Hanabi
Carousel Conventions
A Competitive System
by <INSERT MAIN CONTRIBUTORS>
Version α.13
(last updated 27 April, 2023)
This page is an autogenerated conversion of the LaTeX document to HTML. It may have some unexpected presentations.
The main objective of this set of conventions is twofold: to win competitions, and to have fun whilst doing so. In practice, this means three things, prioritised as follows:
maximising expected score (instead of winrate)
minimising turn count
giving players a reasonable amount of flexibility.
Note that “flexibility” is not used to mean the ability to tolerate mistakes – that is incompatible with our aims – instead, it means that we would like to empower players with a large range of possible “moves” on any given turn.
The convention set heavily derives from H-Live Conventions, but there are many fundamental differences, and we suspect that the conventions will continue to diverge over time.
Here are a list of fundamental differences in the approach of these conventions with that of the H-Live conventions.
While H-Live conventions state that it tries to maximise expected score, in practice we do not find this to be the case – it may have something to do with the heavy culture of scorehunting, which is only recently beginning to change. These conventions aim to address what to do in dire situations, where achieving max score may be far-fetched.
The H-Live conventions do not aim to minimise turn count, unlike these conventions.
These conventions may change very quickly and without warning. They are intended for a very niche audience, and so proposals have a much faster turnover rate.
H-Live conventions have historically taken the viewpoint that not every situation or sequence of moves should be defined. These was meant to increase the error tolerance. These conventions do not take such a viewpoint. Note that this does not mean there are no “known mistakes” (indeed, that is impossible for any developed convention system), but that there are fewer situations where this would be the case.
H-Live conventions try not to have “feature bloat”. Rarely-used conventions are sometimes deleted. We would never do that – we love feature bloat.
H-Group convention levels are ordered by their “complexity”. Our convention levels are roughly ordered by how frequently they are used.
If we had to condense the ideas in these conventions to a single paragraph:1
Utilising more situation-dependent conventions (in the spirit of earlygame, endgame, low-score phase, hard variants, etc.)
Using discards to signal shift instead as well as blind-plays.
Maximising the probability that signal shifts can be used, which also means far less finesses of 2+ cards.
Introducing more “n tech”, conventions related to cluing certain ranks under special circumstances
Developing more late-game conventions which minimise turn count.
Introducing a hierarchy of discard quality.
More ways to extend the early-game.
These convnetions have been typeset using LaTeX, and the developers
of these conventions collaborate via Overleaf. Contact
Tony Wang#1806 (UserID: 541318134699786272) on
Discord to get access to the
overleaf. Please join the Hanabi
Central Discord server before contacting. Once you have access to
this document, you can make comments on the conventions using Overleaf’s
commenting system.
This document is just an easy way for our group to get started with
developing conventions, being more organised than a Google Doc, but less
organised than a fully-fledged website in the spirit of the H-Group conventions website.
Ideally, when these conventions become larger and a bit more stable,
we’ll probably switch to hosting them on a webpage, so that we can more
easily track version history, etc.
As of 2022-02-08, there is a lack of examples in this document. We hope
to add more in the future.
This section is incomplete.
A proposal, not yet in
effect.[<PROPOSER>]
Needs review/under
review.[<INSTIGATOR>]
This convention is deprecated,
ignore for now.[<INSTIGATOR>]
↑Fn: Play the n-th finesse position.
↓Fn: Discard the n-th finesse position.
| Term | Definition |
|---|---|
| Alice, Bob, Cathy | The first, second, and third players respectively |
| Slot n | The n-th left-most card (Sn) |
| Chop | The right-most unclued card |
| Focus | The card primarily referred to by a clue |
| n-th Finesse Position | The n-th left-most unclued card (Fn). When n is not specified, assume n = 1. |
| Globally Known | Information is Globally Known if each player knows it. |
| Common Knowledge | Information is considered Common Knowledge if it is globally known, each player knows it is globally known, each player knows it is globally known that it is globally known, and so on. In this way, basic conventions like direct clues result in Common Knowledge, whereas something like a 5CM is often globally known but not Common Knowledge. |
| Blind Card | A card which does not have any positive clues on it |
| Blind-play | Playing a blind card. |
| Blurry Card | A card which has a positive clue on it, but its identity is not common knowledge. |
| Blurry-play | Playing a blurry card. |
| Finesse | The blind-play of F1 into a connecting card |
| Bluff | The blind-play of Bob’s F1 into a non-connecting card |
| Ignition | The blind-play of F1 from an advanced move which is not a finesse or bluff |
| Ejection | The blind-play of F2 as a signal shift |
| Discharge | The blind-play of F3 as a signal shift |
| Charm | The blind-play of F4 as a signal shift |
| Blast | The blind-play of F5 as a signal shift |
| Alakazam | The blind-play of F6 as a signal shift |
| Peel | The discard of F1 as a signal shift |
| Objection | The discard of F2 as a signal shift |
| Necro[Tony] | The discard of F3 as a signal shift |
| Melt[Tony] | The discard of F4 as a signal shift |
| Leak[Tony] | The discard of F5 as a signal shift |
| Kaput[Tony] | The discard of F6 as a signal shift |
| Referential Clue | Any clue whose focus is not one of the cards touched. |
Convention 1 (Clarification of focus precedence). When determining the initial focus of any clue, we find the most precedent type of card that was touched, and say that the focus is on the leftmost of touched cards of that type. The precedence table is as follows:
Chop
Unclued (non-chop)
Chop-moved
Clued, Baton-discarded, blaze-batoned, safety charmed
Finessed, prio-ed, GD-ed, and blaze-GD-ed
Pulled cards (including CMIs)
Pushed cards (e.g. from trash pushes)
Convention 2 (Clarification of finesse positions). In H-group conventions, finesse positions are enumerated by unclued cards, going from left to right. In Carousel conventions, they are enumerated by unclued cards, left to right, and then by chop-moved cards, left to right, and then by clued-and-potentially-playable (but not fully known) cards, left to right.
Convention 3 (Bluffs (Generalised)). If Alice clues an n-away card to Cathy, then Bob should ↑Fn.2 (Example 1). (Example 2). (Example 3). (Example 4). When calculating n, only take common knowledge into account.
Note that it is extremely important that a card is either completely known to be trash or completely known to be useful. That is, if playing the correct slot into a Generalised Bluff does not demonstrate to Cathy that the card is trash (as can be the case when cluing with rank or cluing with colour in multi-colour variants), then Bob must instead use a different signal:
Convention 4 (UT Peel). Every UT Discharge should be a UT Peel instead. (Example). If the clue only introduced one new card, the clued player should treat the trash clue as unnecessary (Example).[russ]
Convention 5 (Trash Bluffs). Trash bluffs and finesses still exist XD.
Convention 6 (Peel Elimination Principle). If a peeled (or blind-discarded) card is not trash, players should make elimination notes for the other copy.
Convention 7 (Necessariness). All “unnecessary” clues are considered “necessary” if the extra component is a chop move. Otherwise, they can still be unnecessary or necessary.
When the score is less than the number of suits (ultra-low score phase), most colour clues that introduce new cards are referential. This phase is more commonly called Referential Phase.
Convention 8 (Referential Clues). If a colour clue during Referential Phase has focus precedence ([it:focus-prec-unclued]) Unclued (non-chop), then the true focus is the precedence ([it:focus-prec-chop]) or ([it:focus-prec-unclued]) card to the right of the right-most touched precedence ([it:focus-prec-unclued]) card. This is always a Play Clue.[Tony] (Example). If a colour clue touches a newly-introduced card on chop, then the clue is not referential, and the focus is on that chop card (Example). If a referential clue results in ↑Fn, then the referred card should be CM’ed. Otherwise, it is marked as F’ed.3
Convention 9 (Referential Bluff Connection). If a referential clue results in ↑F1, this indicates that the referred card is 1-away, but unlike in Hyphenated conventions, it may not necessarily be playable (Example 1). (Example 2). This convention also applies to 5-pulls (Example).
Convention 10 (Referential Prompts). A referential clue should only be a prompt if it refers to a 1-away card (Example). If the card is two-or-more-away, then Bob should prefer the blind-play interpretation instead (Example).
Convention 11 (Dump Trucks). Every double ignition is instead to be taken as a Dump Truck. This means that Bob should play the first finesse slot that Cathy can also play. If Cathy cannot play any finesse slots, then Bob should find the first one-away-from-playable card, and trust that he is playing the connecting card.
In the very low score phase (i.e. a score of less than 1.5× number of suits), a 4s clue is never to be interpreted as a Play Clue. If a 4 is to be given a play clue, it should be clued with colour, blind-played, or otherwise the team can wait.
Convention 12 (4’s Dump Truck). If Alice clues the number 4 during VLSP, this indicates a Dump Truck (Example 1). (Example 2).
Convention 13 (Unknown Trash Touch Objection). If Alice clues Cathy, touching two or more cards, and only the focus is useful, then Bob should Object if Cathy had something better to do (such as discarding). If the Unknown Trash Touch is unnecessary, Bob should also CM once. Note that this may create asymmetric CMs. This move should only be performed during Positional Phase if it is unambiguous.
Convention 14 (3’s Spectral Blind-play). During referential phase, a rank 3 clue is never to be interpreted as a direct play clue. Instead, Bob should ↑Fn where the 3 is of the n-th colour, wrapping around if necessary. In this way, Cathy should always know roughly what colour the 3 is. Note: When playing variants in a competition, a team may choose to order the colours (mentally) in a different order, so as to maximise the value of this convention.[cana]
Convention 15 (1’s Choice Peel). If Alice has a choice between using a referential clue to focus a 1, but instead clues rank to the 1 directly, without touching any other 1s, the player not clued should mark their F1 as KT and peel.
Convention 16 (Unknown Trash Objection). During referential phase, unnecessarily touching trash for all non-focused cards using a rank clue is signalled by ↓F2. Note that this is not considered unnecessary if there is no referential way to get the card without touching trash, or if the cluer is trying to stall.
Convention 17 (Unknown Dupe Necro). During referential phase, unknown dupes using rank are signalled by ↓F3. Note that this only works if exactly two new cards were introduced by the clue – otherwise it is a Unknown Trash Peel. The reasoning behind this convention is that it is useful for the team to be able to use Dupe Tech.
Convention 18 (Tempo Clue Ignition). If Alice clues Bob, causing a Tempo Clue Chop Move, but Cathy sees that the chop-moved card is trash, then Cathy ignites. This causes Bob to un-chop move the card. Note that in these cases Bob should not get Cathy’s F1 card since it may break the communication channel.[cana]
Convention 19 (Low-Score Phase Tempo Clue Redefinition). Usually, tempo-cluing an unpromptable card does not trigger Tempo Clue conventions. However, we modify this so that in the Low-Score Phase, it does still trigger Tempo Clue conventions.[cana]
Convention 20 (4’s Dump Train). During the Referential Phase, 4’s Dump Trucks can be ineffective, because referential clues can touch a lot of cards, meaning that there might not be very many cards left to be played blind. We extend the Truck into a Train by introducing blurry-plays: A card which has played onto the stacks was blurry-played if it was clued, but not fully known. If a player runs out of blind-play slots, they should move into blurry-play slots, going from left to right. Note that this convention has higher precedence than a Dump Truck where the first blind-play connects to the second blind-play. Example: outside of referential phase, Alice would try to play B1 into B2, but in this case Dump Trains take precedence and Alice ↑F4, signalling for Bob to blurry-play Y2 as F4.
Note that as a consequence of the previous convention, any “context” play that occurs right after a 4 has been clued should actually be treated as the “blind” component of a 4’s Dump Train.
Convention 21 (4’s Dump Truck with Colour). A colour clue to a known 4 in Very Low Score Phase indicates a dump truck in the same way that 4 clues do. This means we can sometimes get colour information on a 4 instead of recluing it. Outside of Very Low Score Phase, it may still be a Dump Truck if the 4 is two-or-more-away.[Tony]
Convention 22 (4’s Dump Truck with Locked hand). If a 4 is clued in very low score phase, but one of the players is locked or has no unknown blind plays or blurry plays, then the 4 indicates a double ignition stacked onto the other player. The other player should play these cards in order unless they have context the cards can be played in either order. In this case, they may trigger priority by playing them out of order.[Tony]
Convention 23 (4’s Dump Truck Chop Move). If Bob is asked to Dump truck but there are no playable nor one-away-from-playable cards in Cathy’s hand, and there are no blurry-plays, then he is being asked to peel the first useful-finesse position card (which does not duplicate anything). Cathy should then Chop Move this card.[Tony]
Convention 24 (Dumpster Fire). If at any point the card with highest discard priority is bombed, this indicates a Dumptruck on Bob and Cathy, if the team agrees the bomb was not a mistake. This kind of Dumptruck is called Dumpster Fire. If at any point the card with second highest discard priority is bombed, this indicates that Bob should ↑Fn and Cathy should ↑F(n+1). This is called a Dumpster Fire Trainwreck. When the team is at 8 clues, a bomb of the highest discard priority card does not trigger anything, a bomb of the second highest discard priority card indicates a dumpster fire, and a bomb of the third highest discard priority card indicates a dumpster fire trainwreck.
In Positional Phase, at the end of the game, players lose the ability to perform reverse finesses, and gain the ability to perform positional discards at any time.4
Convention 25 (Positional Phase). Positional Phase begins when the players reach a score greater than 3 times the number of suits, AND the pace is higher than twice the number of clues remaining. It remains in effect until the end of the game.[tony]
Convention 26 (Positional Discards). A positional discard signals that the next player can play that slot right now. Alice cannot positional discard for Cathy in general, though there are exceptions discussed later. Furthermore, it is Alice’s responsibility to protect Bob from positional-discarding useful cards. Hence, if Alice clues Bob, touching an unplayable card, then Cathy should not assume a Reverse Finesse and Bob should not assume a play clue. Instead, Alice was protecting Bob from Positional-Discarding that card. Hence, Cathy can then deduce that she should play the same slot (this also means Bob can now discard normally).
Convention 27 (Positional Misplay). Alice gave Bob permission to Positional Discard for Cathy, and Bob instead bombs the slot, this is a Positional Misplay, which works the same as it does in H-Group conventions.
Convention 28 (Declined Positional Discard). Alice gave Bob permission to Positional Discard for Cathy, and Bob instead directly clues Cathy’s card, this is a Declined Positional Discard. If both a Positional Discard and a direct clue makes Cathy play the card, then Alice should interpret this clue as Bob trying to protect Cathy from Positional Discarding that card, and Alice should then also play that slot. Note that this move is slower than a Positional Misplay, but may be required when the team is at two strikes.
Some of these may be truly "advanced strategies" (as of 2023-01-05, this is probably not the case), but otherwise some of these conventions are simply yet to find a home in one of the levels.
Convention 29. Sort out interaction between delayed referential plays vs. probability of being playable.
Convention 30 (Generalised bluff value principle). A generalised bluff does not occur when no new information is given to the card clued by playing into a generalised bluff (i.e. there is no reason to be doing a generalised bluff).
Convention 31 (5 Trainwreck). Cluing (recluing?) a 5 in referential phase indicates a trainwreck.[Tony]
Convention 32 (Declined reclue shadows). When Alice declines to finesse Bob by recluing a previously clued but unknown card in Cathy’s hand, Bob should shadow-play the finesse position which indicates to Cathy which card Alice could have reclued. (That is, Bob’s shadow-positions are extended on the left by Cathy’s matching clued cards.)[Tony]
Convention 33 (Prio change?). Prio → single ignition?[Tony]
Convention 34 (Referential Reverse Finesse Exception). During referential phase, direct clues are still allowed if it could be a finesse which gets 2+ cards.[cana]
Convention 35 (Fill-in Dump truck). Filling in the colour of a 4 in VLSP when it’s 2+ away causes a Dump Truck[cana]
Convention 36 (OCM Swaps). See Kipipi OCM swaps.
Convention 37 (Trainwreck). Bombing a card one away from chop means Bob should play Fn and Cathy should play F(n + 1)[Tony]a
Convention 38 (Reverse UTTO). If Alice clues Bob in the scenario described in the UTTO convention, then Cathy should demonstrate that Bob’s non-focused cards were trash retroactively by Objecting. Note that this move should not be performed during Positional Phase.
Convention 39 (Reverse Suboptimal Peel). If Alice clues Bob rank when colour is always better (regardless of what Cathy has in her hand), then Cathy should peel.
Convention 40 (Unnecessary TCM Discharge). If a card is TCM’ed when it could have been saved directly, then the trash move is unnecessary. Bob should Discharge.
Convention 41 (Extinguished Blaze). Between very-low score phase and high score phase, a blaze discard should be signalled by a discard of the corresponding slot instead of a blind play. During high score phase, the player with the “ignited” hand should only blind-play if the blaze was unnecessary, otherwise he should discard as normal.
Convention 42 (Peel Value Principle). Outside of very low score phase, a clue cannot simply get two trash cards.[russ]
This section is incomplete.
In normal hyphenated conventions, we have the following signal
shifts:
KT push + ↑F1 = Trash Push Finesse or Unnecessary Trash push
KT push + ↑F2 = Trash Push CM
KT push + ↑F3 = Trash Push Trash
KTCM+ ↑F1 = CMignition
KTCM+ ↑F2 = bad CMejection
Play clue + ↑F3 = UTDischarge
In these conventions, we generalise to the following: Let Alice clue Cathy an unknown trash card to Cathy, and suppose that Bob can demonstrate that the card is trash via a trash bluff. If there was a better way to get Bob to play F1, then Alice must be intending something else.
Suboptimal trash bluff + chop moved card is also trash = ↑F2 as jump bad chop move ejection.[Tony]
(Some stuff on clue-count-specific stalling. Card number stalling.)
For reference, here’s the H-Group Stall Table:
| Action | Earlygame | Double Discard | Locked Hand | 8 Clues |
|---|---|---|---|---|
| (1) Play or Save clue | Yes | Yes | Yes | Yes |
| (2) 5 Stall (Note FPE) | Yes | Yes | Yes | Yes |
| (3) Tempo Clue | - | Yes | Yes | Yes |
| (4) Fill-in Clue | - | Yes | Yes | Yes |
| (4) Locked Hand Save | - | - | Yes | Yes |
| (4) 8-clue Save | - | - | - | Yes |
| (5) Hard Burn | - | Yes | Yes | Yes |
Note that one great reason an 8-clue save is allowed at 8 clues but not during a locked hand is because lower-value clues are much more acceptable at a higher number of clues. We can probably generalise this, producing specific tables for each scenario (earlygame, DDA, etc.) which incorporates the current clue count.
I (Tony) feels like there’s some room here for new conventions. We already have OCMs, and with 1s usually being the first known trash cards, I feel like we could perhaps do a bit more with them. Maybe:
Convention 43 (1s trash tolerance). In games with 5 or more suits, when all but one 1 has been played, any 1s clue is treated as known trash.5[Tony]
We inherit H-group conventions, except for the following:
Convention 44 (Modified Pink Turnabout Ejection). Playable pink card mis-clued with a pink 5 clue that would usually trigger a Pink Turnabout Ejection doesn’t, and instead triggers the Generalised Bluff Interpretation. (Hence do not misrank-cards in this way, otherwise a Taffy finesse will be assumed.) A Pink 5 clued with a rank 1 clue still triggers a Turnabout Ejection as normal.
Convention 45 (Spectral 3s and Bubblegum Bluff). Spectral 3s and Bubblegum Bluff have the same precedence.
We inherit Carousel Pink conventions, and H-group conventions, except for the following:
Convention 46 (Save clues). Dark pink 4 should be saved with 5 instead of colour.
Convention 47 (Non-focused trash status). In Trash Chop Moves, all touched cards are assumed to be trash immediately, and discard order can trigger a Trash Order Chop Move. However, in a Trash Push, while the focused card is promised trash, the non-focused cards are not promised as trash. Bob should decide whether to discard the touched cards or his chop based on context. His choice should not trigger anything.
Convention 48 (Loaded White Assumption). We use the Loaded White Assumption convention. See this link.
This section is incomplete.
| Focus Precedence | Tony, adapted from H-Group |
| Generalised Bluffs | Caña and Tony |
| Peel (name) | Frosty104 |
| F[2] to F[6] peel names | Tony |
| UT Peel | Tony, Russ |
| 1’s Peel | Tony |
| Reverse Suboptimal Peel | Tony |
| Unnecessary TCM Discharge | Tony |
| Extinguished Blaze | Tony |
| Peel Elimination Principle | Frosty104 (name by Tony) |
| Peel Value Principle | Tony |
| Referential Phase | Tony, inspired by Referential Sieve |
| Referential Clues | Tony |
| Referential Bluff Connection | Tony |
| 4’s Dump Truck | Tony, inspired by Kipipi |
| 3’s Spectral Blind-play | Tony |
| Stalling | Tony |
| 1s Trash Tolerance | Tony |
| Positional Discards | Tony, Caña, adapted from H-Group |
| Positional Misplay | Tony, Caña, adapted from H-Group |
| Declined Positional Discard | Tony |
| Blurry-play | Tony |
Convention 49 (4-Push (2022-03-19)). If Alice clues the number 4 during VLSP, and the 4 is on chop, this indicates a 4-Push, pushing the first unclued card to the left of the 4 on chop.[Tony] (Example 1). (Example 2). (Example 3).
Changed
Convention 50 (Bluffs (Generalised)). If Alice clues an n-away card to Cathy, then Bob should ↑Fn.6 (Example 1). (Example 2). (Example 3). (Example 4). When calculating n, only take globally known cards into account. Unknown trash cards are considered to be one further than the end of the stack for their suit (Example).[russ]
into
Convention 51 (Bluffs (Generalised)). If Alice clues an n-away card to Cathy, then Bob should ↑Fn.7 (Example 1). (Example 2). (Example 3). (Example 4). When calculating n, only take globally known cards into account.
Changed
Convention 52 (UT Peel). If blind-playing is not enough[russ] for Bob to show Cathy that a card is trash, then Bob should peel instead (Example). If the clue only introduced one new card, the clued player should treat the trash clue as unnecessary (Example).[russ]
into
Convention 53 (UT Peel). Every UT Discharge should be a UT Peel instead. (Example). If the clue only introduced one new card, the clued player should treat the trash clue as unnecessary (Example).[russ]
Changed the convention Focus Precedence to Clarification of focus precedence in level 1. Added convention Clarification of finesse position to level 1:
Convention 54 (Clarification of finesse positions). In H-group conventions, finesse positions are enumerated by unclued cards, going from left to right. In Carousel conventions, they are enumerated by unclued cards, left to right, and then by chop-moved cards, left to right, and then by clued-and-potentially-playable (but not fully known) cards, left to right.
Added 4’s Dump Truck Chop Move and 4’s Dump Truck with Colour into the Advance Strategies section.
Convention 55 (4’s Dump Truck with Colour). A colour clue to a known 4 in Very Low Score Phase indicates a dump truck in the same way that 4 clues do. This means we can sometimes get colour information on a 4 instead of recluing it. Outside of Very Low Score Phase, it may still be a Dump Truck if the 4 is two-or-more-away.[Tony]
Convention 56 (4’s Dump Truck with Locked hand). If a 4 is clued in very low score phase, but one of the players is locked or has no unknown blind plays or blurry plays, then the 4 indicates a double ignition stacked onto the other player. The other player should play these cards in order unless they have context the cards can be played in either order. In this case, they may trigger priority by playing them out of order.[Tony]
(Note there have been a lot of missed changelogs since the last one, including the formation of Level 3 with Tempo Clue Ignition, Low-Score Phase Tempo Clue Redefinition, 4’s Dump Train, 4’s Dump Truck with Colour, 4’s Dump Truck with Locked Hand, Dumpster Fire, Position Phase, Positional Discards, Positional Misplay, and Declined Positional Discard, along with the introduction of Variant convneionts: Modified Pink Turnabout Ejection and Spectral 3s and Bubblegum Bluff in the Pink convnetions, Save clues and Non-focused trash status in Dark Pink, and the Loaded White Assumption in White.)
Added the terms Globally Known, Common Knowledge, Blind Card, Blurry Card, and Blurry-play into the Basic Definitions. Added an attribution for the blurry-play to Tony in Convention Attribution.
Changed
Convention 57 (Bluffs (Generalised)). If Alice clues an n-away card to Cathy, then Bob should ↑Fn.8 (Example 1). (Example 2). (Example 3). (Example 4). When calculating n, only take globally known cards into account.
into
Convention 58 (Bluffs (Generalised)). If Alice clues an n-away card to Cathy, then Bob should ↑Fn.9 (Example 1). (Example 2). (Example 3). (Example 4). When calculating n, only take common knowledge into account.
Fixed a reference that the Reverse UTTO convention made to the UTTO convention.
many of these ideas have not yet been implemented.↩︎
Consider swapping the values for 4s and 5s?↩︎
Cluing chop used to be a push, and there are some arguments for making it wrap around... The reasoning for a clue to chop not being referential is that it allows more ways to get cards on chop, which are more important to get. Not sure if this is a actually beneficial though...↩︎
Idea: Extend this to when number of useful cards left is relatively sparse, for some given metric (e.g. number of cards left to clue).↩︎
Actually, we could potentially extend this to 2s, 3s, etc... that would be interesting to test.↩︎
Consider swapping the values for 4s and 5s?↩︎
Consider swapping the values for 4s and 5s?↩︎
Consider swapping the values for 4s and 5s?↩︎
Consider swapping the values for 4s and 5s?↩︎