For large group behaviour you’re better off looking at cooperative game theory which is a branch of game theory that deals with games of more than 2 players and the formation of cooperating groups known as coalitions.

It’s a much more complex topic than basic 2 player strategic game theory, so I don’t see it discussed nearly as much outside of subject matter experts.

I guess I should explain a bit more then.

The term “player” in game theory doesn’t mean a person, it means a collection of rows or columns in a payoff matrix. Basically just a table of numbers. One player is all the rows, one player is all the columns.

A strategy can be either a pure strategy (select one row or one column of the table) or a mixed strategy (assign percentages to every row or every column of the table, so that all percentages are non-negative and the total equals 100%).

In a 2x2 payoff matrix, each player has 2 possible pure strategies (pick column A or column B, row 1 or row 2) but infinite possible mixed strategies (e.g 33.186794% column A and 66.813206% column B) since an infinite number of pairs of percentages can add up to 100%.

Mixed strategies can be thought of as introducing probability into the situation. If you choose a mixed strategy of 50% column A and 50% column B you could think of it as using a coin toss to make the decision. But game theory itself doesn’t do the coin tossing, it just assumes the expected values of the percentage times the payoffs in those entries of the payoff matrix.

Any mathematical textbook will do it. Try Springer.

It’s quite simple really. Games in game theory are represented with a payoff matrix which shows the utility for each player. Pure strategies are defined as rows or columns in the payoff matrix. The math of game theory doesn’t care about why a player chooses a particular strategy, only its payoff.

I would define a purely rational player at minimum as one chooses a dominant strategy, when one is available. You’re free to expand that to mixed strategies and games where (strong or weakly) dominant strategies do not exist. Irrational players would be anyone who is otherwise not a rational player.

This isn’t very interesting in basic game theory. It becomes a lot more relevant in cooperative game theory, which can have more than 2 players and players forming coalitions.

You clearly have not studied game theory, as you are talking out of your ass. Go pick up a textbook and learn something.

On the contrary, game theory doesn’t assume rationality or irrationality whatsoever. Game theory looks at all possible outcomes and investigates different strategies that lead to those outcomes.

Rational strategies can lead to defection in games like the non-iterated prisoner’s dilemma, and this is a Nash equilibrium. However, the infinite iterated prisoner’s dilemma allows cooperation to emerge even with rational strategies.

The superrational strategy leads to cooperation even in a one-shot gang of prisoner’s dilemma

Perhaps Voyager had more storage in its systems, due to being a newer model of ship? It was more advanced in a bunch of other ways as well (variable geometry nacelles, class 9 warp drive).

The thing that got me to really like spiders is when I learned that spiders are actually tiny mechs! Their legs are powered by hydraulics, rather than directly moved by muscles! I just thought that was so adorable!

I just call it footy at this point. That way nobody confuses it for handegg.

This is why Amazon was under investigation for antitrust by (then) FTC Chair Lina Khan. That she wasn’t able to see her case all the way through the courts will continue to annoy me for a very long time.

Well, either modern matchmaking algorithms are absolute dogshit at doing this, or there just aren’t enough low-skill players out there to be matched with. Because if you’re just a casual player, you won’t be losing 50% of games, you’ll be losing 100% of games. Even at the lowest of the lowest tiers, you’ll still be losing quickly and often if you don’t put sweat into it.

It’s mathematically not possible to maintain a 50% win rate across any group of players unless everyone has exactly the same skill level. The proof is complicated but the idea works like this:

• assume not everyone has the same skill level
• ignoring duplicates, there exists a player with the highest skill level in the group
• the highest skill level player always gets matched with players of lower skill level, winning >50% of their games as a result
• the players who play vs the highest skill player end up with less than 50% win rate, so the system gives them more matches against lower skill players to bring it up to 50%
• these lower players then have too many losses, so match them more against even lower players
• repeat the above process like dominos falling (mathematical induction) until you reach the lowest skill level player
• the lowest skill level player has no one lower to match against, so they cannot reach a 50% win rate, thus there is at least one player with below 50% win rate

So there you have it. In practice, matchmaking systems need to compromise on the skill they match people with if they can’t find enough players of the appropriate skill level. This results in a wider range of skill levels ending up in the same game when not many players are online. This can result in even more players ending up above or below 50% win rate, depending on where they stand skill wise.

Those oils may be quite hard to find, depending on what country you’re in.

Caramelized sugar is one part of the picture. Another part is Maillard reactions of milk proteins, which give ghee a nutty quality. Perhaps you could toast some nuts and include that as well.

Glad to see the “working as intended” responses. Linux as a computer for people to use and Linux as a hobby can sometimes be at odds. It’s not a problem at all if someone’s able to use a Linux computer without noticing.

Replacing ghee with mustard oil isn’t appropriate in every dish. Mustard oil has a spicy bitterness that doesn’t belong in traditional sweets usually made with ghee, for example. You could use coconut oil instead but now you’re introducing coconut aromatics which will change the whole character of the dish.

Freshly made ghee has the aroma of toasted marshmallows. To replace it you need to find something else with those qualities.

I already have more games than I could ever finish in a lifetime — in 10 lifetimes — and they’re all digital, in big folders full of files. If I had those thousands of games in physical form I’d need a library in my house full of shelves to store them all, yet digitally I can carry them all around in my pocket!

Fish emulsion, plant compost.

Yes, like the racquet technology isn’t going to help Joe Sixpack weekend warrior. It takes all that training to be able to fully utilize the technology. The racquet size increase has led to so much more consistency with striking the ball that rallies last way longer now. Longer rallies require way more conditioning to survive!

Not hugely better, no. Marginally better, yes.

The racquet technology impact in tennis has been enormous, with the largest difference being size and weight. Traditional wood tennis racquets maxed out at around 65 sq in of string area but weighed up to 400 grams (mixed units, I know). A modern graphite tennis racquet can achieve 100 sq in of string area while decreasing the weight to 300 grams!

Lighter weights allow a player to generate a lot more racquet acceleration without killing their wrist. At the same time, the larger string area gives a lot more margin for error when striking the ball. Players in turn responded by changing their swing planes to a higher vertical angle, coming up over the back of the ball to generate a lot of topspin (and string technology helps with this too). The topspin further increases margin for error by making the ball dive down into the court instead of sailing long (see Magnus effect).

All of this has combined to allow tennis players to hit the ball far harder than they had in the past, with the increase far exceeding what you’d expect from physical training alone. Give modern players a traditional wood racquet and they’ll spray the ball all over the place, making huge numbers of errors, until they force themselves to not swing so hard.

No, those people move from red states to blue states. That migration has been going on for a long time. It’s one of many reasons why the states are so polarized.

I love this. I love that she’s out in the forest. I love her enigmatic expression. There are no dark nights, no neon lights, yet she is cyberpunk to the bone. Well done!