There are two questions we must consider, according to Bayes: What is the prior probability of living in a simulation, and given we live in a simulation, what is the probability of winning the lottery?
We can invoke your argument at either point, and I’m not sure which you intended.
-- Is 10^-8 enough evidence to overcome the prior improbability? In this case, “prior” means just before we bought the ticket; so we have a lifetime of evidence to help us decide whether we live in a simulation. (Determining this may be difficult, of course, but the lottery argument presumes we can get some distinguishing evidence in various ways!)
—Is 10^-8 actually so much lower than the probability of winning the lotto in a simulation? It could even be higher, depending on what we think is likely!
Other commentors pointed out the second possibility, but I dodn’t think of the first until your post. We might accept the idea that winning the lotto is rather more probable in a simulation, and yet reject the idea that we should believe we’re in a simulation if we win, simply because the simulation hypothesis is much more complex than the regular-world hypothesis. We are then “safe” unless we win the lotto twice. :)
There are two questions we must consider, according to Bayes: What is the prior probability of living in a simulation, and given we live in a simulation, what is the probability of winning the lottery?
We can invoke your argument at either point, and I’m not sure which you intended.
-- Is 10^-8 enough evidence to overcome the prior improbability? In this case, “prior” means just before we bought the ticket; so we have a lifetime of evidence to help us decide whether we live in a simulation. (Determining this may be difficult, of course, but the lottery argument presumes we can get some distinguishing evidence in various ways!) —Is 10^-8 actually so much lower than the probability of winning the lotto in a simulation? It could even be higher, depending on what we think is likely!
Other commentors pointed out the second possibility, but I dodn’t think of the first until your post. We might accept the idea that winning the lotto is rather more probable in a simulation, and yet reject the idea that we should believe we’re in a simulation if we win, simply because the simulation hypothesis is much more complex than the regular-world hypothesis. We are then “safe” unless we win the lotto twice. :)