Friday, September 28, 2012

A Lottery Thought Experiment


In this post, I'm going to lead you through a thought experiment based on a theoretical game called Tomo. Tomo is pretty simple: you buy any number of tickets at a fixed price, and each ticket has a certain chance of winning and paying out a fixed price reward. In Tomo, the chance of winning is not affected by how many tickets have been sold, and neither is the payout per ticket. So it's not like a 50/50 raffle, in which the total number of tickets bought by anyone in the game decreases the chances of any particular ticket winning, and the payout increases as more tickets are bought. It's more like a slot machine, in which each pull of the lever costs a certain amount and has a certain chance of paying out. As a further simplification, Tomo does not have degrees of success on a single ticket. Each individual ticket either wins and pays out or it doesn't, there is no variability in how much a winning ticket can pay out.

Tomo is a game that, aside from these basic rules, can be played many different ways. The person running a game can decide how much a ticket will cost, what it's chance of winning will be, and what it's payout will be if it wins. The people running Tomo games always have enough resources to cover the winnings other people make, regardless of how much that might be, so they can set these figures however they want.