A naïvely constructed die - i.e. a perfect cube, but with pips dug out for each face - will already bias in favor of 6 rolls and away from 1 rolls simply because six pips require removing more material (and therefore mass) than one pip. Likewise with 5/2 and 4/3. The "precision" dice used in e.g. casinos address this by filling in the pips with material exactly as dense as the die's base material; the injection-molded dice in most board games (let alone wooden dice) obviously ain't constructed with that level of care.
This is also part of the reason why some dice games - particularly those typically played with cheap dice - deem 1 to be more valuable than 6 (example: Farkle) or require at least one 1 roll to win (example: 1-4-24). Or they'll require some number of high dice to make the game ever-so-slightly less brutal (example: Ship-Captain-Crew).
Yes. Very funny for the author to spend a lot of time talking about null hypothesis testing, but not actually running a control experiment to test the null hypothesis that his dice are actually different from the stock dice.
I like to believe that Klaus Teuber secretly specified dice biased towards 1-2-3, strictly for personal benefit in games, and the author’s approach has obscured a much greater effect in that direction.
Catan is played widely enough that many groups tend to introduce their own house rules[1]. E.g. one of my rules is: rolling 2 is the same as rolling 12, so these hexes are slightly less undesirable.
I guess if this really matters, you could come up with some set-up rules to swap some 3s with 11s, 4s with 10s, etc, so that biases towards 1-2-3 are less impactful. But that would be painstaking and annoying. I absolutely wouldn't care to do that, unless we track ELO and have an evenly matched group, which is a bit absurd in a casual game. And as in any strategy game FFA, everyone will still gang up against the current leader (even with imperfect information).
I remember a retired engineer was selling perfectly balanced dice intended for RPG players. RPG players are going to gravitate toward the most unfair dice they perceive in their set. I appreciate his enthusiasm but he’s only going to sell those dice to competitions and maybe GMs.
I think that’s one of the reasons GMs sometimes make a high roll from the player into a punishment. Especially by asking for the roll first and telling what they were looking for after. It’s a way to balance out the consequences of unintentionally loaded dice.
About the last point- I remember hearing somewhere, though it could be an urban legend, that that's precisely the reason early Dungeons & Dragons (OD&D/AD&D era) had so many variations within different dice roll mechanics for whether or not a high (or low) roll was good or bad (ie high rolls for your attack was good, high rolls for initiative were bad).
If the player used the same dice for all rolls, a balance check against biased or loaded die was therefore built directly into the game, with the perk of making it very obvious if a player was using specific dice for specific rolls
You reminded me, and I think I have some, or at least some variety of these as a set of 10d6. Metal, and the pips are precisely machined to such depths where they're perfectly balanced. Nice bronzed finish, with black pips.
Also, if someone is obviously cheating with a loaded die at an RPG game, they're not the kind of player that should be invited back. Most characters have ways of increasing their modifiers to rolls that matter most to them (My current ranger is 1d20 +16 for Perception), and having high-enough base numbers can mean that anything other than a natural 1 is usually some kind of success.
I would like to have Laura Bailey’s dice checked by an independent party for instance. Her substantial superstitions about good vs bad dice are an example of what I’m talking about above. Lucky dice don’t have to be intentional cheating, but people who have lucky dice are likely cheating in plain sight.
Seems like the solution to that (from a cheater's perspective) would be to bias the dice toward the mid-range numbers, but I don't know enough about D20 layouts to know if that's feasible.
It looks in the photo at the bottom like that the pips are painted on, not dug out. While that might bias things slightly, I'd expect that the amount of paint used is minimal.
I just checked a cheap set of dice in my 100-games-in-1 box, and the 1 dot is both wider and deeper than the 6 dots on the 6, the dots in the 2 also seem a bit deeper than the ones on the 6 side. I don't have any precise instrument to measure them, but it could be that the mold designer accounted for the removed (well.. not cast) material for the dice.
An interesting way to spice up any board game is to openly use loaded dice, but without any player knowing which numbers it favors. This adds a layer of strategy to whatever game you're playing, although it loses its appeal when people start taking out their calculators.
I think so much about how Catan showed up, got really popular, and then more or less right after that two of its huge characteristics (open trading + dice rolls as the primary decider of things) have almost completely disappeared from modern game design.
There's still dice rolls in some games of course, but open trading in particular feels like something that people really don't want in games anymore. And I totally get why
Catan, like Monopoly (or I guess Cricket and Baseball) has am awkward interminable nature to it, especially at high player counts
Long trading discussions are one component of this. The pure randomness of dice meaning that the internal economy can be all messed up for a while also plays into this
There are games with more consistent runtimes that also don’t get bogged down by people with a high chatter:play ratio.
I like hanging out with people to play games but Catan is in that category of game where just one overly annoying person can just make a session totally suck.
I’d rather play something like Carcassonne or some other modern games that involve competition and territorial management like El Grande where I at least have an idea of how long it’ll take.
I also just don't think Catan is actually all that "fun" once you've played a couple of times.
It's a decent intro board game because the mechanics aren't terribly complex, you don't have to manage too many pieces, and there's so much randomness that any given player can win if they're even vaguely trying.
But that last bit is also its achilles heel - there's so much randomness that the strategy is basically ankle deep. It just becomes a session of "do I have friendly people at the table" or "can I cajole/harass people into bad trades".
Neither of those are all that fun (at least to me). There are much better social games, and there are much better strategy games.
Western empires et al. The trading also allows limited bluffing (you'll get what you want but also probably smth negative). But it takes all day in no small part due to open trading.
This might be a better cheat for… I dunno, maybe risk? Or monopoly?
In settlers, trade is always important… getting an early lead can get you ganged up on. At least in my experience, the best way to win is to look like you are in second place, line things up (get close to some crucial port for example) and then rocket past the Designated Villain only when doing so will get you a really solid lead.
Just lay low with slightly larger hands early on. You can afford this since your total resource production needed to win isn't as dependent on an early settlement or city. Maybe let yourself get hosed by the robber once to build sympathy. With more extreme number hexes rolling more consistently, your card accumulation will be less spiky, so you should have a smoother endgame even if others won't trade.
FYI if you are suspicious that your opponent is cheating, it's easy to verify if dice are loaded or not: drop them in a glass of water a couple of times. If every time the same side ends upwards they are loaded.
Tangentially related but one of the reasons casinos use translucent dice is to make it easier to perform visual inspections to check for injected weights under the pips, etc.
Interesting to think about- would it really matter if the casino was loading their dice? Craps allows you to bet for/against almost every possible bet and you usually have people playing pass/don't pass and come/don't come on the same table. Offering weighted dice to screw some players out of their money is probably going to result in the other players making just as much if not more back. Superstitious players absolutely would notice a "streak" and switch their bets to match it, and the casino isn't going to be able to swap/take away the dice without killing the vibe and making those same players cash out.
Feels like it's in their best interest to have a "fair" game where they skim some percentage of odds off the top.
For a casino? In practice, yes, fair games are perfectly consistent with greedily skimming a game, and fair games draw gamblers.
That said, when organized crime gets involved, somebody always thinks "if I rig this, I'll do EVEN BETTER!" Maybe they're a corrupt employee skimming from the house, maybe they're a loyal employee skimming for the house, but unless you have something like the Nevada Gaming Control Board forcing fairness on them, you basically never get it. At least, from what I've read on the subject. Source: I've read some books on card counting & otherwise beating the odds in casinos, and this my vague memory.
And it's ironic that the house wants to rig games, because a biased game means a mathematically savvy individual can go in and calculate how results differ from "fair" games, and can then skim some profits for themselves if the bias is larger than the house advantage.
A lot of money in craps gets bet on odds that are close to even-money. It's hard, I think, to weight dice so that the house would increase their take by a measurable amount.
A lot of the effective value of a casino is gamblers ruin -- gamblers stop betting when they run out of money, but the house can't run out of money. If the game has sufficient variance and the players are not aware of the bias, then the house still wins.
It's for a reason similar to this that the only game I will play in casinos is craps.
It's not hard to imagine ways to get cheated out of a "fair" bet in card games, roulette, slots, etc. whether it's a mechanical cheat, sleight of hand, adjustment of odds, or whatever. Not saying it happens or is even a common occurrence but it's very easy to imagine ways it COULD happen or has happened in the past that are impossible for the player to detect.
Craps is the only game it feels like to me where provided the payout odds used are the same standard you see everywhere and the dice aren't metallic there is virtually no way to cheat the player/a bet in a way that wouldn't also benefit another player/another bet.
It is in their best interest to have a fair game. The transparent dice are to prevent the players from cheating the casino, not prove it's fair to the players.
Nothing to do with scruples, but I don't think casinos need to load dice too. They already have 'loaded the maths' and this is in the open - over time they win. Why act covertly in an underhand way, whilst also providing the opportunity for gamblers to test themselves against probability? You'd think they wouldn't want to jeopardise their market provision and need the belief of their consumers to maintain this.
I won a Settlers game against my boss who never invited me again. I don’t know what was wrong with his dice but we saw 6’s about three times as often as 8’s which makes me think one of the dice was borked and was rolling unevenly. I was in the picking rotation in a way where I ended up with several 6’s and I just steamrolled the entire game.
One time my buddy Mike cleaned up a game of settlers by focusing his entire empire around a '2' tile. We rolled snake eyes dozens of times during that game. We used the same dice every time we played (once a week for over a decade) and never had another game like that one.
I’ve played a bunch of Catan. The included wooden dice are all terribly biased. Not in the same way, but enough that a sets owner knows, at least subconsciously, what numbers their set favors.
The best way I’ve found to mitigate this is to have a bag of assorted dice with the set. The various sizes and materials, with a swap out at every game, makes sure the dice bias isn’t predictable.
Regarding dice decks. I find they make the game sterile. A near perfect bell curve means you can anticipate number droughts or floods, aiding in robber strategy.
Expand on that last? How would you anticipate a drought or flood from a bell curve? These are independent rolls… you’re not heading into gambler’s fallacy territory, are you?
The dice deck has a perfect bell curve of dice rolls, this means the same number of 6’s and 8’s, 4’s and 10’s. If you go on a tear you can pull most of the 6’s from the deck in short order, a flood. Making it difficult or impossible to pull anymore till the deck is reshuffled, the drought. Meanwhile the odds of pulling other cards go up.
This is somewhat mitigated with cards that require you to reshuffle the deck. Even with shuffle cards included the numbers are too evenly distributed or balanced removing any feeling of randomness or luck from the game.
With a dice deck, you no longer have independent rolls, and you can count cards. You could probably mitigate by shuffling early, like casinos do for blackjack.
> the standard scientific protocol tells us to conclude that we have no “significant” evidence that the dice are biased. (Notice that this is subtly different from having evidence that the dice are not biased! Confusing these two statements is a common mistake, even for trained phd scientists, and especially for medical doctors.)
but shouldn't it be "no significant evidence that the dice aren't unbiased"? that's different from either
Yes. Leaving “significant” out of the second one leaves the impression the author is pointing out that non-significant evidence is still evidence. That distracts from the actual point that “absence of evidence is not evidence of absence”
It's kinda funny that the magnitude of the effect of this "cheating" is significantly less than the magnitude of the effect of who goes first or second.
Another way to look at board games and sports in general is as an alternative to war - settling disputes in a non-violent way and building social cohesion in the process. In board games there are no real losers and in war there are no real winners. So a win at all costs strategy may not be necessary.
It's like Risk but you submit each round's actions in advance and they are resolved simultaneously, rather than turn-by-turn. All of the action is off the board, not on it. Coalition-building, intelligence gathering and managing trust—even when betrayal is inevitable.
I slowly learned when i started playing catan, that by playing against another player, you are virtually guaranteed to lose. You can only win if you cooperate with others. A valuable life lesson.
This is neat, but I was expecting the soaking to affect the dice more. Is this enough to really affect how you play? The naughty and nice players had equal number of dots, but I feel like you usually have more uneven choices than that.
Seems like it'd be more advantageous to make people over/underestimate the chance of being robbed, but this didn't affect the chance of a 7. Is that the same no matter which side you soak?
I remember somewhere, might have been the Catan Android app, had an option to use cards instead of dice. The cards had all the combinations so no number could come up more often than it should. Never got to play it that way but it looks like an interesting solution to people complaining certain numbers come up too often.
The cards are interesting, they include a card to force shuffle the deck in order to make sure there is some randomness in the outcomes.
Even with the forced shuffle cards, the outcomes fall too much in the bell curve and make the game feel sterile. Because if you get a flood of 5’s and 6’s you know a drought is soon upon you.
Well, get creative and find some middle ground. Maybe add a rule that player that has no cards on hand and gets no resources in this turn can reshuffle.
Interesting - kind of reminds me of "bag randomization" that some versions of Tetris use. Bag is filled with an equal distribution of all possible pieces and dealt randomly until empty at which point the pieces are placed back in the bag and the process is started all over again.
The one I was talking about would be cards from 2 to 12 representing both dice, one card for 2 and 12, two cards for 3 and 11, and so on. So you would need six cards to represent 7, but your point still prevails.
Assuming this article is sort of tongue-in-cheek, I'll add something in the same spirit: The fact that the number of rolls required for the game is too low to be able to detect the unfairness does not imply that "it’s scientifically impossible for our opponents to know that we’re cheating." That's fallacious reasoning. In any situation where people actually cared about this and suspected a cheat, they could just say "Let's stop the game for a bit, roll the dice a bunch of times, and run some tests". There's no requirement that the dice only be rolled when required for the game. (If you refused to allow the test, that would obviously be even more suspicious.)
If parties are willing to roll the dice hundred or thousands of times and end up arguing about significance, the easier thing to do would be to bring a cup of water and roll them a couple of times in the water or load the water with salt till the dice float lol
But yeah it's tongue in cheek, talking about bayesian probability for the water stains opposite the sixes
Thinking about how this can be used to my advantage the next time I play Catan. I play with someone that wins almost every time and is a real dirty deal-maker (trades with you then blocks your path), so it would be good to get her back.
Soak the dice to shift the most common to be 5 or 9 rather than 6 - 8? Is that possible?
The "criticism" of a p-value was strange to me, because it's never taught to be an "end all" answer to a question, rather it's taught as a way of determining statistical significance. Every stats or economic analytics course I took in college explained that hypothesis rejection involved critical thinking in addition to p-value analysis.
Settlers brings out my angry side. I had a period of playing 1 on 1 with my wife, and she kept winning. That wasn't the frustrating part - what I didn't like was how early leads compound into larger leads as the game rolls on. So you know you are going to lose, and you just keep losing more. Much like Monopoly.
At least with games like chess, you might be down but you still have some hope of coming back with some maneuvering.
Maybe what I didn't like was the parallels with life. There's not usually a rabbit in the hat to come out on top, the rich just get richer.
Settlers is a poor 2 player game: It's really designed for more. Then balance comes form bashing the leader mechanisms: Unfavorable trades, robber uses always hitting them and so on.
You can apply The Settlers of Zarahemla setup and trading rules to Catan (while avoiding the additional mechanics in Zarahemla) to create a 2-player Catan. It does have the problem xivzgrev mentioned if you do not each secretly adopt different atypical strategies each game.
I think that might be a function of playing 1 on 1. At some point (when settlers was still only popular in Germany), we (4 player game) played with one of my best friends flatmates who was at the time winning a lot of the tournaments in Germany. He would consistently whoop our butts no matter how the game started (and all others of us were pretty big board gamers as well). It was amazing to see how little he relied on chance, his dominance became even more apparent once we used the cities and knights extension.
I never played enough Settlers to pick up on this but I totally get it with Monopoly, and I feel like this is bad game design when it happens.
Monopoly feels like the game might take 4 hours but you know 20 minutes in that you're hopelessly behind and cannot come back. Then it's just 3 hours and 40 minutes of torture.
If you're doomed to lose the game should be over quick.
In the case of Monopoly that feeling is the point of the game:
> The history of Monopoly can be traced back to 1903,[1][8] when American anti-monopolist Lizzie Magie created a game called The Landlord's Game that she hoped would explain the single-tax theory of Henry George as laid out in his book Progress and Poverty. It was intended as an educational tool to illustrate the negative aspects of concentrating land in private monopolies. She took out a patent in 1904. Her game was self-published beginning in 1906.[9][10]
> If you're doomed to lose the game should be over quick.
I think most people are in this situation in life, but would disagree with you. The game itself was intended as an educational tool to illustrate the negative aspects of concentrating land in private monopolies, hard to get the message when it's over quickly.
For what it's worth, if you play Monopoly by the actual rules, and you don't act stupidly stingy on your trade offers, a 4-player game of Monopoly shouldn't take more than 30-45 minutes.
The problem is, people of course don't like losing, and everybody loves a comeback story. So people play with house rules that constantly inject extra money into the game, which prolongs the game's purpose: For all the wealth to consolidate to a single player.
House rules in Monopoly are so common that a lot of people don't even realize they're playing house rules!
Do you give money for landing on Free Parking? You're playing a house rule.
Do you give $400 instead of $200 for LANDING on Go? You're playing a house rule.
Do you allow purchasing Hotels when there aren't enough houses? Do you allow building to not be even? Do you use some sort of object to act like a hotel because the game only comes with 12 hotels in the box? You're playing house rules. The fact there are only 12 hotels and 32 houses was a deliberate design choice to force players to trade and allow one player to horde all the houses and hotels.
You can't mortgage properties that have buildings on them. You must sell the buildings first, and you only get half of what you paid for them from the bank. When you unmortage, you have to pay an extra 10% fee. You don't collect rent on mortgaged properties. If you play any differently, you're playing a house rule.
Rolling doubles 3 times sends you to jail. That's actually NOT a house rule!
Speaking of jail, you DO still collect rent while in it! This means that deliberately staying in jail can actually be a strategic move if another player is possibly about to land on your dark Green properties (Baltic, North Carolina, Pennsylvania) while your opponent owns the Oranges, which you're likely to land on immediately after leaving jail.
Don't get me wrong, Monopoly is a shitty game for many reasons, but "Games take 2+ hours" is not one of them unless you're playing it wrong.
All that, and you didn't mention auctions. If you don't buy it from the bank at the list price, it's up for auction and everything should be owned pretty quick.
Monopoly’s maybe the only board game I prefer playing in computerized form.
Even the one on the NES is totally fine.
Rules enforced without having to remember them, auctions run for you, nobody has to be the banker, no manual book-keeping for how much is owed where and mortgage status and all that.
Plays so much faster and smoother than the real thing, and no dumb house rules making it last forever for no good reason.
Not exactly a parallel with monopoly, which I agree, is like life, where early advantages results in the rich getting richer, the injustice makes it boring and frustrating.
In Settlers there are actually strategies and "luck" is more evenly distributed. You can vary your approach or strategy - ex: by focusing on upgrading to cities as early as possible to give you 2x advantage, regardless of starting locations.
Parallel to life: birth location determines most of luck in life (opportunities, income, connections, friends), but you can increase this advantage by moving, within certain constraints (education, visa, marriage, etc.).
Nevertheless, luck is certainly the most important factor.
In a better and not broken world, laws (rules of the game) will try to avoid the 1st and reflect the later. Ex: antitrust, immigration, affirmative action, etc.
Settlers might have less of a snowball effect than Monopoly, but it's definitely there. Pretty much any resource-gathering game is going to have it. If your resource numbers get rolled early on, you get to be the first one to build a city or a third settlement. Then your income is higher, so you'll get to the 4th point faster. And so on.
Like another commentor said, the intended fix for this in Settlers is social dynamics: the leader is going to be blocked from the best settling spots, isn't going to get favorable trade deals, and is going to get hammered by the robber. The key strategic gameplay in Settlers is not about profit maximization (that's pretty easy to do), it's about minimizing any appearance that you're a threat until it's too late to do anything about it. If players never collaborate to take down the leader, then early gains can definitely beget later gains.
Even with the social fix, there’s usually one person (sometimes two!) in a four-player game who does nothing wrong but is basically out by the second or third time around the board, just hanging around to help the one or two other non-lead players harass the leader but with no viable path to victory short of an insane run of luck with the dice (or, if you’re me, as soon you realize this has happened to you, you help the leader get ahead faster so you can move on to a better game sooner…)
We are living in the renaissance of board game design right now. Settlers is a step forward from Monopoly but is still just a roll-and-do and it also suffers horribly from king making and other design problems. There are so many amazing board games out there right now for every skill level and taste.
I think we gotta explore the card game space more. There are a lot of simple and addictive card games where you can get in the zone playing 4 hours straight.
Parks for a novel game design, gorgeous artwork and tactile pieces. Mid complexity.
Pandemic Legacy for one of the best experiences you'll have with the same group of friends over months (cooperative, play through once over 12-24 sittings). The game builds in complexity as you play so it starts reasonably simple (though the first season starts with the basic ruleset of Pandemic so if you've played that it's a head start but not necessary).
Kingdomino and Cascadia for quicker terrain building games, I consider these fairly similar though Kingdomino is quicker and simpler. These I can play with anyone.
Paperback if you already like word games like Scrabble etc, and want to dip into playing a deck building game.
The Crew if you like trick-taking card games, it's a co-op variant to games like Bridge or Euchre.
Carcassone is an oldie but goodie. Very social compared to many competitive games, as though it's turn based everyone wants to have their say for what you should do with your piece. Compared to e.g. Wingspan where you're largely ignoring/out of the loop for what's going on with everyone else all the time.
Vlaada Chvatil games just tickle something for me. Space Alert is hugely fun, probably best due to the chaos and also the fact that at least we can see the inevitable failure that's coming together, and nobody is the lonely runt, but so is Galaxy Trucker, Dungeon Lords, and as a quick social game, Codenames.
I recently joined a board game club after many years away from the hobby.
I’ll echo the recommendations above. Scored wins in Azul and Loot. Played Isle of cats and Wingspan.
Games around the 3-4 players seem to have best flow and pace. I may buy wyrm (sister game to wingspan) just for the card designs.
I did play a game of Twilight Imperium for 12 hours, which I won. Mostly newbie’s but with a host who’s provided guidance on the rules. Great fun but perhaps something to work up to.
I agree on the 3-4 player idea, more players is hard because people have too much downtime. I enjoy and have played several games of Twilight Imperium but you need a good group who are willing to play fair even if the game is hopeless for themselves.
Coup is a good all-rounder. One of the few games that works for 2 or more players. Easy, simple, and not too long. You can even play with a standard 52-card deck if you want.
Diplomacy is a masterpiece and surprisingly beginner-friendly, but it's very hard to get a game going, cause first off you need exactly 7 people. I played online with friends on Backstabbr.com, and yeah it only took 5 minutes a day, but each game lasted 1-2 months. Or it'd be 2-4 hours in-person.
Oh yeah, forgot to mention the 2-player game I invented that requires no pieces. It's based on haggling.
Designate one player as the seller of an imaginary product and one as a potential buyer. The buyer needs a random secret number B from 50-100 which is the max they can pay, and the seller needs S from 0-50 which is the min they'll sell for. Use an RNG if you have one, otherwise you can do it yourself: Have both think of two random numbers from 0-100. Each says one number but not the other. Add the other person's number to your secret one, mod by 50, then add 50 if you're the buyer.
Negotiate over the price until either a sale is made at P or someone unilaterally kills the deal. Seller wins (P - 50) points, buyer wins (50 - P). If the deal dies, seller loses S points, buyer loses (B - 50). I hope I remembered these right. Then switch sides and repeat.
Just One (best party game ever designed)
Splendor (intro to "engine builder" games)
Carcassonne (intro to tile laying games)
Sushi Go (intro to "drafting" games)
Scout (intro to climbing/shedding card games)
All of these are very inexpensive and rules light and very approachable for beginners.
It's designed better for 4 players. In that case, 3 other players directing all 7 robbers and knight robbers to the clear lead really acts as a negative feedback loop to counter any snowball. That's not nearly as possible from just 1 behind player