How many throws of a die would it take you to conclude that it was loaded? 4? Let's say I gave you a magic die that has the property that it's fair to begin with, and then at some point it will switch to being loaded. How long would it take you to be sure that this switch had occurred? 4 throws?
There are more variables than you may realize.
First, it depends how loaded. We'll need to define the degree of load, I will make an assumption soon.
Second, it also and mainly depends on whnether being loaded is a common occurence.
We need to know the chance of it becoming loaded. If we knew that it can only become loaded once every 100 years, then for sure 4 throws is not enough to conclude it is likely loaded.
But if you told me that at some point each day, the die will become loaded and throw only sixes, then the math changes.
If the die is fair, the chances of four sixes in a row would normally be .077% (i.e. once in 1296 throws).
Now suppose this die is thrown every ten seconds, and that it will become loaded at some point each day (86,400 seconds in a day)
There are 8640 throws per day. There is a one in 8640 chance of the die becoming loaded on any given throw. At four successive 6's it is more likely that the die is still fair than that it became loaded exactly 4 throws ago.
At 5 sixes in a row, the chances are just under 50% that the die just switched to loaded.
At 6 sixes in a row, the odds are heavy that the die became loaded.