Memorizing convention without understanding - Playing 1's in black games

[Divinus]

TLDR: Some people play 1's wrongly in black because they misunderstand the reasoning behind the play of 1's in non black games (when a 1 clue can play several ones).

Recently I have seen a lot of players insisting on a particular way of playing the black game, but when I ask why they think it should play that way the result is always a variation of "because it's convention" or something, without any reasoning behind it, even when I ask directly.

Granted every convention has axioms that ultimately are distilled to "because it's convention" but apart from these basic axioms a lot is built on top with logic, at least partially. For example: current BGA convention has 3/4 basic axioms (there might be minor ones too):

0 - Players play rationally.
1 - A clue means play left, unless:
2 - Number on chop means save.
3 - Good touch principle.
(Other conventions have different basic axioms - that is how I am using the term "convention" - to denote a set of rules that forms a language of hanabi, not as a reference to a particular rule within the language).

Let's see an example:
How can we justify finesse with those? Isn't finesse a basic axiom too?
If you see P1 clue R2 to P3 and you are P2, while the pile is empty, what to make of it?
Axiom 0 will tell you the clue must mean something, and you also know that if you do nothing the player will bomb. So there must be something we can do to prevent the bomb. Correcting the card violates axiom zero, since we are assuming a mistake. So we conclude we must have the missing link. So we check if any of our marked cards match the missing link. If they do we play it. If they don't we also need to do a little bit more thinking. If I you are P2 and have no marked cards, which slot is R1 located at?
The reasoning is that this play (the finesse) is only possible at that moment and not sooner - if it was sooner it would have been done so then. So you conclude that it was your newest card, that caused a change in game state, that allowed this play (the finesse) to happen, therefore the most likely position for the missing link to be is 1st slot. Again axiom 0 is very important. While it is just likely that the card is at slot 1, knowing others play rationally will allow you to understand that the clue giver must give you something to go by - it can't clue the finesse and let you guess the slot the missing link is in, so the most likely position (1st slot) ends up being the correct one. You can then build on top of this for more advanced plays and so on.
You can just memorize finesse means play first slot without understanding the reasoning behind it, and in virtually all cases you will be fine. However there are other cases where memorizing without understanding leads to errors.

That such case is not understanding what makes people play 1's in a row in non black games, and then try to apply that to black games.

In a non black game if you are clued 1, and your game looks like this: 1-1-1-x, you are expected to play all ones, one after another, unless someone corrects.
Now, I have seen people arguing this still applies in black games. However the reasoning presented is just because it is convention, they say. I suspect those people (including several high ELO players), are just memorizing how 1's play in non black games and trying to apply it to black games. They fail to understanding the reasoning 1's play like they do in non black games.

So let's delve deeper into how can a 1 clue can play several ones in a non black game.
Suppose 3 piles are empty and 3 have 1's played.

What is the difference between a 1 clue that marks 1-1-1-x and a 2 clue that marks 2-2-2-x?
The one clue will play all ones (unless corrected), while the 2 clue will only play the left two (the others requiring prompts of some kind, e.g. direct clues, finesses, etc.). At first glance it seems that 1's play different than other numbers, as if there is an inversion of the burden of proof: you must tell the player if a 1 is not playable, but the opposite to the player with the 2 clue . And here lies the misunderstanding a lot of people make.
1's don't play differently from 2's, or any other number when it pertains to this situation. They have the same set of rules applied to them. The difference is caused instead by game state.
What I mean is - what makes all 1's be played is the combination of the good touch principle + all non junk ones are playable. The reason is not because 1's play differently.
As such this applies to all numbers. If all non junk 2's are playable a 2 clue that marks 2-2-2-x will also play all twos. And so on for 3's, 4's and 5's.
In fact many people intrinsically apply this rule midgame, usually to play cards saved early - if I have a 3 marked and all non junk 3 are playable then I can play the 3 even without knowing its color (because of good touch I know it's not junk - and because of game state I know all 3's are playable).
What makes a 1 clue at the start of a non black game play all ones in a hand like this 1-1-1-x is not because 1's are special, it is because all piles start at zero making all ones playable.

You are now maybe starting to realize where I am arriving at.

In black games, not all 1's are playable at the start. But because people don't understand the reasoning behind why a 1 clue plays all ones in non black games, they think it must work the same. It doesn't.

In black games a one clue at the start that marks 1-x-1-x, only plays the left one, the other requiring some sort of prompt to play.
Black games are analogous to non black games where all colors of a particular number are playable except one color.

So in a non black game, where all 2's are playable except for one color, a 2 clue marking 2-x-2-x will only play the left 2.
It will only play the right two as well, if the player can see both 2's that are not playable at the moment (either in discard or other player's hand).
In the same sense, in a black game, a 1 clue at the start that marks 1-x-1-x will only play both 1's if the player can see the 1k (the only 1 not playable at the moment). And people even start to play them from the right to gain tempo on sharing that information.

Now players that don't really understand this think that in black games 1's work differently from other numbers. They also only give clue 1 when 1k is on chop.
Here are some examples: if a hand looks like this 1b-1mc-1k-1y, and there are no other 1's in view, they will not clue 1, because they think it will prompt a play of all of them (like in non black games), with the caveat that you can't color the black one to warn the player - hence don't give that clue. They also don't do it in cases like this: x-1mc-1k-x, preferring to mark the 1 mc alone and then spend another clue for the save. They will expect you to play all 1's in a hand marked like this 1-1-1-x even if you dont see 1k. And so on.

The thing that bothers me most is that this creates a completely unnecessary ruleset just to play black, where 1's are different from other numbers, while in other games it doesn't happen. And this is contrary to the spirit of BGA convention -> built to be efficient without overhead (compared with others). the BGA convention became a victim of its own success - no overhead allows people to memorize without understanding, and then create unnecessary complexity due to the lack of understanding destroying the beauty of this convention. If you want complexity go play hyphenated or other highly developed conventions. BGA convention is supposed to have low overhead and be simple.

Ones in black games are just like any number in non black games where all colors bar one are playable. Period.

In the same sense a player will not play both 2's in a 2 clue marking 2-x-2-x if not all 2's are playable, in a black game a player can't play both 1's in a 1 clue marking 1-x-1-x (unless it sees 1k of course).

What prompted me to write this was the following case:

First turn in a black game I received a hint marking my hand like this 1-1-1-1 -> All for cards are 1. I play the left card.
But then I don't see 1k anywhere and no one prompted me to play another 1 (by finessing or marking directly), and people were not busy with other clues, they were discarding already (almost at 8 clues). So comes my second turn and there were no clues to give. I discarded 1st slot, the first card not marked, and it was 5R. They told me I should have played the 1's in a row but failed to show the reasoning behind it (in typical hanabi vitriol just told me to learn the game).

The thing is if we draw the analogous situation in a non black game it is easy to see why they are wrong:
Suppose all 2's are playable except for one color and you receive a 2 clue marking 2-2-2-2 - all cards marked with 2.
You play the left one, but don't continue playing the others until prompted (unless you see both 2's that are not playable at the moment).
But 1's in black games are exactly like this situation - a number where all colors are playable bar one (the black).

Those players failed to understand the reasoning why a 1 clue can prompt several 1's in non black games, and just memorized it. Then they tried to apply it to black games: "a one clue at the start plays all ones - thats how it goes - if you dont you play bad". It only plays all ones in non black games because all ones are playable, which does not apply in black games.

End Rant

[Romain672]

Axiom 0 will tell you the clue must mean something, and you also know that if you do nothing the player will bomb. So there must be something we can do to prevent the bomb. Correcting the card violates axiom zero, since we are assuming a mistake.

Funny enough at 3 players, I did a bad clue in one of my first game on a trash card to make it playable. Next player corrected it, which let us save two cards in his chop.



Outside of this, here is the reasonning for your problem:
- 1s are always playable except for k1. That means if you receive 1 clue: 1-1-1-x, it's likely your others 1s are playable (assuming no dupes, 83% with 6suits).
- Now, imagine that r0, y1, g1, b1, w1, k3 has been played. You receive 2 clue: 2-2-2-x, it's likely your others 2s are playable (assuming no dupes and no k2 play, 55%).
- Now r0, y0, g1, b1, w1, k3 has been played. You receive 2 clue: 2-2-2-x, it's still likely you others 2s are playable, but not from much. Where is the limit? At which % of playable 2s you should assume your others 2s are playable at the point to play them?

For simplicity, since 2s are often not playable, that rule change for 1s & 2s.
My 83% is pretty high because k1 is single.

[Blacktango]

Hi,

(Firstable, sorry I didn’t read the entire post which was too long for this early morning : )

I think it’s more useful consider by default all 1s being playable (even with black powder). In most cases this convention saves more hint tokens.
The counterpart is when the Bk1 is between multiple 1. Then we need more tokens than without this convention.

I agree with you about the conventions. All convention have edge cases, and the game is great because you have to deal with them.
When you understand them, you can chose to "breaks" the conventions and create great techniques (like bluffs).

To play well with the conventions, players need to be understanding and flexible.

[Divinus]

Axiom 0 will tell you the clue must mean something, and you also know that if you do nothing the player will bomb. So there must be something we can do to prevent the bomb. Correcting the card violates axiom zero, since we are assuming a mistake.

Funny enough at 3 players, I did a bad clue in one of my first game on a trash card to make it playable. Next player corrected it, which let us save two cards in his chop.



Outside of this, here is the reasonning for your problem:
- 1s are always playable except for k1. That means if you receive 1 clue: 1-1-1-x, it's likely your others 1s are playable (assuming no dupes, 83% with 6suits).
- Now, imagine that r0, y1, g1, b1, w1, k3 has been played. You receive 2 clue: 2-2-2-x, it's likely your others 2s are playable (assuming no dupes and no k2 play, 55%).
- Now r0, y0, g1, b1, w1, k3 has been played. You receive 2 clue: 2-2-2-x, it's still likely you others 2s are playable, but not from much. Where is the limit? At which % of playable 2s you should assume your others 2s are playable at the point to play them?

For simplicity, since 2s are often not playable, that rule change for 1s & 2s.
My 83% is pretty high because k1 is single.

You need to compare like for like.
A black game (say 6 colors), where you receive 1 that marks 1-1-1-x (assuming no dupes) has 5 ones playable and one not playable.
A game (black or not) with the same number of colors (say 6 colors), where you receive 2 that marks 2-2-2-x (assuming no dupes and all 2's playable except for one color), has 5 twos playable and one not playable.
No change in probability. But in any case probabilities are not useful, because the limit you talk about is 100%. Hanabi play only deals in absolutes (with the exception of end game when you know you have a playable card but not where it is). No one in this convention plays based on probabilities. There might be others that do. This is quite obvious if I give you a clue 4 marking x-4-4-x where all fours but one color are playable - you play the first but not the second, even though probabilities are in your favor. The threshold is always 100%.
Same thing with ones in black.

[Divinus]

Hi,

(Firstable, sorry I didn’t read the entire post which was too long for this early morning : )

I think it’s more useful consider by default all 1s being playable (even with black powder). In most cases this convention saves more hint tokens.
The counterpart is when the Bk1 is between multiple 1. Then we need more tokens than without this convention.

I agree with you about the conventions. All convention have edge cases, and the game is great because you have to deal with them.
When you understand them, you can chose to "breaks" the conventions and create great techniques (like bluffs).

To play well with the conventions, players need to be understanding and flexible.

I'm not sure if it saves more hint tokens to be honest. I seriously doubt it is that easy to conclude.

But to counteract your point, there is a trade off between always having the best rules in a convention and simplicity.
For example: saving 2's at the start in more than 2player games is better than not doing it (the reason is because the cause of not perfect games being the duplicate of the last card being discarded - and discarding a 2 at the start might make other cards of that color discarded vs the situation where the 2 is saved and played). But even though it is a superior move, this convention does not deal with it correctly -why? Because the spirit is simplicity and low overhead - so it trades these kinds of optimizations for not having too much overhead. If you mark a 2 that is not a save, it will trigger a finesse or a direct play (if there are no 2's in the discard and at least one 1 on the piles). It doesn't treat 2's any different, even though it is an improvement, because that compromises the spirit with which the convention was built.

The case with 1's is the same. But here it is not even clear that it is a better move (like in the case with the 2's above), so there is absolutely no reason to do it.
It's absolutely fine if people want to explore conventions that try to maximize every little detail at the expense of simplicity and overhead - that is why I recommended to check out hyphenated for those who want to explore that path - that convention is developed way beyond BGA convention, at the expense of simplicity.

My point is that in BGA convention a number clue only plays more than one number (1-1-1-x or 2-2-2-x or x-3-3-x, etc) if all of them are playable (not the case with 1's in black games, but the case with 1's in non black games) or if you see all the non playable ones (the case in black games if you see 1k, for example). In other conventions it might be different and even better, but not on this one, because not only there is no strong case for it - it also goes again the spirit of the convention.

[Romain672]

No one in this convention plays based on probabilities. There might be others that do.

Right, we agree on that.

Just one example, r1 is played:
First player give 5 clue on r5 to third player. You, as second player, should assume without thinking you got r2+r3+r4. But this is unlikely. So, what I would really advice is what are the others possibilities for that clue to be?
Does that player didn't wanted to discard because it's turn 4 and give a 5-stall?
Does this player see a good fix with a 4 clue later on?
Did you miss anything else?
What I mean with that example: you don't play with probabilities normally, but you can find lots of situations where thinking about probabilities can be really beneficial for your own game.

But when people after the game, try to talk about conventions, and try to see how to improve them, the probabilities can be great.
What we want is something simple (this has even more value with bga's conventions because the community is big, and got players which have differents objectives), if possible is logical/can be find 'on-fly', and something effecient.

What you are proposing is kinda the same complexity (maybe slightly easier), kinda logical (but both ways look logical), and not effecient.
What bga's community has done got same complexity, kinda logical, and effecient (ie my probabilities higher).
(What I though you was maybe proposing, is something with very high complexity (probabilities), kinda logical too, and effecient. But since in your last post you disagree with probability, you didn't.)

Do you understand my point?

My point is that in BGA convention a number clue only plays more than one number (1-1-1-x or 2-2-2-x or x-3-3-x, etc) if all of them are playable (not the case with 1's in black games, but the case with 1's in non black games) or if you see all the non playable ones (the case in black games if you see 1k, for example). In other conventions it might be different and even better, but not on this one, because not only there is no strong case for it - it also goes again the spirit of the convention.

IE: probabilities higher. You may not like it, but just compare my two first numbers: 83% and 55%. The difference is huge. Assuming to never play others 1s is first make that player be lost in which 2s are playable (or waste 2/3 clues to clue colors on those 1s), while the drawback of not playing them would only be good in 17% of cases, and even in most those cases, reclue 1 is often available.

Btw about maths:
1-1-1-x assuming no dupes and leftmost playable: 12/13*9/10=0.83
2-2-2-x assuming r0, y1, g1, b1, w1, k3 played, no dupes, leftmost playable, and k2 not played (for simplicity): 7/9*5/7=0.55
Just ask me if you want I develop the math part, I can do it.

[Romain672]

I guess the main counterpoint would be to tell that 83% is not enough, which can be a fair point.
Especially since that number decrease if others not k1 1s are visible or clued.

But I mean, if you get g1-k1-y1-x, you play g1.
Then:
- if we assume you should play others ones, you either receive a 1 or a yellow clue and skip k1
- and if we assume you should not play others ones, you receive a yellow clue, and still have no info about the other one

Your main gain will be with a hand: r1-x-k1-x, you could clue 1 to save k1. But that upside doesn't look much appealing to me.

[Travis Hall]

Those players failed to understand the reasoning why a 1 clue can prompt several 1's in non black games, and just memorized it. Then they tried to apply it to black games: "a one clue at the start plays all ones - thats how it goes - if you dont you play bad".

Or, maybe you could consider the possibility that some very good players who do understand the logic behind the conventions have already considered your points and reached different conclusions.

There’s already a pretty long, detailed thread examining play of 1s in Black Powder games. You should probably find it, read it, and familiarise yourself with what has gone before. I’m not going to try to reproduce all of that for you here. I may say some more here, but you should definitely do that research.

[Travis Hall]

Your main gain will be with a hand: r1-x-k1-x, you could clue 1 to save k1. But that upside doesn't look much appealing to me.

Usually, 1r is going to be bluffed out, with a hand like that. No gain at all when that happens, and then we save 1k.

Really, what has been going on is that we like the early efficiency of playing out all 1s marked. We don’t want to lose that, because we need to make up the efficiency somewhere else. So we just clue such that 1k reads as a save, and occasionally spend an extra token in certain rare situations where we can’t.

[Travis Hall]

Divinus, you’re worried about treating 1s differently, aside from game state, and think that playing more than one when multiple 1s are clued is treating them differently. However, the example you provided - a hand marked all 1s - is not an example of treating 1s differently. There are analogous situations when you would be expected to play on in a similar manner for other numbers.

If you have two cards marked 4 (say - it applies to any number) and you know from context that neither is trash, and at least one is playable (which would be the case if all 4s except those had been either played or discarded - but in other situations too), you should wait until your partners have had a chance to correct (free from excessive token pressure, not busy with other things, you know you haven’t been holding colour blockers) and then assume the playable 4 is on the left, and play it.

Now that I’ve typed out that example, I realise it’s probably more common to satisfy all those conditions with 5s, during the late game. But no matter.

The point is, we assume the playable is on the left, and for the sake of efficiency, we allow our partners to make that assumption when it is correct. When it is not correct, we clue a correction.

When you received a clue marking all four of your cards as 1, you know (from Good Touch) that at least three of those 1s are playable. Otherwise, you should be receiving a different clue, or a correction. Since at least one of them is playable, and your partners have been free to correct, you assume the leftmost is playable, and play it. That’s the same as the late-game 4s and 5s.

It is entirely possible that your partners in that game were blindly following a pattern they had learnt without understanding why that pattern occurs. There are certainly a lot of players (especially in the expert range) who do that. But that doesn’t mean that there aren’t underlying reasons for those patterns even when Black Powder is added to the game. There is such a reason. You just hadn’t spotted it yet.