There are some games where if you take a decent amateur and put them up against a world champion, the amateur still has a chance to win some small but non-trivial percentage of games. There are other games where even a pretty good player has almost no chance of competing. For the purposes of this discussion, I’m going to label the former more luck based games and the latter more skill based games.
Under this classification, what would be considered the most skill based game ever? Are there any games for example, where if the 10th best player in the world played the 20th best player in the world, they would win 95+% of the time?
I’ll go with Chess. I don’t think the 10th best beats the 20th best 95% of the time, but I’m pretty sure the best player comes close. Perhaps Go, but I don’t know enough about it.
How do solved games work into this? There are plenty of games in which a player who knows the solution can win 100% of the time against a player who doesn’t know the solution, given the option of going first or second.
If that option is decided randomly, of course, everything breaks down :). But there could be a meta-game.
Let’s take Nim, a solved game with a relatively simple solution. If you pit me against a player who doesn’t know that solution, randomly choosing who goes first, and we play a series of 100 games against each other with the winner being the one who wins the most rounds, I’ll almost certainly beat the pants off that opponent, no matter how well they play without the solution. Against an equally-skilled player, that is, a player who also knows the solution, I’ll only win about half the time.
To put the question on a factual (though still debatable) basis, I think we’d want to put the players in non-overlapping tiers. That is to say, if a Tier 1 player plays a Tier 2 player, the Tier 1 player will almost always win. If the Tier 2 player plays a Tier 3 player, the Tier 2 will almost always win, and so on. The question, then, would be which game has the greatest number of tiers.
A game of pure luck, like Chutes and Ladders, Candyland, or War, would then have only one tier: If you had a World Championship of Candyland, and then put the winner of that in a best-of-ten versus someone who had just picked up the game, they’d still most likely go five and five.
A simple solved game like Nim would have two tiers: Tier 1 would consist of everyone who knows the solution, while Tier 2 would consist of everyone else. There will still be some differences of skill among the Tier 2 players, but not enough that the best Tier 2 player would always beat the worst (thus creating a new tier).
For chess, we can look at Elo ratings. I’m not finding exact numbers for 95%, but (if I’m reading the tables right) it looks like a player 366 points above his opponent should win about 90% of the time, while a player 677 points above should win about 99% of the time. Let’s eyeball that as a difference of about 450 points being the 95% cutoff. The lowest ratings are either 0 or 100, depending on governing organization, and the highest are about 2900 for humans, or an estimated ~3300 for computers. That would give chess 7 or 8 tiers.
I’m not sure where to start for estimates for other games.
I originally meant to say game or sport so I’m fine with a broad interpretation of what a game is. Let’s define it as any competitive activity for the time being.
In that vein, would some kind of weight lifting activity be up there? When I was weightlifting, I was always surprised by just how narrow the gap between easily achievable and total failure was.
I don’t know much about tennis, but it seems like the best player in the world during a given stretch (like Federer a few years ago) is almost always in the finals, and usually wins. I do know a lot about golf, and it’s quite different – even Tiger Woods during his peak years only won about one tournament in three (except for that insane stretch from 1999 to 2001 when he won over half, which is like a baseball player hitting over .500 for three years), and it’s not at all unusual for the #1 golfer in the world to finish out of the top ten, or even miss the cut (out of the top 50% or so).
Interesting approach. I suspect there are more than 7 or 8 tiers, though. For example:
My seven-year-old can always beat my three-year-old at chess, since the three-year-old is guaranteed to make an illegal move pretty early on and forfeit the game.
An avid chess-playing third grader can always beat my seven-year-old at chess, since my daughter barely knows the rules of the game and would need almost constant reminders as to how the pieces move.
I can likely beat that avid chess-playing third grader all the time (assuming we have a low standard for “avid”), since I’ve played the game for decades and read a few books on the subject.
Almost anyone on the ELO chart you mention can beat me at chess all the time, since I’m terrible at it and only play a game once every few years.
I suspect there are a lot more layers like that, but I could be wrong.
Let’s not get too nitpicky about the precise definition, the tiers at the low end are always going to be rather fuzzy since you’re moving into extreme amateur land. I suspect the more concrete formalization is how “wide” each tier is rather than how many of them there are although the two are obviously closely related.
I was assuming that an Elo rating of 0 corresponded to “knows how the pieces move and won’t make an illegal move, but otherwise selects moves basically randomly”. I admit that I’m not sure about that, though.
I think this question is a little bit problematic - I mean, there are tons of games out there that are very skill based and rank amateurs will have no chance against even moderately seasoned players (Every fighting game ever). But due to the way skill curves tend to work, I don’t think there are any where people in the top 20 or so are so widely separated that the difference between 10th and 20th would be 95% wins. Though there are probably some (Tennis?) where the difference between FIRST and 20th is that big.
The Elo scale is defined in terms of differences between scores, and so one could add a constant to all scores and the meaning would be the same. That being the case, though, you can choose the meaning of 0 however you want, and so I would assume that it was chosen at the random-moves level.
And as a minor note, it’s “Elo”, not “ELO”. It’s not an acronym; it was developed by a guy name Elo. Yeah, it surprised me, too.
I agree I don’t think the measure is a good one. For example I think becoming one of the top 100 soccer players in the World is far harder than in any sport. You have to start playing from a very young age, putting an insane amount of practice and even then your chances of even approaching the top 100 are insanely small.
On the other hand there is a real continuum of ability. For example the English football pyramid has at a rough guess 100,000 players. At the top of the pyramid (the Premier League) there are undoubtedly a number of players in the top 100 in the World (the Guardian had 28 Premier League players in their 2015 top 100 players in the World) and right at the bottom you have second string teams of Mid-Sussex village teams. The pyramid is divided in 23 tiers, but whilst there is a clear improvement as you go up each tier, there is an exchange of players and teams and the level of ability of players forms a continuum.
Of course this is all a function of the huge amount of players playing soccer. The game itself is not that difficult to play competently, but is nuanced enough that the difference between a top pro and amateur is apples an oranges.
For the record I would say snooker is the game that requires the most skill. By this I mean it is so hard to get to a level where where games even resemble the games of professional players. In my time down the snooker hall I’ve only seen once or twice the kind of game-winning break (i.e. 80-100+) that is a standard feature of professional games.
There are rankings in Scrabble and good players tend to overcome the inherent randomness of drawing tiles. Skill (work knowledge, board vision, rack management) all take time to develop.
I’m not entirely sure what question is being asked.
Is it comparing skill vs luck? Because there’s definitely a distinction between a game like Scrabble or Poker in which it’s at least plausible that your kitchen table player could just run hot as the sun and defeat the best player in the world; and one like Go or Chess, in which the likelihood of that happening would end up being a number so small that it would be impossible to express.
There’s also a question of “how much better is the best player in the world than the 10th best player in the world”, which is certainly interesting, but it’s a little hard to precisely define what that is measuring. And of course, that varies a lot based on how good the best player in the world is compared to his/her peers, which varies by time. In Tennis, there have been times recently when one player was MILES better than anyone else, and other times when that wasn’t the case.
Another question is “how likely is it for a team/competitor from the ‘2nd division’ to defeat a team/competitor from the top division”. That’s also kind of interesting… I’ve seen some interesting discussions on the SDMB about how likely a pro sports team is to lose to a college team, and the answer seems to vary by sport, with by far the least likely being NFL vs. college football. For a lot of other sports, you can just someone playing a single position running really hot, or a once-in-a-lifetime group of talented players all at that college in the same year. But NFL teams are so huge, and there are so many components, physical and mental and organizational, that go into a team’s success, that it would require an insane confluence of events for a college team to beat an NFL team.
Elo rating, as with all objective rating systems, say little to nothing about the activity they’re rating. It’s a statistical analysis of the players involved which predicts the chance that one player defeats another, designed so the prediction increases in accuracy as more data (match outcomes, players) arrives.
All the system can say is that a player of a higher rating is likely to defeat a player of a lower rating, with the difference in ratings describing just how likely that is. The actual number of that rating is meaningless by itself. The range that was chosen was purely arbitrary; zero is not even able to represent anything special.
(also, there are many games for which totally random play would actually be better than the worst humans)