psycho-statistical theory of gambling (let's play money making game!)
Another aspect of Kingdom of Loathing I find interesting is the Money Making Game (the name is a shout-out to the original Legend of Zelda, which most players are probably too young to remember... o_O). A player publicly posts a wager of any amount, another player takes it, and the game randomly decides who wins. The winner gets all the meat (money), minus 0.1% for the house.
I'm pretty sure all of us know what will happen if you play the MMG, but we're a small minority. I've had a lot of people protest when I tell them they can expect to lose 0.1% of everything they bet in the long run, and I hear the gambler's fallacy over and over (this is when someone assumes that because they've lost six times in a row, they must have a big win coming up). There are plenty of sophisticated elder players who will warn others against the lure of the MMG, but even more who are gradually impoverishing themselves while professing the virtues of their various Martingale systems.
The Martingale is an 18th century betting system that essentially says to increase your bet every time you lose, so that if you win you'll come out ahead. Eventually, by chance, you'll have a big win, at which point you should take your money and leave. This is theoretically sound (I think it resembles one theory about how the universe was created from spontaneously generated annihilating pairs of mater-antimatter particles)... as long as you have unlimited time and an infinite bankroll. With an exponentially-increasing wager, you're very likely to eventually go broke, at which point you can't continue trying to make up for your losses.
The fact that people are playing with Martingale (or just making enormous bets for the thrill of it) may be part of the reason the population is so slow to wise up. The prediction that you'll lose 0.1% of your money is only observable at an individual level if people make lots of small bets. But most people make huge wagers that quickly make them either strike it rich, or lose 100% of their money. That makes it easy for people who are susceptible to the lure of gambling to notice the big winners and ignore the big losers.
So now I'm thinking about what would really be observed, given different models of player behavior. If everyone made one big wager and then quit, the distribution of winners and losers would be 50/50. If everyone kept playing, wagering only a small proportion of their bankroll, the distribution would tend towards 0/0, with everyone breaking even minus the house's take. But if winning tends to make people bet even higher next time (which isn't part of the Martingale system, it's just an emotional response), then the distribution should actually tend towards 0/100, because once you go broke you have to stop playing. But people are constantly getting meat from NPCs, and so there's always a fresh supply of suckers. In fact, this is probably the reason the MMG exists -- if players can farm money by killing monsters, and then trade it among themselves, the player economy will suffer neverending inflation unless there's a way to suck money back out (this is unrelated to the much more obvious reason gambling exists in the real world, but in both cases the goal of the house is to take the players' money).
The fact that MMG outcomes are "lumpy" means that there is at least one generalizable situation in which playing the game is rational: if you have a limited-time opportunity to buy something you value very highly, and you can't make enough money before the deadline, it might make sense to gamble. If you have a 50% chance of losing $10,000 and a 50% chance of winning $10,000, your statistically expected outcome is (0.5*-10,000)+(0.5*10,000) = zero (or, say, -$100, if the house is taking a 1% cut). But if you have the chance to pay $20,000 for something that you'd value at $40,000, then a win is worth much more than a loss -- (0.5*-10,000)+(0.5*30,000) = an expected outcome of +$10,000! Sadly I think that the reverse is more often true in the real world: A win of $100,000 means that you have an extra $100,000; a loss of $100,000 means that the bank forecloses on your home and you lose custody of the kids. But people don't like to think about that one, and since the outcomes you think about more seem more intuitively likely, they don't recognize the true risk.
In contrast to this is the much-deprecated phenomenon of poor people buying lottery tickets -- I think they must figure that winning big would change their lives forever, whereas the dollars they lose on the lottery would never add up to anything meaningful anyway. Depending on how much they're spending gambling and what their other expenses are, it's possible they could be right (though in most cases they surely aren't).
I'm sure this topic has been treated at length by the statisticians. The reason I'm devoting time to chewing it over is that it's a hybrid statistical concept that I haven't dealt with before. In my training we always thought in terms of continuous distributions and large samples, or in terms of small samples creating noise but not fundamentally changing your outcomes. High-stakes gambling involves all sorts of psychological influences, and has a very non-continuous range of outcomes due to the two issues I've talked about (the ability to go broke, and the possibility that wins and losses of equal amounts can have different utilities). It's a situation where players aren't using logical analysis, but they are using some kind of analysis, and it's darn interesting to try to figure out what it is.
I'm pretty sure all of us know what will happen if you play the MMG, but we're a small minority. I've had a lot of people protest when I tell them they can expect to lose 0.1% of everything they bet in the long run, and I hear the gambler's fallacy over and over (this is when someone assumes that because they've lost six times in a row, they must have a big win coming up). There are plenty of sophisticated elder players who will warn others against the lure of the MMG, but even more who are gradually impoverishing themselves while professing the virtues of their various Martingale systems.
The Martingale is an 18th century betting system that essentially says to increase your bet every time you lose, so that if you win you'll come out ahead. Eventually, by chance, you'll have a big win, at which point you should take your money and leave. This is theoretically sound (I think it resembles one theory about how the universe was created from spontaneously generated annihilating pairs of mater-antimatter particles)... as long as you have unlimited time and an infinite bankroll. With an exponentially-increasing wager, you're very likely to eventually go broke, at which point you can't continue trying to make up for your losses.
The fact that people are playing with Martingale (or just making enormous bets for the thrill of it) may be part of the reason the population is so slow to wise up. The prediction that you'll lose 0.1% of your money is only observable at an individual level if people make lots of small bets. But most people make huge wagers that quickly make them either strike it rich, or lose 100% of their money. That makes it easy for people who are susceptible to the lure of gambling to notice the big winners and ignore the big losers.
So now I'm thinking about what would really be observed, given different models of player behavior. If everyone made one big wager and then quit, the distribution of winners and losers would be 50/50. If everyone kept playing, wagering only a small proportion of their bankroll, the distribution would tend towards 0/0, with everyone breaking even minus the house's take. But if winning tends to make people bet even higher next time (which isn't part of the Martingale system, it's just an emotional response), then the distribution should actually tend towards 0/100, because once you go broke you have to stop playing. But people are constantly getting meat from NPCs, and so there's always a fresh supply of suckers. In fact, this is probably the reason the MMG exists -- if players can farm money by killing monsters, and then trade it among themselves, the player economy will suffer neverending inflation unless there's a way to suck money back out (this is unrelated to the much more obvious reason gambling exists in the real world, but in both cases the goal of the house is to take the players' money).
The fact that MMG outcomes are "lumpy" means that there is at least one generalizable situation in which playing the game is rational: if you have a limited-time opportunity to buy something you value very highly, and you can't make enough money before the deadline, it might make sense to gamble. If you have a 50% chance of losing $10,000 and a 50% chance of winning $10,000, your statistically expected outcome is (0.5*-10,000)+(0.5*10,000) = zero (or, say, -$100, if the house is taking a 1% cut). But if you have the chance to pay $20,000 for something that you'd value at $40,000, then a win is worth much more than a loss -- (0.5*-10,000)+(0.5*30,000) = an expected outcome of +$10,000! Sadly I think that the reverse is more often true in the real world: A win of $100,000 means that you have an extra $100,000; a loss of $100,000 means that the bank forecloses on your home and you lose custody of the kids. But people don't like to think about that one, and since the outcomes you think about more seem more intuitively likely, they don't recognize the true risk.
In contrast to this is the much-deprecated phenomenon of poor people buying lottery tickets -- I think they must figure that winning big would change their lives forever, whereas the dollars they lose on the lottery would never add up to anything meaningful anyway. Depending on how much they're spending gambling and what their other expenses are, it's possible they could be right (though in most cases they surely aren't).
I'm sure this topic has been treated at length by the statisticians. The reason I'm devoting time to chewing it over is that it's a hybrid statistical concept that I haven't dealt with before. In my training we always thought in terms of continuous distributions and large samples, or in terms of small samples creating noise but not fundamentally changing your outcomes. High-stakes gambling involves all sorts of psychological influences, and has a very non-continuous range of outcomes due to the two issues I've talked about (the ability to go broke, and the possibility that wins and losses of equal amounts can have different utilities). It's a situation where players aren't using logical analysis, but they are using some kind of analysis, and it's darn interesting to try to figure out what it is.