I love ancient board games. It's amazing to think about chess and how rules have been changed slightly over time for 1000 years. The game has since been stable for about 500. The computer era is revolutionizing the game again and maybe will usher in new popular variants (Fischer random, no castle chess) as our understanding of the game evolves.
Richard Garfield (mathematician and designer of Magic the Gathering and others) used to give a talk about randomness in games.
He talked about the history of chess, and how there used to be a lot more variants of the game (some even being a 4 player game with dice!), and over time competitive players naturally will want to remove random elements from the game.
But on the other hand, some amount of wild unpredictability is important to attract players - there's a softening of skill gaps.
In some of my own pursuits, I've seen things that make me agree.
Pool has little randomness, and therefore it is very difficult to beat a player who is better than you. The best players want to eliminate the possibility of that happening by making longer races, racking their own balls, winner breaks, things like that. Pool is dying for it.
Meanwhile poker has a large amount of short term variance (luck) and it keeps bad players interested for years and years. The worst player in the world can sit and beat the best players in the world at any given moment. Poker is still going as strong as ever-- maybe more strongly than ever at this point. People are coming out of the woodwork this year itching to play.
I think most of the greatest, longest- lived games in the modern era will need a high amount of randomness, because of computers doing analysis. Even more, with the absent of solvers and the like, many poker variants cannot be solved in real time and all-encompassing strategies cannot be developed. More computational power could change that in the future, I guess.
The machine doesn't care about randomness. Poker variants people actually play get tackled by machines.
Cepheus http://poker.srv.ualberta.ca/about is an approximately perfectly strategy for Heads Up Limit Hold Em. That is, the two player game of Texas Hold Em poker with fixed bet sizes. There are almost certainly other approximately perfect strategies, which would break even against Cepheus over the long term, but you can't beat it. The best an opponent could hope for is to merely get lucky briefly, for which you might just as well play Roulette.
In principle if you could memorise Cepheus you could play the same strategy, but it's basically a vast number of fractions/ percentages so you're not going to -- and it's important to note that while the strategy is unbeatable it is not the best way to extract money from weaker players. If you want to grind money playing poker you need to focus on taking $1000 from that holidaymaker playing $5/$10 before anybody else realises they're soft, not on trying to break even with a machine.
Heads Up No Limit which was still being played a fair amount not so many years back, is crushed by AI. Pluribus beat the best players in the world, comprehensively. Unlike Cepheus, Pluribus doesn't have an incredibly boring yet precise strategy mapped out that you could copy, it's a result of AI learning. Its bet sizing feels a bit weird to humans, but it ends up taking their money, so, whatever.
You've picked two of the easier games to solve--heads up games. More specifically, heads up games with specific stack depth
There is no AI that can play well, for instance, in a 9-handed game with varying stack sizes, while itself and some competent players are 600BB deep and some other players are 40bb deep.
It takes a specific, narrow ruleset to tailor an AI to be able to play it at such a high level. Or more compute than we currently have in real-time.
Pluribus' matches against pros had each hand reset to 100BB.
Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post. In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros. Additionally, no human can realistically implement an AI strategy, meaning the AI is not a big detriment to the actual game of poker, as it's currently played.
>Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post. In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros.
To be clear about why this might be true for someone who doesn't know much of poker strategy--the AI is (I presume) going to optimize for strategies that can't be beaten by changing one's own distribution of plays (for (simplified) example, if the AI raises a given hand 20% of the time and folds 80%, it's doing so because even if opponent were to call 100%, fold 100%, or something in-between; it wouldn't change the overall expected value of that hand with that distribution of plays). Professional human players, on the other hand, will absolutely cotton onto a player whose distribution of plays is not optimal and can therefore be exploited for profit.
Cepheus doesn't care about "stack depth". It's just brutal statistics, this strategy beats your strategy unless your strategy is also approximately perfect regardless of what strategy you have. Good, bad, newbie, pro - it doesn't matter.
Yes, if it's very chip poor, Cepheus could run out of chips before it stops being unlucky and takes your money, but that's unavoidably true anyway in Poker due to it being a game of chance as well as skill.
Cepheus is actually a good Rorschach test for players who say "GTO" a lot. If you actually grasp what game theory optimality is about, you see Cepheus and you're like "OK, I'm done playing Heads Up Limit" (and indeed although it was once somewhat common you won't find any professionals playing this for some years now). But if you're the sort of person for whom it's just another phrase to sling around, like complaining you had a "bad beat" when you were never better than evens, chances are you see Cepheus and you think "I could beat that". Oh dear.
> Also, notably, the bot can still lose in the short term to terrible players, which was the thrust of my post.
This is exactly the useless observation I'm complaining about. Poker is a game of chance so of course anybody might get lucky in the very short term. If what you value is the fact you could win despite being terrible at it, just play roulette and save everybody else the trouble.
> In fact, given its bluffing frequency, it might actually do worse against weaker players than it did against pros.
It isn't about "doing worse" here and that's yet more of the mindset that got you into trouble here. The machine doesn't care about "doing worse" it just wins statistically over time. A grinder needs to make rent and buy groceries, so for them being up $50 after a full day feels like losing, it is losing. But the machine doesn't need money.
Again, if it's just about being able to get lucky and get some sort of temporary "High" from that, I'd commend roulette over poker, or, if you like cards, try blackjack.
No, there aren't any academics showing off bots that play full ring. Of course, there weren't any academics showing off that they could count Blackjack. At least not until after they were run out of Vegas with a fortune of the casino's money... Grinding online full ring with AI is not academically interesting, but it would be profitable. The former would cause you to publish (like Cepheus) the latter not so much.
Good to note that Pluribus is trained with Counterfactual Regret Minimization rather than deep learning, same as Libratus, the first AI player to beat professional players in Heads up no limit Texas Hold' em.
I'm not sure about the relation between Pluribus and Libratus- I think Pluribus is a newer version of Libratus, essentially?
Greg Costikyan's book Uncertainty in Games is another good source.
And this topic frequently comes up in wargaming circles (frequently enough to be annoying :-)). Some feel that nondeterminism is a crutch for the low-skilled while others feel that it is the only reasonable way to handle a low-fidelity model of reality or that it teaches the valuable skill of how to deal with the bag of rotten lemons that the universe periodically hands you.
You can tell he's going a little from memory, but the points are all still there. His arguments that skill and luck are not opposite sides of the same spectrum is quite good.
In many games, it's pretty clearly part of the design that the random elements are there to provide rubber-banding— particularly in games with more than 2 players, where sometimes you try to win without looking too much like it, so you avoid getting ganged up on (think: the robber in Settlers).
This is why I really like cribbage. There's a major element of randomness based on the cards you're dealt, but lots of opportunities for strategy in how you play them. New players have a chance but more experienced players tend to make better choices with what they have.
> Does "white moves first" actually affect the game, though?
Materially, no, though it probably makes it less complex for humans by slightly simplifying the pattern recognition issues, particularly in the opening.
Because white goes first. The phrasing and context becomes important. There are two statements that are true but without them as context you end up with a misleading notion:
First player wins more than second in chess (because there's a slight advantage).
White goes first in chess.
Therefore, white wins more than black in chess.
However, that conclusion (what you present) is valueless without the context. If you reversed which color starts the game then we'd end up with "black wins more than white in Chess" as a conclusion and your statement would be false. And if there was no specific color which always started, we'd be left with just the first statement: First player wins more than second in chess.
Unless there are hidden psychological effects (which good players will attempt to surmount, as a matter of course), mirroring the board placement will make no difference.
There is no asymmetry of moves other than the starting position of the king and queen, so all strategy will simply be mirrored if the king and queen are mirrored.
> ... the ability of pawns to be queened was restricted while the original queen was still on the board, so as not to cause scandal by providing the king with more than one queen.
I read "It's All a Game" by Tristan Donovan and the chapter on chess was definitely one of the most fascinating. There are so many little bits of human history frozen in amber by the rules.
I had no idea the game had middle eastern origins for instance. The rooks used to be war elephants hence how they "charge" across the board in straight lines (they were adapted into rooks as the game was Europeanized). Also the reason you never capture the king, which used to be the shah, and resign instead is because killing a rival shah was a big no-no!
So many interesting tidbits in that book. Highly recommend.
Seems like the precursors might have originated from India but what would evolve into what we today call "Chess" seems to have been taking shape in Persia (Iran).
Do the historians who track these things have some metric that they determine that separates 'precursors' from the game itself or is it a human "you know it when you see it" or consensus? Just curious. I imagine it's something similar to how we answer the question "Are these distinct species?" (which doesn't really have a great answer).
Thanks for the recommendation - I will check it out.
In "Do Dice Play God", another great book, I learned that the earliest dice (probably used initially for diving the future and only later for gambling) had rectangular sides instead of square ones.
I wonder if (a) that was because their creators didn't understand even the very basics of probability, or (b) if the idea of fairness and each number being rolled with equal frequency just wasn't important to them. Not sure.
A rectangular die would basically only have 4 sides, still very useful for rolls. Landing on the square side would be like a coin landing on its edge: possible but would be a re-throw.
> The computer era is revolutionizing the game again and maybe will usher in new popular variants…
It’s going to be fascinating to see. I can imagine games getting “frozen” with hard coded rules and clear Official Rules too. I expect that to happen to word spellings, for example, with most everything we write having a layer of autocorrect in the loop. Digital games could do the same, when you can’t make house rules without programming your own variant.
> Digital games could do the same, when you can’t make house rules without programming your own variant.
Or go the other way, as low-/no-code customization tools and online distribution make it easier to make and share variants than it is to do so at any scale with physical games, subject to the openness (both in design and social factors like IP status) of the base game.
I enjoy thr Royal Game of Ur and even made my own board. One recommendation I'm trying to propagate is to use 4 "2-sided" randomizers instead of a 4-sided randomized for purposes of more strategic play (normal distribution versus flat). I usually play with a reroll 0s option or my ultimate house rule: 0s get you maximum 1 free reroll token.
I highly recommend Xiangqi and Shogi. They both feel very chess-like but also very different. They're a little tricky to learn to play if you're not familiar with Chinese characters (Xiangqi) or Japanese characters (Shogi), but once you get familiar with the characters used in the games, it's easy enough.
Shogi is really neat in that captured pieces can be returned to the board by the capturer. You don't have different colored pieces, but directional pieces to show which side they belong to.
Xiangqi is my favorite of the two. To me, it feels like a better depiction of war than Chess. The equivalent of Chess's king stays in a small area, there's a river separating the two sides of the board which some pieces can't cross, there's a catapult for interesting ranged attacks. Maybe I've just grown a bit bored of Chess over all the years and Xiangqi is just relatively newer to me, but Xiangqi feels a lot more fun to play, IMO.
Well would you look at that, you are right. The different layout fooled me, with the pawn row being smaller. It even has the same number of different types.
I'm actually working on a rogue-like chess game as an independent project right now! It got me thinking and researching more deeply about variant chess. My favorite so far is Fog of War.
There were a few patches to chess in the mid to late 20th century that disallowed promoting a pawn to an enemy piece (this was useful for forcing a smothered mate), and to prevent vertically castling to a pawn that had been promoted into a rook on the 8th rank (notated as 0-0-0-0-0-0).
Not exactly fundamental changes, but still amusing that they needed to be made after so many centuries.
It seems like an AI can now be trained just by encoding the rules and having it play itself (no database required to bootstrap). This should be great for variants (assuming enough processing power) since you will always be able to find a partner.
I think paying an AI won’t be very satisfying, though. You can’t do sneaky things to a player that is essentially statistics on steroids - even if you pull it off, it’s likely not that you were sneaky that gave you the win, you just found a pattern it didn’t know. It’s dead, cold, calculating. Beating a human will always be more interesting, because you can talk about it, “ha, you could’ve mated me then in two moves,” etc.
Humans will never be replaced by anything less than humans.
Intriguingly, mancala is the Egyptian Arabic name for that game.
Some very early boards from e.g. Aksum in Ethiopia were identified by archaelogists as mancala boards, but are more likely to have been for Senet.
It's probable that the Ancient Egyptians played both, but I don't believe the record is clear on where mancala came from and at what time it reached Egypt, presuming that isn't where it came from, which it might be.
I was always under the impression that a form of backgammon was on the ancient Mesopotamian/Sumerian scene around the same time -- though, now that I actually come to look for a good source to support that notion, I'm struggling to find one.
Wikipedia and other sources just say "backgammon can be traced back nearly 5000 years" [0]
Random wiki pages are one of the things that give HN its pleasant Old Internet atmosphere to me. Sometimes I've thought about sampling over wikipedia uniformly at random, submitting to HN, and observing the trends in what rises to the top.
What if there were a recommender system in the loop that looked at which articles tend to be voted up and then would be more likely to submit articles that it thought HN would find interesting — would a uniform distribution filtered by a "probability to be well-upvoted" be a good way to do this?
Because people (such as me!) found it interesting and up-voted it.
Per the guidelines:
> What to Submit
> On-Topic: Anything that good hackers would find interesting. That includes more than hacking and startups. If you had to reduce it to a sentence, the answer might be: anything that gratifies one's intellectual curiosity.
Taking a look, I don't really see any concrete lessons to take away. Maybe the most concrete thing is that a 3 block is valued at 20 while a 2 block is valued at 8.
Unfortunately, this heuristic is probably just arbitrary, and nearly any set of weights would probably still produce a meaningful result since the main strategy is just Expectimax search. Disappointing. I was really hoping for some intuition that a human could apply
Winning such a tournament meant you can write efficient C++ code (so you can search more states during the allocated turn) and you can invent/feature-engineer good heuristics that estimate how close is a board state to winning the game.
I don't remember what heuristics was used, I don't even remember the rules :)
But I've uploaded the source to github a few years ago:
Thanks! I think these days the idea is to replace hand-crafted heuristics with (deep) reinforcement learning. But adversarial search by minimax and friends is still the core of AI players, far as I can tell.
I remember as a kid having a shareware sampler that had some very nicely done videogame versions of Senet, Hnefatafl, the Royal Game of Ur, and some sort of a Pueblo board game . Peak late 90s skeumorphism, complete with little rendered win/loss cutscenes. Unless I can find that CD, it's probably gone forever though
There are a lot of people out there who remember shareware CDs. I'm always surprised by that particular aspect of software nostalgia. Same with things like ads in computer magazines; lots of people remember extremely well.
I am so happy to see mention of Senet anywhere - I have been addicted since I saw it featured on an episode of Lost back in highschool. About a decade ago, I found a Windows version that supported online play, that I played heavily with my then long distance girlfriend. I introduced the game to my family, and my mom even sewed together a fabric board for playing during flights. We play as a family any time I visit. A few weeks ago, I started writing up a text based version of it in Java, but put it on hold for the moment.
I can't remember the exact book, but contained in a book about Ancient Egypt, there was the rules, paper pieces and a sample board for this game - we used to play it all the time as kids.
My grandpa helped us make a wooden set of pieces and a board before he passed, it was a a great little intro to woodworking project.
The modern rules are largely just a guess, but the rulesets I've played with are... so-so. There is enough excitement, I guess, but nearly every game comes down to 50/50 luck. It's incredibly difficult to gain any sort of strategic edge.
It's a curiosity,. But you should probably rather be playing backgammon.
On my games to create is still this idea of an AI generated super board game. For example I feed it in all board/unit/move/turn/winning/losing conditions etc, and it spits out a random game.
Players can then play and vote on new games so that the popular and good ones rise up.
It's super sad that the history of Senet is mostly unknown.
The texture we have of Chess history for example is part of the allure. That the rules have changed, we know how they changed, why they changed, how people played in the past, etc.
> Espen Aarseth asked if the game Senet could be said to still exist, given that the rules were unknown. In response, Alexander de Voogt of the American Museum of Natural History pointed out that games did not have a fixed set of rules, but rules varied over time and from place to place.
The game is the rules. Those people played different games. If you can do anything you want with it, it's a toy, not a game.
If everyone forgot and lost the rules to pinochle, would we say pinochle still exists because people are playing poker with the same deck of cards?
The rules are what matters, yes, but the naming of games is a classification problem over sets of rules. This is most obvious with competitive video games, which have complex rules that are tweaked often - each balance patch changes the rules a little, but it's still the same game. The boundaries are fuzzy, and even the players may disagree about what constitutes enough change to be a different game.
With Senet, we don't even know how much the rules have changed, so it's hard to say. But hopefully the reconstructors did well enough that an ancient player wouldn't say "what game is that?" but instead "that's a goofy way to play Senet."
Here is the reference wikipedia gives for the two historians who have tried reconstructing the rules[0].
It seems that only "tomb images" and some game boards and pieces are used in the reconstruction. The article doesn't suggest that any rules have a basis in history. What rules we have are fabricated from nothing but the pieces, like reconstructing the English language from nothing but the alphabet.
Pretty close to a physical sport, if we assume that most of that code is involved in simulating something resembling physics, or in running simple robot players.
Like, how much of a basketball game is concerned with the actual Rules Of Basketball vs. simulating a bunch of people playing basketball? And if you made Space Basketball with characters with superpowers who kept getting balance tweaks as the player community figured out holes in the rules, most of that simulation code would stay the same, as the tiny percentage of rules code evolved.
I get your point, but really is anything like this so black and white? What about "house-rules"? If I am playing Pinochle with several additional house-rules (that either add or subtract from the "official" Pinochle rules) then what am I playing? On one hand I could see the argument that I am technically no longer playing official Pinochle, but it seems wrong to say that I am playing a game that is completely distinct from Pinochle. It seems more accurate to describe games (and honestly most other human activities) as existing on a continuum of more-or-less instead of a rather black and white boolean reality.
You'd be playing a variant that directly evolved from pinochle. There's an undeniable lineage there.
If you reverse-engineered your own rules from scratch knowing nothing but what a deck of cards looked like, it would be silly to claim you'd rediscovered pinochle.
Say we fling a chess set out into space and ten million years later and alien civilization discovers it and concocts a game where they take turns placing pieces on the board like some elaborately-scored tic-tac-toe, would you say they rediscovered Chess?
It's funny you should mention chess, because early modern chess was at one time considered just a variant of chess[0]:
> The queen replaced the earlier vizier chess piece toward the end of the 10th century and by the 15th century had become the most powerful piece;[64] in light of that, modern chess was often referred to at the time as "Queen's Chess" or "Mad Queen Chess".[65]
There was still some variation in the rules until the 19th century:
> The rules concerning stalemate were finalized in the early 19th century. Also in the 19th century, the convention that White moves first was established (formerly either White or Black could move first). Finally, the rules around castling were standardized – variations in the rules of castling had persisted in Italy until the late 19th century.
Is chess with different castling rules still chess? Chess without en passant?
Plus, it's easier to point to the set of rules that were standardised in the 19th century and call that chess. For a game like senet, there may never have been a standard set of rules. Or there may have been multiple standards that were all fairly popular, like poker.
Compare the changes to the rules of chess you've described to the descriptions of senet's rules referenced by the wikipedia article[0]. If these are the best attempts at senet rule reconstruction that the article author could find, then I must assume that the rules are basically made up from scratch with nothing but a game board, some pieces, and the vaguest of references to the game in ancient texts. Familiarity with one of these so-called senet rulesets would be of no use at all to somebody playing the other, and I'm sure familiarity with both would be of no use at all to somebody wishing to play senet with any ancient player.
Classifications can be fuzzy, but they're not just a giant meaningless void of gray where anything goes. Chess has variants that can be placed on an evolutionary tree. Senet appears to have nothing but a handful of naive attempts at total reconstruction from practically no information. The game that was historically called senet appears to be lost.
You're calling on examples of strongly-pedigreed, well-informed. very slight game variations, and claiming they're equivalent with a whole-cloth supposition of the rules based on nothing but an examination of the board and pieces.
The gradual evolution of a well-documented game doesn't really compare with uninformed assumptions about how a game might work based on little more than mere physical artifacts.
If you fling a chess set out into space, once it is disconnected from it's environment, does it enter a macroscopic superposition of states and start playing itself?
Of course you're right. But the rules are not entirely unknown. For example, archeologists found the pieces. So, they know the dice are involved. And they likely correspond to rules for other similar games (roll and move, like backgammon or Ur).
So, it's not entirely black and white. Historians are pretty sure about some of the rules, but it's possible there were other rules we don't know. The rules played today are a balance between historical accuracy, and just trying the different theories and playing the one that seems the most fun.
That might seem like just making things up, but that's what the quote is referring to. It's hard to say what set of rules was the most common, but there is some reason to believe that the current set of rules is as least similar, and might have been played due to the way that these games didn't have 1 concrete set of rules. "House rules" meant that there was often many different sets of rules in place. Think how checkers has sets of rules that allow for non-forced jumps, flying kings, etc. Maybe your can't tell whether your set of rules was the most common set, but if your rules are based on evidence, it's likely that it was played similar to that somewhere.
I urge you to read the sets of rules invented by the senet historians referenced in the wikipedia article. I think you are overstating their knowledge of the game. From wikipedia:
"Although details of the original game rules are a subject of some conjecture, senet historians Timothy Kendall and R. C. Bell have made their own reconstructions of the game."
Here is the citation[0].
My belief is that these are two completely different games, and therefor probably completely different from any ancient iteration of senet.
Using the same game board and (some of) the same pieces is totally insufficient to call a game a "variation". Is old Japanese text, which adopted the Chinese writing system, a variant of the Chinese language?
This question is more like asking whether a card game qualifies as poker.
There is no natural boundary with which to say that a game has so many variants from Platonic poker as to no longer qualify. Any abstraction proposed as a criterion for classification is just that, an abstraction, since poker is a socially-constructed category.
