 We're going to play the two thirds game and it's going to be awesome. If you can predict the right answer, that'll definitely be no mean feat. Let's play a little game with the other thumb viewers. If you're in a place where you can do so, scroll down to where you can leave a comment. Try not to look at any other comments and don't worry, I won't do anything interesting up here for a little while. You can pause if you need a little more time. Now, enter a number between 1 and 100 that you think will be two thirds of the average of what all the other commenters guess. You may change your mind by the end of the video, but please, honor system here. Take your best crack at it now. Good to go? Okay, let's talk about why this game is particularly interesting. There's an important difference between chess and poker that doesn't have to do with cards or betting or the general attitude of how cool top tier players are. In poker, until everyone's hands are revealed, there's always something the other players know that you don't, and vice versa. No matter how good of a player you are, the best you can do is hazard a guess about what sort of cards everyone else is holding. On the other hand, in chess, the only thing you can hide from your opponent is your strategy. The pieces, their positions, how they move, all of that information is shared between both players. At higher levels of chess, the amount of shared information is even greater. Both players know that Urusov gambit, all its variations, how likely it is to result in a victory for black or a stalemate, and the best responses to it. Importantly, that's not the only information that's shared. Both players know that the other player knows that information. Both players know that the other player knows that they know that information. It's tempting to think of that as some sort of recursive word game. Like we're just saying, I know that you know over and over and isn't this fun. But in reality, each of these statements is a unique fact unto itself, with a unique set of implications totally unrelated to the other levels of knowing. Every step you take down that infinite rabbit hole of mutual knowledge has serious significance for behaviors and strategies. For example, take a game of poker in which you only have a pair of jacks. Usually you're the only one who knows that. Pretty simple. You can fold or you can try to bluff your way to victory, while your opponents don't know anything but your body language and how much you're betting. But what if you mean forward a little too far and I see your hand? Now I know that you only have a pair of jacks, and the strategic landscape is totally different. If you bluff, it would be easy for me to use a decent hand to clean you out. If you fold, I now have some additional information about what you're likely to do with a weak hand. That's all well and good. But if you happen to notice me staring over your shoulder when you lean forward, now you know that I know that you only have a pair of jacks. Which again is a totally different scenario, with a number of potential strategies unique to that situation. Which is totally different from the situation where I notice that you've seen me looking over your shoulder, where I know that you know that I know that you have a pair of jacks. Whatever level of mutual knowledge where that chain ends, there's the potential to exploit the asymmetry of knowledge, to bluff or riddle some strategic advantage out of it. Game theorists describe the situation where all players know a thing, as well as knowing that all players know it, and knowing that all players know that all players know it, all the way to infinity, as common knowledge. Which is a little frustrating because that term already has an established meaning. Thanks guys. Personally, I have trouble simulating strategies and responses beyond about three or four iterations of mutual knowledge. It just gets fuzzy trying to figure out the Russian nesting doll of knowing about knowing. This is why the act of stating something publicly is categorically different than simple communication between individuals. It's easy to think of something like a public service announcement, or a flyer, as a device solely meant to transmit a fact or idea to its audience, but it's much more than that. By putting the information in a place where everyone can see it, you can establish common knowledge, ensuring that everyone knows, that everyone else knows, and so on. That's a much different thing. Take the infamous smoke-filled room experiment by Lataine and Darlene, two psychology researchers who were investigating variations on the bystander effect. In the experiment, a group of students were left alone in the classroom to complete a questionnaire. After a while, the room began filling with smoke, as though there might be a fire somewhere in the building. Loan students would usually respond to the simulated emergency, but if they were in groups of three, they'd respond less than half of the time, and only one time in ten if they were paired up with a couple of actors who were instructed not to react to the smoke. That seems pretty crazy, right? The building might be burning down for all they know, and most people seem to ignore the potential danger, or at least fail to alert anyone else to the fact. The authors of the paper attribute this phenomenon to a combination of social pressures, both conformity and a desire not to appear foolish or cowardly or something. Think of what a fire alarm means in this context. Yes, it alerts people to the possibility of a fire and warns them to exit the building, but it also establishes a sort of common knowledge, a group awareness that, by some objective measure, this is an emergency situation, and we can react to it as though it were an emergency without looking like idiots. This is also one reason why the ability to control mechanisms of common knowledge, things like protests or the internet or posting notices in public places, can be such a big deal. Limiting the spread of a particular bit of information is exceptionally difficult, but if you can keep it from becoming publicly visible, if you can hold some sort of ambiguity as to who's aware of it and who isn't, you can use that uncertainty to maintain a status quo that would otherwise be cause for some sort of response. That might sound like a tool solely for fascist dictators, but it might also be useful for navigating social scenarios that might otherwise be awkward or risky. Live psychologist Steven Pinker has argued that we regularly use deliberately ambiguous phrasing and implication in innuendo to leave our conversational partners some wiggle room in what they choose to hear in our speech. Rather than stating everything explicitly, we can use the lack of common knowledge as a sort of plausible deniability, so we can feel our way to a decision that's probably acceptable for everyone without direct confrontation. Take the age-old conundrum of deciding where to go to dinner with a group of people. If I start the discussion by stating explicitly that I want Chinese food, that becomes common knowledge, and there are potentially uncomfortable social ramifications. If anyone doesn't really feel like Chinese, they have to decide if they're going to challenge my suggestion, or if they can marshal enough support from the others to overturn it. Basically going to dinner has become a game of thrones, although the opposite extreme can be frustrating, where nobody voices any firm opinions at all. There's a much more comfortable middle ground, where a little uncertainty can help us out. Let's say that I float my hinkering for some wontons by saying something more like, does Chinese sound good to anyone? As though the idea just spontaneously emerged from the ether and I'm not quite sure myself. On some level, yes, we all know that Josh just wants some wontons, but do we know that we all know it? Do we know that we know that we know it? If someone says, eh, we just had Chinese yesterday, although we all know that that means, Josh, I don't want Chinese again. It doesn't have the same sting it would otherwise if I had laid everything out there and gotten shot down. Computer scientist Scott Aronson has suggested that some of the social difficulties that nerds have can be attributed to a general discomfort with information asymmetry. If you're doing science or mathematics, ambiguity of this sort can be disastrous, but so can trying to make everything that you discuss common knowledge. Which leads us back to the original question. Knowing now what you know about mutual and common knowledge. And knowing that everyone commenting knows that. And knowing that they all know that they all know that. What's your second guess? Please leave both numbers in the comments and let me know what you think. Thank you very much for watching. Don't forget to blah, blah, subscribe, blah, share and don't stop thunking.