Quote Originally Posted by Kaze3434 View Post
i was using the gathering as an example to this games rng. what i am saying is that you cant view each room as tied together. not in terms of rng anyway, because you can still get the odds of someone finishing a dungeon.

note, this is for this games rng

for example, you beat the enemies for the first room. for that room, you have a 50% chance to move to the next one. you pick the right door and move on to the second room. beat the monster again, and doors come up. your chance to continue doesnt get cut in half in the second room, as there is still only two doors, so it is still 50%. this is one reason why its flawed thinking when someone gets mad about melding materia that has a 26% chance. odds say that by the 4th meld, it should go thru, but each meld is independent from the previous one.
There are two different (yet related) concepts that people have been discussing here, and it's important not to confuse them.

The first, which we'll call event probability, represents the chance of any one isolated action happening in a certain way. In the map dungeon scenario, this would be the chance when opening a door that you'll get the correct door. As I briefly mentioned in my original post, this may not necessarily be 50% depending on SE's exact implementation, but it's easier to assume that it is. What this means is that any time you clear a room and go to open the door to the next room, you'll always have a 50% chance of your chosen door being the correct one. That is, regardless of whether you're opening the door to the second room or to the seventh room, you still have a 50% chance of being right.

Another way of representing this is to say, "Given that I've already reached the N'th room, I will always have a 50% chance of reaching the N+1'th room."

This should not be confused with the other concept, cumulative probability, which represents the chance of a given series of events happening in a certain way. In the map dungeon scenario, this would be the chance of reaching a particular room without any pre-conditions. What this means is that if you wanted to figure out your chance of reaching, say, the third room--before you even pop the map in the first place--you need to consider it in the context of the chain of events that will lead you to that outcome. For that particular example, it's very straightforward to derive the cumulative probability using the individual event probability form discussed above:

You have a 50% chance of having the portal spawn once you beat the initial pop.
Given that you had a portal spawn, you have a 50% chance of selecting the correct door from the first room.
Given that you made it to the second room, you have a 50% chance of selecting the correct door from the second room.

Therefore, the probability of making it at least as far as the third room is the product of the individual event probabilities, or (1/2)^3, which works out to 12.5% for any given map. Of course, this doesn't mean that if you did 1000 maps, you would make it to the third room exactly 125 times, but any given sample set should be close to that proportion--assuming SE is using a reasonable PRNG algorithm in the proper way; all bets are off if that isn't the case.