non-trivial number of people in the Western world enjoy gambling with Bitcoin or cryptokitties, and some of them have deep reserves of cash and algorithms to pump more in when they see a trend they like. But the thing about 'playfulness' is it doesn't make a stable store of value or useful medium of exchange: for that you need the amount of new money flooding in to equal the amount of money flowing out. And people move on to playing with new things.
But, you dont need a bank account to send cash as is. You can use a system like western union, or just put cash in the mail.
Western union has high fees, sure, but the money it sends also doesnt lose 10% of its value in half an hour. Exchanging to and from crypto isnt free either, and is required, since approximately 0% of people get paid in crypto, and 0% of goods and services are bought in crypto.
Sending cash in the mail might get lost, stolen or seized, but the same can be said of crypto. Or, you can send something safer like a postal money order which has minimal fees ($1.25 up to $500, $1.75 $500 to $1000).
what's this? quality bait? BTC was up and down all the time, this is normal. Say OP, do you have bitcoins? Because it seems to me you're trying to stir something
Redditors like to think this is a manipulation tactic to incite a plummet in price to buy in at a much cheaper price and ride a slow, gradual wave up before the actual event happens.
https://twitter.com/whale_alert/status/1259258437831188482?s...
Learn to read trading indicators. You'd see that it was massively over bought and bound for a bit of a correction.
Also, if you think this is bad... you haven't been in the shit yet/must be new to this market.
Weekly and monthly charts are showing room to move either way. Stochastic RSI is at mid range on weekly, moving upwards, and has yet to cross over. Same for monthly, except it's moving downwards.
Daily was pretty oversold, but longer term looks to be brighter.
This website suggests it's due to bitcoin halving the block reward soon.
2. If it did suggest that, it would directly oppose the law of supply and demand--a reduction in the rate of increase in supply should increase price, not lower it.