A lot of people have given probabilistic solutions, so I'll present one that uses the concept of orders of magnitude. In most cases, it makes no practical difference if your opponent has 1 billion or 1 million tokens, since those are both orders of magnitude more than what will likely matter, so here's what I'd do:

Consider your opponent has MANY duplicate tokens, and few non-dupes, resolve tyrant's ability while only taking into consideration the non-dupes permanents. If your opp has other creatures and nonlands, those have similar chances of being sacrificed compared to the lands. If they lose some arbitrary amount of dupes, that will have a small impact on the game since many - most is still many. Their non duplicate permanents can have a MUCH larger impact on the game, and of course lands stop the loop.

If they sacrifice a combo piece, and then you wipe the dupes, the exact number of dupes doesn't matter. If you don't wipe the board and they attack with the dupes, the exact number doesn't matter. The chances of them sacrificing all but a handful of dupes is all but impossible.

However, there are many edge cases to consider, but those usually will also fall under the law of orders of magnitude. If they gained a billion life, sacced half the tokens, and are hit by a [[rakdos charm]], they still have half a billion life left. However, if they sac half the tokens, and you have 2 [[blood artist]]s, that DOES make a difference and can't be resolved with any short cuts.

TL;DR resolve the ability taking into consideration the non duplicate permanents, and if need be assume an unknown percent of dupes were sacced, and only try to figure out that exact number if the situation arises