r/todayilearned • u/PeasantLich • 1d ago

TIL that Checkers has been a solved game for almost 20 years. Optimal play is unbeatable, and two opponents playing optimally always reach a stalemate.

https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
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u/jointheredditarmy 1d ago

Wow that is actually a really well balanced game given 1 player goes first

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u/Shimgar 1d ago

It's actually an interesting phenomenon that so many board games just happen to result in draws with perfect play. Especially given most of them were invented long before we could ever know or prove that. Chess, Checkers, Othello, probably Go.

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u/sicklyslick 1d ago

Survivorship bias.

There's probably many many more board games that do not result in a draw (or balanced mechanics) which became either unfun or unpopular enough to have disappeared forever.

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u/WES_WAS_ROBBED 1d ago

ooo now i want to know about all the extinct unfair games!

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u/yodatsracist 1d ago edited 1d ago

Tafl games, also known as Viking Chess. Very fun to mess around with but it’s (obviously) unbalanced and one side has an advantage. These were popular in Scandinavia and are mentioned in the Norse sagas. They were played by the Sami (indigenous non-Indo-European group in Norway, Sweden, and Finland) until the 18th century, though they seem to originate with the Norse.

Fox games (Fox and Geese, Fox and Hounds, etc) are potentially related. They were once popular among the Anglo-Saxons, but variants are played as far away as Sri Link.

Both involve attackers and defenders, with the attackers having more pieces and the defenders being hard to capture.

Both are great with kids! They make you think in different ways. I recommend them, even though in most variants the defenders have an advantage. Edit: Someone below pointed out that Wikipedia talks about how the first published variant was misunderstood and in the original rules it actually favored the attackers. This is true, but most variants overall favor defenders. See here for way too much detail.

Edit 2: if you're looking on US Amazon, the version I had of Tafl is available as "Hnefatafl - The Viking Game - Authentic National Museums Scotland Version". I bought it in about 1998 and it was published by English Heritage, the organization that runs many of England's most famous sites, including Stone Henge. I guess this is the Scottish version. It's also on UK Amazon as "Hnefatafl - The Viking Game", also the blue box Museum of Scotland version. It's got a cool cloth mat instead of a board, and the pieces are such cool looking Viking soldiers I played with them even when I wasn't playing. They're modeled after the Lewis Chessmen (12th-century Viking chess pieces carved out of walrus ivory), which is slightly anachronistic but who cares. I introduced it to my nephews and son and they were obsessed with it. It's expensive like 45 dollars/30 pounds, round about, but I got my money's worth over 30 years. It's literally lasted a generation. There are also a couple of Chinese knock-offs on Amazon but they seem to be roughly the same price. If you're going to buy a Tafl game, it seems like maybe worth getting some version with cool looking pieces. If you go down to the end of the Wikipedia for Tafl games, you can also find places to play online. Not everyone prefers the English Heritage/National Museum of Scotland re-creation.

I have no special recommendation for Fox games, but you could probably just draw the board on paper and find the appropriate number of pieces.

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u/HotterRod 1d ago

From the Wikipedia article you link to:

There have long been controversies concerning imbalance of the game, as rules for certain modern tafl games strongly favor the defenders. This imbalance results from a mistranslation of Linnaeus' rules for tablut, a Sámi tafl game from the 1700s, which were subsequently used as the basis for reconstructions of rules for medieval tafl. Newer translations of Linnaeus' tablut rules reveal a balanced game. After this change, tablut can be said to be slightly in favor of the attackers rather than the defenders: according to statistics, the attackers overall win marginally more often (on average 9% more).

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u/yodatsracist 1d ago edited 1d ago

This is what Wikipedia says, but I think you're understanding what this number means. It's easy to do. Wikipedia is not written in a very clear way.

The first thing to understand is that not all versions of the game are based directly or indirectly on Linnaeus's rules for Tablut (yes, he's the same guy who invented binomial nomenclature so that every living thing has a two part Latin name Homo sapiens, Canis lupus, E. coli, Cannabis indica, etc. — you have to love how 18th and 19th century polymaths find themsleves in random places). So how that version is balanced isn't the end-all, be-all of Tafl game balance. I don't think it's close to the most popular today, anyway.

Second, there are a lot variants, with difference numbers of pieces, rules, board sizes, and configurations. Linnaeus's Tablut, for example, was played on a 9x9 board. Board sizes range from at least 5x5 to 13x13, to give you a sense. I think a lot of the most popular standard variants are on an 11x11 board, though some of the most popular are played on 3x(something) boards. These 3x(something) games are from the Daldos and Sahkku sub families of Tafl games, which I have never played.

Not all of these variants have the same balance, but White (defense) is consistently advantaged in actual observed outcomes. You can see balance statistics that someone obsessively collected for fifty-eight different variants here. You can see that White (defense) has an advantage in most of these variants, I think it's like 36/58 favor white in terms of variants, 2 were statistically balanced, and so means Black (attackers) are only favored in about 1/3 of games. Of the 58 variants, only 17 (again about 1/3) have average scores that give a 10% win or less to one side of the other. Which is to say, most of them are more unbalanced.

What seem to be the most popular variants (that is, the ones in this data set with more than 1,000 games played) are Copenhagen Hnefatafl 11x11; Fetlar Hnefatafl 11x11; Berserk Hnefatafl 11x11 (Nielsen setup); Daldos 3x12; Daldos 3x16; Daldos 3x14; Old Hnefatafl 11x11; and Saami Sáhkku 3x15 (Kåfjord). The average balance ratings for these are +1.30, +1.43, +1.16, +1.08, +1.07, -1.01, +1.05, -1.13. So once again, like I said, most of the most popular variants favor defense (positive numbers) and some favor defense by a lot, on average. The average of the absolute values of the balance rating of these eight most popular variants is 1.15, which I think means that, roughly on average, for every twenty games one side wins, the other side is winning twenty-three. It's not ridiculously out of balance, you might not notice it if you played a few times, but it is consistently out of balance. You may notice that the variants that give more balanced overall numbers are often slightly tilted toward one side for beginners and slightly tilted toward the other side for experienced players. So even these are balanced across all players levels, but they may not be that balanced at any specific player level.

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u/TehSteak 1d ago

How did you come to learn so much about this stuff?

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u/yodatsracist 1d ago edited 1d ago

I bought the game randomly in 1997 as "the Viking Game" at some English Heritage-run museum when I was in 6th grade because it looked cool. I played it with my family for a few years but then didn't play it much for about three decades. Last year, I had a lot of fun playing with my nephews, so I just spent a few evenings reading about it. Nothing special, just Wikipedia and that website that has statistics on it and so much more AageNielsen.dk, and maybe a couple other links.