A common reason for why people came up with the multiverse hypothesis was that they couldn’t fathom that a single universe, if it is all that exists, bears the constants necessary to eventually result in life.
As such, people postulated a whole series of more universes with different kinds of constants. After all, if all kinds of configurations are possible, it is not surprising that atleast one of them would result in life bearing conditions.
Ian Hacking, in 1987, calls this a fallacy. See https://www.jstor.org/stable/2254310. He coined a term called the inverse gambler’s fallacy, which is basically what it sounds like: the inverse of the gambler’s fallacy. What this means is that the number of previous trials of a chance based process do not affect the probability of the current outcome. This is because trials are usually independent, and in the case of the multiverse hypothesis, these universe’s conditions are considered independent.
For example, he uses the example of walking into a casino room and immediately seeing someone roll double sixes. You are asked to consider whether it is now more likely that this occurred on his first try or whether or not this occurred after many previous tries. Hacking says that the probability of THIS specific two rolls landing on sixes has no influence from its past.
Although he is correct that the probability of the current trial has no dependence on previous trials, I don’t think it is true that the number of previous trials has no effect on whether or not the current trial occurred by chance.
Allow me to use an example. Suppose you have a lottery that is conducted by chance, and you observe the same person winning two consecutive lotteries. Let’s call H1 = Chance, H2 = Lottery was rigged, and O = person wins two consecutive lotteries.
If you observe O on the first two lotteries ever played, the probability of O given chance (I.e. P(O|C)) is the same as if you observed it after 500,000 lotteries were played. But how does this imply that P(C|O) is the same. What if a person is more likely or more able to rig a lottery the first two times it’s played then after it’s played 500,000 times? I fail to see how the inverse gambler’s fallacy charge adequately responds to what actually matters. With fine tuning, we don’t care about the probability of constants being certain values by chance. We care about whether the universe was fine tuned: I.e. how likely it is that these conditions happened BY chance.