Recent Board Gaming

Board Games
164

While more players means more information, and thus more opportunity for quality clues, it also raises the minimum bar required for clue quality. And besides memory, the ability to give high quality clues is probably the most important and most difficult skill in the game.

In a 25-point game, 25 cards have to be played to the table, and playing a card requires picking up a card from the draw pile, bringing game end via draw-down one step closer.

Gaining a clue token also requires discarding a card and then drawing from the draw pile. So the number of extra cards available in the draw pile after the 25 draws needed to play 25 points worth of cards, plus the 8 starting clue tokens, determines the maximum clues that can be given throughout the entire game.

# playershand sizein handsdraw pilemax discard turnsmax cluesmin cards played per clue
25104015231.09
35153510181.39
4416349171.47
5420305131.92

For a group of card-counting automatons who always give optimal clues, more cards exposed is probably just plain “easier”. But if we’re talking just about human skill level required to win, and if we agree that giving good clues is at least as important as memory, then more players arguably implies a higher skill level required to achieve a 25-point game. I contend we would normally describe this as “harder”.

EDIT: For clarity, “min cards played per clue” means that each clue must enable this many cards to be played on average. A metric for measuring required clue “quality”.

3 Likes
165

I was thinking something like this but didn’t do the calculations. I had a sense that you were under more pressure to play cards in 5p just because you have fewer discards/player on top of having fewer cards in the deck to start.

166

If you have 5 skilled players, the game will be easier for them since they have more info. 2 cards played per clue, sure. But the extra cards you can see with your eyes are worth how many clues?

You also have to consider that with fewer players, each individual player takes more actions. Thus, one bad player really ruins you. More players means that your weak player makes less decisions, and has less influence on the outcome.

Regardless of these differences, what it comes down to in Hanabi is that you can’t win with any player count unless everyone knows wtf they are doing. Sucky players will sink you no matter how many total players you have.

167

In a 4 player game, 3 skilled players could cover one mediocre player. If 3 players give clues that average close to 2 cards played per clue, and the mediocre player averages closer to 1, you’ll still end up with an average clue quality of around 1.75, well over the 1.47 needed.

By contrast, in a 5 player game with 4 skilled players and one mediocre player, you get an average clue quality of 1.8, which is below the 1.92 minimum needed.

168

Again, you aren’t factoring in the free clues from having an extra 5-10 cards visible right from the beginning.

169

So you’re saying in a 5 player game 4 skilled players could potentially cover a mediocre player? That seems at odds with your previous claim that an unskilled player will always tank the game (the claim I was directly addressing).

170

Depends how crappy they are. Unlike some people I don’t have time to do math.

What we need to figure out is:

Do we care just about perfect games vs imperfect, or do we care about higher average score?

How many mistakes total can the game tolerate with X players?

We can measure player skill based on how many mistakes they are likely to make on average in a game of Y players.

Which number of players tolerates more mistakes on average?

171

Ooo, ouch. But fine, math is hard. :wink:

172

I failed Calculus III 2-3 times.

173

I feel I should mention I have a Math Degree, but I didn’t even think to apply it here :joy:. This one thread has made joining this forum well worth my time! I love seeing the analyst in everyone.

On a side note… I’ve now played even more 5 player hanabi with two new people last night. Still averaged about 16 points. Maybe I need to up my skill level, but with 5 people it feels harder to get everyone clues and it seems there are many blind discard rounds.

Of course this all anecdotal and I should probably actually dive into the numbers more to see if this “feeling” is backed up by the data somehow…

1 Like
174

I would also like to add that I believe this is only partially correct. You get a bonus clue/time token for each color you complete 1-5. Thus in a perfect 25 point game, wouldn’t you also have 4 bonus clues? If this is taken into account, it could be argued that those minimum cards played per clue ratios could go down a bit.

For instance in the two player variant, completing two colors would net you 2 extra clues for a max clues of 25 according to your table. Then your min cards played per clue would only need to be 1.

So I think there is some credit to what Scott is saying about card availability because I still get nowhere close to 25 when only playing with 1 other skilled player. And we have yet to discuss how giving a clue to a player with only 4 cards in their hand as compared to 5 should give you a better shot at identifying multiple cards.

@JettisonJoe Thank you again for making that table and giving my brain a construct to work under!

1 Like
175

That’s a great point, actually, I forgot about the bonus clues. That should lower the played-per-clue values a bit at all levels.

Regarding card availability, I’ve been wrestling with which is more salient - the pure number of cards available, or the number of hands available. An additional hand is an additional chance at coming up with a quality clue, while in general extra cards are extra bits of information you can use to disambiguate the state of your own hand.

That said, I still contend that both activities (formulating quality clues and learning about your own hand via inference) are difficult. So while more hands may give you more opportunities to come up with a quality clue, that’s still not as powerful an advantage as lowering the bar for clue quality, which opens the door for unpracticed players to be somewhat carried by the rest of the group.

I should also note that my friends and I arrived at roughly this analysis one night when (after having previously played many 22-24 point 4p games), we were soundly destroyed in our first 5p game. So certainly confirmation bias may be coloring my view somewhat.

1 Like
176

So whats the best score you have come up with two players? If we were just going on your table, one would assume that 2 players gives the best chance. However, my friends find its often harder to get 1’s out when playing with only 1 partner, thus closes out options on an otherwise good hand. Then take into account that both players might have good hands and be forced to discard. This resulted in us discarding both 3’s of a color on several occasions, thus forging 3 points for that stack. The highest we got with 2 players was 18… Though there was definitely some alcohol involved :stuck_out_tongue:

Bringing me back to my main question → whats your best score in each player configuration?

177

Regarding 2p, I was thinking about your result there and how to explain it. I don’t have any concrete data to offer, because we’ve only ever played 4-5p at our table. But my guess so far is that fewer cards being exposed means that the order of the draw pile matters more, and that winnable orderings are harder to get.

My sense of my group’s performance (although I will definitely have to start logging our scores in earnest now :smiley:):

4p - Many games, and we consistently score 21+.
5p - I think we scored like 13 the one time we finished.

I’ve also started 5p games a couple of times in various lines at PAX, but they’ve always been cut short before tallying the final score.

1 Like
178

I guess since there are so many factors at play here, I will just keep recording my scores and report back in another month ish. Hopefully we’ve learned more strategy and have improved on our averages.

179

Cool, I’ll do the same, though I’m not quite ready yet to throw in the towel on analysis as a parallel exercise.

180

True… I’m just not sure how to even quantify what the optimal hand size would be. I mean, I guess it would be simple enough to test. Like play with 4 people but have 5 or 6 cards per person… Should have more playable cards, but they might be harder to identify and bring down your average number of plays identified per clue…

181

PAX West:
1x 1846
1x Quartermaster General
3x Sheep ‘n’ Sheep
2x Black Friday
1x Medici
1x Spirit Island
1x Wind the Film!
5x Codenames Duet
5x Downforce
5x Magic Maze
3x Aton
3x Sticheln
2x Familiar’s Trouble
1x Dice Forge
1x Exit: The Secret Lab
1x Notre Dame
3x Onitama (new)
2x The Climbers (new)
2x Sagrada (new)
1x Adrenaline
1x Clank! (new)
1x Ghost Court (new)
1x Dread (new)
1x Ex Libris (new)
1x Dice City (new)
1x Twins (new)
1x Unpublished Prototype (new)

Turns out you can play a lot of things in 5 days at a convention ;]

As you can see there a lot of things we played a lot in our extended friend group… most notably Black Friday, Downforce, Magic Maze, and Sticheln.

Thursday is when everyone arrived, and I first had the chance to play Codenames Duet, which is easily my favorite way to play Codenames, now. Keep in mind that I’m unusual, and preferred to play the Codenames 3p variant.

Friday Anthony and I slipped into the “GenCon games” room and played a few things - The Climbers, Ex Libris, and Twins. The Climbers didn’t appeal to me, and Ex Libris only feels like Sheep ‘n’ Sheep grafted to some frustrating worker placement. I liked Twins more than Kobayakawa, but only barely - and I don’t care for Kobayakawa at all.

The GenCon games room wasn’t a waste of time, because I like learning new games! But it didn’t result in any purchases (we already own Lisboa, Spirit Island, Festival of Thousand Cats).

Anthony had learned Sagrada on Thursday, and we played a 2p game. I enjoyed it, but now I know I don’t need to own it.

Saturday Anthony and I made it to the convention center early and learned Onitama and Dice City. Dice City was a bit too slow for me, Onitama was fine, which is very good if you adjust for my lack of enthusiasm for 2p perfect information abstracts ;]

We had a little single elimination Aton tournament on Saturday, which I lost (of course) because I’ve only ever played against a single opponent, but we had a blast.

Sunday was packed with longer games… Scott had a prototype, Anthony had Spirit Island, I had 1846. After dinner we all played Exit: The Secret Lab. I’d like to make these disposable escape rooms a ‘convention thing’ now that we’ve done 3/3 Exits and 2/3 Unlocks that are currently available…

I didn’t plan on it, but I was pulled into two RPGs over the weekend, Ghost Court and Dread. I’ll absolutely play either game again. I would have preferred a more traditional ‘slasher movie’ scenario for Dread instead of the pulp Cthulhu game we played - I played with a group of strangers thrown together as a pick-up game, and I was self-conscious about crossing boundaries without an x-card. Everyone just went gonzo anyway. I really wanted my character to get run over by a car in the climactic scene but it didn’t feel right to use Dread’s ‘heroic sacrifice’ rules to kill myself off. Fun times.

Monday is when I learned Clank! (second favorite new game after Codenames Duet.) Then we finished off the convention with Magic Maze and Sticheln at the hotel bar before everyone went their separate ways. :]

1 Like
182

It was a fun weekend with fun games and people.

1 Like
183

Man, more SticheIn happened and I did not get a chance to clear my name for horrible tired play