To be clear, we are not certain the physical constants of the universe can vary and if they can, by how much. It is the assumption of those who use the fine tuning argument for God that they can vary by a great degree. Let’s assume they're right and, for the sake of argument, nail it down to five constants. The following compares winning the universal lottery to winning the actual lottery.
To win a State lottery, one needs to match five specific numbers.
For humans to live in this universe, it needs five physical constants to have specific values.
If I alone play the only draw of the lottery ever allowed and I guess the five numbers at random, the odds of me winning the lottery are 1 in 100,000.
If the only universe to ever exist forms randomly , the odds of that universe having the variables that support human life are 1 in 100,000.
Can either scenario happen by chance? Yes, but I’ll grant that it’s enough of a long-shot to be suspicious that the lotto was fixed or the universe was designed.
Now, imagine 100,000 people play the lottery. There’s about a 64% chance someone will win.
Imagine 100,000 universes form either concurrently or sequentially. There’s about a 64% chance that one of these universes have constants that support human life.
This illustrates how a sufficiently large multiverse should remove any suspicion of a cheater nor a designer.
Now, imagine a lottery in which each player plays different numbers so every combination is covered when 100,000 play. When the number is drawn, someone is ensured a win while everyone else loses.
Imagine a universe in which every combination of constants can support some manner of intelligent life. Human’s might not exist, but whatever is here in our place could likewise make a fine tuning argument for their God.
It would not be a valid argument because, whatever the constants, someone is here to claim that no one could be here otherwise. This illustrates the anthropic principle at work.