Behind this brutal title, I just want to post a little text I began to write more than a year ago. Someone asked me to publish it to start a discussion. It's very far from being completed, lacks figures and needs more work, so be indulgent.
I consider myself as a very strong hannabi player, but I haven't played it for more than a year so I'm rusted
Here is the text:
The purpose of this text is to deduce from pure logic all the conventions (such as finesse, reversed-finesse, or bluffs), so that the term “convention” can simply be eliminated from the game. An extremely logical player (with some autistic abilities ^^) could play Hannabi (almost) perfectly on his first game if he uses pure logic. As the reader progresses through this document, he will discover new ways to consider clues, the action of giving a clue, and the action to discard.
Vocabulary:
Chop: the rightmost non-clued card in the hand.
R means red, W means white, M means multicolor.
P1: the player to play.
P2: the player to play after P1
P3: the player to play after P2
P[x+1]: the player to play after P[x]
Critical card: card that, if discarded, prevents from reaching 30. So, all 5s, but also any 2, 3 or 4 cards when their corresponding doubloon is discarded.
….
As a starter, let’s discuss the drawing a of new card that occurs after a player has played a card, or discarded a card from his hand. It’s not specified in the rules that this new card must be put in the left of the remaining hand. Putting this card at random somewhere in the hand would simply confuse the holding player as well as the other players. One example is when you’re given a blue clue for your first card. From that point, you know that all the cards on the right of the clued card cannot be blue, which is a valuable piece of information. Inserting a card at random inside the hand would simply break the efficiency of this mental note, and so it should be avoided. As a conclusion, the freshly drew card should be placed on the left of all the other cards. This way, it’s easier for all players to identify quickly the new fresh card on every hand: it’s simply the leftmost one. Making it simple is a key concept to reach 30 points.
Since players must play the low numbers before the high numbers, it’s obvious that giving high numeric clues at the beginning of the game does not lead to any progression (except for the 5’s that must be saved, since they are critical cards). The idea behind giving a clue is to draw the attention of ALL players on that card, and sometimes (only sometimes!), it means the card is to be played immediately. Since fresh cards are put on the left, all the other cards are pushed to the right. This can be seen as the life of the card. Its birth is on the left, and its death is on the right.
When the player has to discard a card, where should he choose it? Since the idea is to make the game as fast-paced as possible, a fresh card that is playable is clued almost all the time immediately. So, in the opposite, useless cards are not marked and tend to finish at the right of the hand. This explains why we discard from the right: it’s pure logic and not linked to any convention.
Suppose there’s a 1R on the table, and the player after you just drew the 2R. Also, he has the 2W farther in his hand (1W is not on the table). Should you give the R or 2 clue? In both cases, the fresh is marked and will be played (more on this just after), so the degree of freedom can be used for another purpose. Since the number of clues is limited, you want to mark as much useful cards as possible, as long as you don’t clog too much the hand of your teammate. When the clues combine as time passes, players can sometimes deduce 3 cards of their hand while they are only given 2 clues. So, in this case, you would choose the numeral “2” clue. But what if the player also had the 3R in his hand? Even if you clued R to mark the 3R, the player, after having played the 2R, cannot deduce the card to be playable. You will need to mark it again by giving 3 (or giving again R, it depends on the situation). So, we’re at 2 clues for 2 cards. Instead, if you gave 2, and then you give R, you clearly draw the attention on the red, and the player can play it. You end up with 2 clues for 3 cards. Now, what if instead of the 3R, he has a 4R in his chop? Well, it’s still better to mark the 2, even at the cost of losing the 4. When you play a 3-player game and the last turn applies, you can do the sequence 3-4-5 at the end. So 4s, and even 3s, are expendable. But you want to keep the 2s to play them as soon as you have the corresponding 1.
Let’s start again from the numeral 2 clue. How can the player know he should play the leftmost 2 on his hand (the 2R, not the 2W)? Suppose 3 complete turns occurred before he drew the 2R (and with each of these turns, the 2W slowly moves to the right of the hand). Then the numeric “2” clue is given. It’s pretty obvious that if his 2W was playable, the other players would not have waited 3 turns to tell it, since it simply slows down the game. Hence, the “play from left” convention is in fact a pure logic conclusion. When a clue hits multiple cards, you play the one on the left, since it’s fresher (except when a chop card is clued: more on this later).
Color or number?
Suppose all the 1s are on the table. You’re P1 and P2 has 2R. Should you give 2, or red? Giving 2 let P2 in the mist, since he cannot deduce which 2 it is. On the contrary, giving red draws the attention on the red sequence, and P2 knows it can only be the 2R or 2M. The color gives thus more information and should be preferred, when possible, over the number
(TODO: add visuals for the next paragraph)
But what about the saves? Suppose the 4R is discarded and P2 has 2R in fresh and 4R in chop. If we choose the color to protect the 4, then it means that all the colored clues should be taken very cautiously throughout the entire game, because as soon as one colored card is discarded, any color clue that clues a card in the chop could be interpreted as a clue to save, and not a clue to play. So, in our case, P2 would discard instead of playing, because he’s not sure of what to do. He would then need another numeric clue to precise the 2, and then another one to precise the 4. We end up at 3 clues for 2 cards! Instead, if we used the 4 to mark the chop card, it immediately draws the attention on the number, and thus on all the discarded 4s. On the next turn, it’s then possible to clue R to now draw the attention on the second card of the hand (because P2 has discarded the card on the left of the 4), and, at the same time, to state that the 4 is also red. 2 clues for 2 cards: a better option.
Choosing a numeral clue for protection comes also simply from the 5 protection. It’s completely natural to mark 5s with the numeral “5” clue.
So, at this point of our comprehension of the game, color is for play, while numeral clues are for protection.
Try not to mark useless cards.
Since the freedom of cluing (cypher or color) can be used to mark additional cards that will be played in the future, the players don't discard collaterals. A collateral is a card that is marked as a side-effect of cluing another card that is to be played immediately. They remain in hand until they are playable. Because of this, players try not to clue useless cards. Useless cards would just stay in the hand until the end of the game and would demand an extra clue to be understood as discardable. It's important here that you MUST NOT spend a clue to make a player discard a useless card. This precious clue might be needed later. However, if the player has his hand clogged, then it's more important to free one slot in his hand. Sometimes, players will play a "not-well-defined" collateral card because they do the assumption that players only clue useful cards. Making this assumption is a mistake, because you cannot always avoid to clue useless cards (typically in middle and near-end game). It's of course a very good practice to try not to clue useless cards, but sometimes you have no other choice. So, by playing a collateral card, you must answer two conditions. The first one is that you cannot have 2 bombs on the table, since playing a false card could just end the game. I've lost so many games because of players addicted to risk. The other condition is that, if your play fails, it must not compromise the game. Suppose there is 1 bomb, all the multis and the [1-4]green on the table. You play your green thinking it's the 5g, but it turns out it's the 3g. Well, it's still ok. The 5g is still in the deck (otherwise you're really stupid) and will arrive later.
Useless cards marked in a hand are not absent of all information. Suppose [1-4]yellow and [1-4]multi are on the table and you have a card clued yellow. Another player has 5y and anotherother (just invented the word ^^) player just draws the 5m. Well, if you have nothing to play, you can now discard your yellow card, and all other players will understand that you just discovered it's useless. It's important to note that the information given from your discard move becomes useless if your card was precisely clued for a discard.
Discarding a useless card ONLY means that you know it's useless. It NEVER points towards any other cards. It OFTENS points to the fresh card some player just picked, but you cannot create a hard rule out of this. Nevertheless, some players will try to deduce more to that. For example, if there are sure that you JUST discovered NOW that the yellow is useless then it would mean that one of them just drew the last 5. But how can they know you didn't discover it one turn earlier (because both 5 were already there of course), but you had something to play... So, you see, playing from the discard of a useless card is risky and context-dependent.
Finesse. You’re P1. 1R on the table. P2 has 2R in fresh and P3 has 3R in his hand. What happens if you clue R on P3? P2 will immediately see that if he does nothing, P3 will play a wrong card. Since P1 wants to reach 30 points (and thus his red clue bears some logical meaning), it means P2 must do something so that the play of P3 will be good. It means he has the 2R somewhere in his hand. Where? Well, since this special clue of P1 occurred now, it means that P2 must have drew the 2R very closed from now: the fresh card! He can play it blindly.
They are two other cases when P2 does not play the leftmost card, and both are when he has an already-clued card that can fill the gap. A red card or a 2 card on his hand is valid. Now what happens if he has two 2 clued cards in his hand? Then he would choose the leftmost one, and there is NOTHING logical behind this choice. The only thing we can say is that as left is considered as life while right is death, P2 would choose life over death. This is a case where experience shows that systematically choosing left yields more easily to the 30 points.
In the case where P2 both has a R card and a 2 card, the choice depends on the relative position and when the red or the numeric clue was given.
[Introducing reverse] Reverse is to allow the play of 2 cards with one clue, but in sense opposed to the finesse sense.
No bypass.
Let’s put the 2R in P3’s hand as fresh, and you’re P1. Should you give the clue to P3, or leave it to P2? If you see the 3R is P2’s hand, of course you might go for the reversed-finesse. If P2 already has something to play, you should give the clue since you want the game as fast-paced as you can. In other cases, you should leave it to P2 by discarding. Since this action advances the game by one card, P2 is now in the position with the most information. You might even have a small chance of drawing the 3R. By doing a finesse or a bluff, P2 can give you a clue to trigger the play of the P3’s fresh card. So, as a conclusion, we can deduce it’s more optimal to let P[x-1] clue for P[x].
Because of that strong conclusion, it’s now possible to deduce something when a player bypasses the one that should give the clue (P1 does clue P3 instead of discarding). In that case, it might mean that P2 should discard to remove an annoying card, or, with very advanced players, that P2 should play a card that has been clued as a collateral. If the deduction of the right action is too difficult, discarding should always be the safest choice.
Play over save. Since reaching 30 points is difficult, and is rarely achieved before the last turn, you want to play the cards as fast as possible. The more you discard, the more likely you end up blocked in a situation where the copy of the card lies at the end of the deck. So, when a player has a 5 as the rightmost, if he has something that can be played, clue him to play! From this moment, he’s not allowed to discard anymore until he has played his clued card. He might even have a chance to draw a card that you can clue with a color to protect the 5 at the time!
An even more advanced play (to use with caution) is the clue over save. P1 has a card that he could play, if clued. It’s P2’s turn with 1 clue token, and P3 has an unsaved 5 in the discard position. Typical players will protect the 5, and thus will force P3 to discard. A more advanced play is to discard, so that P3 can give the clue to P1. P1 plays, so you’re back at the same situation with one clue. This cannot be done if P1’s rightmost card is to be protected, because you would end up with 1 clue token and 2 player’s chop to save.
[the text ends so far....]
I consider myself as a very strong hannabi player, but I haven't played it for more than a year so I'm rusted
Here is the text:
The purpose of this text is to deduce from pure logic all the conventions (such as finesse, reversed-finesse, or bluffs), so that the term “convention” can simply be eliminated from the game. An extremely logical player (with some autistic abilities ^^) could play Hannabi (almost) perfectly on his first game if he uses pure logic. As the reader progresses through this document, he will discover new ways to consider clues, the action of giving a clue, and the action to discard.
Vocabulary:
Chop: the rightmost non-clued card in the hand.
R means red, W means white, M means multicolor.
P1: the player to play.
P2: the player to play after P1
P3: the player to play after P2
P[x+1]: the player to play after P[x]
Critical card: card that, if discarded, prevents from reaching 30. So, all 5s, but also any 2, 3 or 4 cards when their corresponding doubloon is discarded.
….
As a starter, let’s discuss the drawing a of new card that occurs after a player has played a card, or discarded a card from his hand. It’s not specified in the rules that this new card must be put in the left of the remaining hand. Putting this card at random somewhere in the hand would simply confuse the holding player as well as the other players. One example is when you’re given a blue clue for your first card. From that point, you know that all the cards on the right of the clued card cannot be blue, which is a valuable piece of information. Inserting a card at random inside the hand would simply break the efficiency of this mental note, and so it should be avoided. As a conclusion, the freshly drew card should be placed on the left of all the other cards. This way, it’s easier for all players to identify quickly the new fresh card on every hand: it’s simply the leftmost one. Making it simple is a key concept to reach 30 points.
Since players must play the low numbers before the high numbers, it’s obvious that giving high numeric clues at the beginning of the game does not lead to any progression (except for the 5’s that must be saved, since they are critical cards). The idea behind giving a clue is to draw the attention of ALL players on that card, and sometimes (only sometimes!), it means the card is to be played immediately. Since fresh cards are put on the left, all the other cards are pushed to the right. This can be seen as the life of the card. Its birth is on the left, and its death is on the right.
When the player has to discard a card, where should he choose it? Since the idea is to make the game as fast-paced as possible, a fresh card that is playable is clued almost all the time immediately. So, in the opposite, useless cards are not marked and tend to finish at the right of the hand. This explains why we discard from the right: it’s pure logic and not linked to any convention.
Suppose there’s a 1R on the table, and the player after you just drew the 2R. Also, he has the 2W farther in his hand (1W is not on the table). Should you give the R or 2 clue? In both cases, the fresh is marked and will be played (more on this just after), so the degree of freedom can be used for another purpose. Since the number of clues is limited, you want to mark as much useful cards as possible, as long as you don’t clog too much the hand of your teammate. When the clues combine as time passes, players can sometimes deduce 3 cards of their hand while they are only given 2 clues. So, in this case, you would choose the numeral “2” clue. But what if the player also had the 3R in his hand? Even if you clued R to mark the 3R, the player, after having played the 2R, cannot deduce the card to be playable. You will need to mark it again by giving 3 (or giving again R, it depends on the situation). So, we’re at 2 clues for 2 cards. Instead, if you gave 2, and then you give R, you clearly draw the attention on the red, and the player can play it. You end up with 2 clues for 3 cards. Now, what if instead of the 3R, he has a 4R in his chop? Well, it’s still better to mark the 2, even at the cost of losing the 4. When you play a 3-player game and the last turn applies, you can do the sequence 3-4-5 at the end. So 4s, and even 3s, are expendable. But you want to keep the 2s to play them as soon as you have the corresponding 1.
Let’s start again from the numeral 2 clue. How can the player know he should play the leftmost 2 on his hand (the 2R, not the 2W)? Suppose 3 complete turns occurred before he drew the 2R (and with each of these turns, the 2W slowly moves to the right of the hand). Then the numeric “2” clue is given. It’s pretty obvious that if his 2W was playable, the other players would not have waited 3 turns to tell it, since it simply slows down the game. Hence, the “play from left” convention is in fact a pure logic conclusion. When a clue hits multiple cards, you play the one on the left, since it’s fresher (except when a chop card is clued: more on this later).
Color or number?
Suppose all the 1s are on the table. You’re P1 and P2 has 2R. Should you give 2, or red? Giving 2 let P2 in the mist, since he cannot deduce which 2 it is. On the contrary, giving red draws the attention on the red sequence, and P2 knows it can only be the 2R or 2M. The color gives thus more information and should be preferred, when possible, over the number
(TODO: add visuals for the next paragraph)
But what about the saves? Suppose the 4R is discarded and P2 has 2R in fresh and 4R in chop. If we choose the color to protect the 4, then it means that all the colored clues should be taken very cautiously throughout the entire game, because as soon as one colored card is discarded, any color clue that clues a card in the chop could be interpreted as a clue to save, and not a clue to play. So, in our case, P2 would discard instead of playing, because he’s not sure of what to do. He would then need another numeric clue to precise the 2, and then another one to precise the 4. We end up at 3 clues for 2 cards! Instead, if we used the 4 to mark the chop card, it immediately draws the attention on the number, and thus on all the discarded 4s. On the next turn, it’s then possible to clue R to now draw the attention on the second card of the hand (because P2 has discarded the card on the left of the 4), and, at the same time, to state that the 4 is also red. 2 clues for 2 cards: a better option.
Choosing a numeral clue for protection comes also simply from the 5 protection. It’s completely natural to mark 5s with the numeral “5” clue.
So, at this point of our comprehension of the game, color is for play, while numeral clues are for protection.
Try not to mark useless cards.
Since the freedom of cluing (cypher or color) can be used to mark additional cards that will be played in the future, the players don't discard collaterals. A collateral is a card that is marked as a side-effect of cluing another card that is to be played immediately. They remain in hand until they are playable. Because of this, players try not to clue useless cards. Useless cards would just stay in the hand until the end of the game and would demand an extra clue to be understood as discardable. It's important here that you MUST NOT spend a clue to make a player discard a useless card. This precious clue might be needed later. However, if the player has his hand clogged, then it's more important to free one slot in his hand. Sometimes, players will play a "not-well-defined" collateral card because they do the assumption that players only clue useful cards. Making this assumption is a mistake, because you cannot always avoid to clue useless cards (typically in middle and near-end game). It's of course a very good practice to try not to clue useless cards, but sometimes you have no other choice. So, by playing a collateral card, you must answer two conditions. The first one is that you cannot have 2 bombs on the table, since playing a false card could just end the game. I've lost so many games because of players addicted to risk. The other condition is that, if your play fails, it must not compromise the game. Suppose there is 1 bomb, all the multis and the [1-4]green on the table. You play your green thinking it's the 5g, but it turns out it's the 3g. Well, it's still ok. The 5g is still in the deck (otherwise you're really stupid) and will arrive later.
Useless cards marked in a hand are not absent of all information. Suppose [1-4]yellow and [1-4]multi are on the table and you have a card clued yellow. Another player has 5y and anotherother (just invented the word ^^) player just draws the 5m. Well, if you have nothing to play, you can now discard your yellow card, and all other players will understand that you just discovered it's useless. It's important to note that the information given from your discard move becomes useless if your card was precisely clued for a discard.
Discarding a useless card ONLY means that you know it's useless. It NEVER points towards any other cards. It OFTENS points to the fresh card some player just picked, but you cannot create a hard rule out of this. Nevertheless, some players will try to deduce more to that. For example, if there are sure that you JUST discovered NOW that the yellow is useless then it would mean that one of them just drew the last 5. But how can they know you didn't discover it one turn earlier (because both 5 were already there of course), but you had something to play... So, you see, playing from the discard of a useless card is risky and context-dependent.
Finesse. You’re P1. 1R on the table. P2 has 2R in fresh and P3 has 3R in his hand. What happens if you clue R on P3? P2 will immediately see that if he does nothing, P3 will play a wrong card. Since P1 wants to reach 30 points (and thus his red clue bears some logical meaning), it means P2 must do something so that the play of P3 will be good. It means he has the 2R somewhere in his hand. Where? Well, since this special clue of P1 occurred now, it means that P2 must have drew the 2R very closed from now: the fresh card! He can play it blindly.
They are two other cases when P2 does not play the leftmost card, and both are when he has an already-clued card that can fill the gap. A red card or a 2 card on his hand is valid. Now what happens if he has two 2 clued cards in his hand? Then he would choose the leftmost one, and there is NOTHING logical behind this choice. The only thing we can say is that as left is considered as life while right is death, P2 would choose life over death. This is a case where experience shows that systematically choosing left yields more easily to the 30 points.
In the case where P2 both has a R card and a 2 card, the choice depends on the relative position and when the red or the numeric clue was given.
[Introducing reverse] Reverse is to allow the play of 2 cards with one clue, but in sense opposed to the finesse sense.
No bypass.
Let’s put the 2R in P3’s hand as fresh, and you’re P1. Should you give the clue to P3, or leave it to P2? If you see the 3R is P2’s hand, of course you might go for the reversed-finesse. If P2 already has something to play, you should give the clue since you want the game as fast-paced as you can. In other cases, you should leave it to P2 by discarding. Since this action advances the game by one card, P2 is now in the position with the most information. You might even have a small chance of drawing the 3R. By doing a finesse or a bluff, P2 can give you a clue to trigger the play of the P3’s fresh card. So, as a conclusion, we can deduce it’s more optimal to let P[x-1] clue for P[x].
Because of that strong conclusion, it’s now possible to deduce something when a player bypasses the one that should give the clue (P1 does clue P3 instead of discarding). In that case, it might mean that P2 should discard to remove an annoying card, or, with very advanced players, that P2 should play a card that has been clued as a collateral. If the deduction of the right action is too difficult, discarding should always be the safest choice.
Play over save. Since reaching 30 points is difficult, and is rarely achieved before the last turn, you want to play the cards as fast as possible. The more you discard, the more likely you end up blocked in a situation where the copy of the card lies at the end of the deck. So, when a player has a 5 as the rightmost, if he has something that can be played, clue him to play! From this moment, he’s not allowed to discard anymore until he has played his clued card. He might even have a chance to draw a card that you can clue with a color to protect the 5 at the time!
An even more advanced play (to use with caution) is the clue over save. P1 has a card that he could play, if clued. It’s P2’s turn with 1 clue token, and P3 has an unsaved 5 in the discard position. Typical players will protect the 5, and thus will force P3 to discard. A more advanced play is to discard, so that P3 can give the clue to P1. P1 plays, so you’re back at the same situation with one clue. This cannot be done if P1’s rightmost card is to be protected, because you would end up with 1 clue token and 2 player’s chop to save.
[the text ends so far....]
