money – Can someone explain Cuba’s two-currency system and the consequences for foreigners?

A little bit of history:

(from the top of my head, there is very little to find about this on the web I think, even in Spanish):

At some point during the Cuban Revolution and before I was born, being in possesion of any foreing currencies in Cuba became illegal (unless you had a special permit from the government). Many Cubans spent time in jail for this reason. Diplomats, tourists (which were rare at that time) and foreigners with a permanent or temporary residence were also allowed to use foreign currencies, and there were special stores (with imported products that could not be found anywhere else in the country) that only them could use, at that time these stores were commonly called “diplo-tiendas”. There was also an alternate currency called “exchange certificates” that only diplomats could use and were only valid on those stores.

After the fall of the Berlin wall, Cuba started to fall into a deep and accelerated economical crisis, the Cuban government started to allow regular Cubans to use this alternate currency in those “special stores” and encouraged them to give away their gold and jewelries in exchange for this new currency. This currency was called by Cubans as “chavito” (no idea where the word came from, I was a child at that time) and the name is still used today in a lesser degree. This was the start of the two currencies system.

In 1994, during the worst period of the economical crisis, the Cuban government decided to open the country for tourism, foreign investment, and small private business. At the same time, they legalized the possession of foreign currencies, and more of those “special stores” were built all around the country. They assumed at that time that only a small percent of Cubans would ever be able to go there, and this was all supposed to be a “short-term temporary measure”. Their goal was to keep tourist and foreign companies as segregated as possible from regular Cubans, but at the same time stimulate the flow of strong currencies into the country.

They started to print yet another new currency that could be exchanged at a 1×1 rate with US dollars, and when you paid with “real dollars” for products and services, you would get your change in that alternate currency unless you explicitly requested otherwise. Later on in 2004 the government decided to forbid using foreign currencies at stores and hotels, and they forced Cubans and tourist alike to exchange their foreign currencies for the Cuban Convertible Pesos. And this is how the mess became permanent.

The two currencies:

Tourists are allowed to posses and to use CUP, but there are certain services and products that are subsidized by the Cuban government, just for Cubans (like theaters, concerts, museums, movies and the food rations that all Cubans receive on a monthly basis). Tourists will have to pay a different price in CUC for those services, and of course there are no subsidized food rations for them.

However it might still be a good idea to have some CUPs available, since buying food from street sellers and fruit/vegies stores or taking public transportation (including the “shared” taxis called “boteros”) is a lot more cost-effective when paid using CUP, specially if you have a Cuban friend (and I mean a real friend) to walk around with you.

The main concern when using the two currencies are the scams, you need to know all the bills and coins of the two currencies.

So we have Cuban Pesos (CUP) and Cuban Convertibles (CUC).
At the time of writing, 1 CUC = 24 or 25 CUP (most of the time), and 1 CUC = 1 USD (most of the time). These exchange rates have been “artificially fixed” by the Cuban government for many years, however they vary depending on the situation. If you want to buy CUC using CUP, the rate will likely be 1 CUC = 25 CUP, if you want the opposite, the rate is likely to be 1 CUC = 24 CUP, and if you want to pay for services (like a taxi,with prices usually set in CUP), using CUC coins, the rate is likely to be 1 CUC = 20 CUP. For example in order to pay a taxi(botero) trip that costs 10 CUP with CUC coins, you will need 2 coins of 25 CUC cents, or 10 coins of 10 cuc cents, etc.

The main difference between the bills are the colors, as you can see in the picture below, CUP are kind of monochromatic, while CUC have many colors in them:

cuc and cup bills

Pictures for all possible CUC bank notes can be found here:

Another difference is the presence of monuments of historical characters in CUCs instead of the picture of the person found in CUPs.

Note that CUP bills that are about 20 years old or more were also printed in many colors, but they are not longer used these days and it would be very unusual to come across one of these. In case you do come across one, they all look more or less like this:

3 pesos bill from 1995

The coins are also easy to tell apart, coins from CUC have all an octagon around them, and they are stamped with landscapes. Coins from CUP are all stamped either with a star or with a picture of an historical character, namely Che Guevara – 3 cup, Jose Marti – 1 cup and (currently rarely found) Camilo Cienfuegos – 0.40 cup.

CUC Coins:
cuc coins

CUP Coins:
cup coins
3 cup coin

Most common scam:

When receiving change in coins, if you get several 1 CUC coins, always review each of them, make sure that you are no getting a 3 CUP coin instead (the one just above with Che Guevara). They are roughly the same size and color, but 8 times less valuable.

Recent events:

The Cuban goverment is currently taking measures (slowly) to eliminate CUC as a currency, for this reason CUP can now be spent almost everywhere (but not the reverse), and when prices are displayed just in CUC the regular CADECA conversion rate will be applied if you want to use CUP.

As of January 2016, state-owned companies (for example most of the stores and supermarkets) are starting to accept some major credit cards as method of payment for goods and services (VISA and MasterCard for example), at least in Havana, so you could also use that as a way of avoiding dealing with currencies. Note that every time you use a credit card, the store rep will ask for a piece of ID and collect as much personal info as he/she can, I guess it will take a few years before they get used to the change and become less paranoid.


As of August 2017, It is illegal for Cubans and tourists alike to export CUC bills or coins.
Cuban citizens and residents can export/import CUP up to 2000.

BANCO CENTRAL DE CUBA (Central bank of Cuba): RESOLUCIÓN No. 18 /2012

UPDATE October 16, 2019

The Cuban government just announced that they will open a new store chain across the country that will only accept USD as currency, but never in cash, just magnetic cards (like regular credit cards for example).

(Is Spanish)

These stores will not accept CUP or CUC. So Cuba now has three currencies… yey!

UPDATE Feubruary, 2020

The Cuban government is taking more steps into removal of CUC as a currency.
CUC is currently not accepted anymore inside airports once you pass immigration/customs, and there is no way to do currency exchanges anymore at that point.

If you happen to have CUC with you at the moment of your departure, make sure to change them back to a foreign currency before you pass immigration/customs.

Can someone explain those free 0.00000001 BTCs?

I’ve just noticed an odd transaction to my wallet address. 1LnNQDKV6DiMnZ2rZ9yXpcnnTh7my1WusP seems to be giving me a free 0.00000001 BTC.

Investigating further shows that I’m not the only one receiving the free 0.00000001 BTC. Take a look at the blockchain transaction.

What is happening? Is this guy using blockchain’s public note as an advertisement spam?

dnd 5e – How do I explain to an AD&D player that items that increase Armor Class in D&D 5e are overpowered?

+2 AC is much more than an 8% improvement, in one case it is as high as 200%.

Erik’s and Quadratic Wizard’s answers do a fine job of comparing the proposed item to existing magical items in the DMG. The trouble is, if I only believe it is an 8% improvement in AC, I’m going to conclude that the DMG is wrong about how strong +2 AC is. So it seems good and necessary to actually correct the notion that +2 AC is only an 8% improvement.

Sure, the number increases from 21 to 23, which is an improvement somewhere between 8-10%. But that is not how we measure the effectiveness of AC or how much it improves when we increase it.

I have constructed the following table. Column 1 shows that hit bonus of the attacking creature. Columns 2 and 3 show the probability of that creature hitting ACs 21 and 23, respectively. Column 4 shows the percentage of attacks that would hit AC 21, but miss AC 23. Finally, column 5 shows the percentage improvement in survivability of the change in AC. Column 5 is how we determine the marginal effectiveness of a change in armor class.

enter image description here

As you can see, even against the mighty Tarrasque (+19 to hit), the improvement is still better than 8%, sitting around 12%. But we aren’t fighting a Tarrasque at level 6. As mentioned in your question, we’re looking more in the range of +4 to +6 to hit, which gives +2 AC an improvement between 50% and 100%, which is quite significant. 50% of +4 to hit attacks that would have hit me before now miss me. In terms of survivability, this doubles my durability. Increasing my AC from 21 to 23 means I can last twice as long (on average) against a creature that has a +4 to hit. That’s a 100% improvement. Not 8%.

How powerful is AC 23 at 6th level?

It’s pretty powerful. As in, most encounters at this level will pose virtually no risk of harm. But let’s try to set up something of an experiment and run some numbers.

Say our paladin with an AC of 23 is out adventuring solo and gets attacked by three blue dragon wyrmlings.

A blue dragon wyrmling has +5 to hit and deals 1d6+1d10+3 (average 12) damage on a hit. Consulting our table, the blue dragon wyrmling has a 15% chance to hit our paladin with an AC 23. Thus, the average damage sustained by our paladin each round is:

$$3 times 0.15 times 12=5.4$$

A 16 CON paladin taking the average increase for hit points each level will have a modest 58 hit points, which means our paladin can be expected to last for 10 rounds before dropping in the 11th round, assuming he doesn’t use any healing spells or lay on hands. For simplicity the wymrlings didn’t use their breath weapons at all.

You take this absurdly reliable talent for not getting hit by attacks and spread those attacks out across the party and this paladin will rarely have to polish his armor.

Now, I would be remiss if I did not mention that AC is not the only part of combat survivability. An armor class of 30 will do you no good against spells that damage on failed saving throws. But AC is still a huge part of combat survivability.

I get that this is oversimplified in comparison to actual combat. But I think it demonstrates the point well enough. In my party of 5, our Paladin plays the tank role very well. Most of our combat encounters are 3-5 rounds and we have 1 or 2 per 4 hour session. We are also 6th level, his AC is 19 and I still feel that he almost never gets hit. From experience, 19 is very good. An armor class of 23 is broken.

So what do I do?

This question has some great suggestions for handling this in a way that is engaging and fun for both the DM and the player: I gave a too powerful magic item at too low level for a bad reason, what to do?
This situation is a little bit different than the specific situation detailed there, but the ideas and principles can still apply.

bitcoincore development – I’m digging further into the open Taproot PR. Can you explain the bip340_test_vectors?

Draft answer (to be continued)

These bip340_test_vectors are used in two places: the unit tests (src/test/key_tests.cpp) and the functional tests (test/functional/test_framework/

There are 15 test cases in all but only 4 distinct secret keys, 7 distinct public keys (3 of them don’t have secret keys) but 15 distinct signatures.

The public key DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659 is reused 9 times for example but the distinct signatures are generated using different messages, auxiliary randomness etc.

The first five test cases have valid signatures (a verification result of TRUE) although the fourth test case (index = 3) has a comment of test fails if msg is reduced modulo p or n (I’m not sure what this means)

That leaves the remaining test cases that fail the signature verification:bip340_test_vectors
Index 5 has a public key that is not on the secp256k1 curve y^2 = x^3 + 7 (mod P) where P = 2^256 - 2^32 - 977 that Bitcoin uses. This elliptic curve is the same for Schnorr as it is for ECDSA. The public key is calculated by multiplying the private key by the generator point and so it must be on the elliptic curve. If it isn’t it is not possible to generate a valid signature. Indeed the secret key is not provided for this public key as there is no secret key that can multiply with the generator point to get the public key.

Index 6 is referring to the BIP 340 design choice to implicitly choose the Y coordinate that is even (each valid X coordinate has two possible Y coordinates, one that is odd and one that is even). If the Y coordinate is odd then it is not following the BIP 340 specification and the signature verification should fail.

Index 7 has a negated message (Schnorr signature algorithm can’t sign a negated message?)

Index 8 has a negated s value (negative signature?)

Index 14 has a public key with a x coordinate that exceeds the field size (P = 2^256 - 2^32 - 977). This is not possible under mod P so no valid signature is possible here.

factorial – Can someone please explain |i!|² = π/sinh(π)

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nt.number theory – Can you explain in pictorial way why there’re much more irrationals than rationals despite they are both infinite in the common usual sense?

This question isn’t likely to stay open as a research-level question, but I will try answer anyhow:

Part of your confusion is the following statement: “despite the known fact that every irrational has 2 immediate neighboring rationals on both sides”. This is not true.

What is true is that between any two irrational numbers there is a rational number; in fact, there are infinitely many rational numbers between any two irrational numbers.

Similarly, there are infinitely many irrational numbers between any two rational numbers.

If your statement above were true, then you would be correct. However, as stated, it is false.

How to explain the k-anonymity model used by HaveIBeenPwned for pwned passwords to a layman?

People are naturally skeptical when they hear about the HaveIBeenPwned pwned passwords search, because who would in their right mind enter their password into a random website? And sure, HIBP uses k-anonymity to make sure they don’t know your password, but if you’re not familiar with how hashing algorithms work and how the k-anonymity model works, that just sounds like a bunch of technobabble from Doctor Who that you probably can’t trust.

How can I best explain the k-anonymity model as used by HIBP to a layman?