Bruce's Idea

Bruce Onder appears with an interesting idea. It does make a difference.

My e-friend Bruce Onder suggested a modification to the yardsale game, where the players bet a percentage of their own wealth, in our case ten percent. You can almost imagine that as a fair way to bet, ten percent of my money against ten percent of yours.

So today, in the absence of other things to distract me, I tried it. The change is simple:

class Person:
    def transact(self, other, prob=None):
        prob = prob if prob is not None else random()
        # bet = min(self.bet(), other.bet())
        if prob > 0.5:
            self.wealth += other.bet()
            other.wealth -= other.bet()
        else:
            other.wealth += self.bet()
            self.wealth -= self.bet()

As Bruce suspected, this really does change things. The game is much more stable. There are generally only a few yellow individuals (folx with less than half their starting wealth), and if you watch them, they get back above half pretty quickly. Only rarely does a red individual show up (less than 25% of starting wealth) and they, too, quickly get back to the conventional cyan color.

That’s not too surprising: the lower your wealth gets, the less you lose but you tend to win big because everyone is more wealthy than you are. I’m not saying I would have predicted the result, because I didn’t even try. But the game runs and runs and the maximum wealth tends to stick around about 2000, double the starting value. After a long run, it still looks like this:

This simulation causes me to wonder about at least one possibility: over a long period of play, does every player tend to be on top of the pile sometimes and the bottom other times? Do people tend to drift from underdog to overdog and back? Maybe I can think of an easy way to test that. Perhaps each individual tracks their high and low and we plot both? Might be easy enough.

In the original scheme, the lower you go in wealth, the less money you can ever make. You can only ever get ten percent of the pittance you currently hold. Meanwhile, the big guys can only ever lose less than ten percent of their wealth, and that minuscule loss gets smaller and smaller as people around them become less wealthy, and as they become more so.

In today’s scheme, when you’re down, you get more than ten percent of your wealth, and often a lot more. When you’re up, you make the same as you would have in the original plan. It’s just that when you lose, you lose more.

We get at least a glimmering of how the rich get richer. If I’m ever to make a lot of money in the market, I have to risk a big fraction of my total wealth. But a very rich individual can put the bulk of their wealth in low-risk investments, with a very large resulting return, and then small slices of wealth in many high-risk investments with a low probability of a large return.

This is why vulture capitalists get rich while the company founders and early investors mostly do not. The VC places many small bets, each with a low probability of a large reward. Since if we place enough low probability bets, some of them will come in, the VC burns a little capital and gets a lot back. Meanwhile, most of the founders and early investors lose. A few get rich: most do not.

So, what do we know? I think we know that the system is rigged, but we were already pretty sure of that. What do we do about it? I have no good ideas here. The system is rigged. Systems like ours are very stable and not easily adjusted to behave very differently.

It would be nice not to have to destroy all the good things in our society to make sure that there is more equity. An equal, very good, chance of starving isn’t really what I had in mind.

No answers here, maybe a bit more understanding. Thanks, Bruce! And thanks to all of you!