I'm using a 50-50 encounter to mean more than die rolls. If attacking a monster with the wrong tactics is an auto-lose, and fighting it with the right tactics is an auto-win, and you're 50% likely to blunder into the right tactics, then you have a 50% chance of winning.
If an encounter is 50% lose by choosing your actions at random (out of the list of what is not obviously stupid), and 30% lose with good tactics, and you're 90% likely to see and apply good tactics, then your 5% to lose it with your bad tactics, 27% likely to lose it despite your good tactics, 5% likely to win in spite of bad tactics, and 63% likely to win with good tactics; it totals to a 32% chance of loss, not a 50% chance of loss.
This assumes that the DM planned the enemy's tactics in advance, maybe with a few contingencies.
Now let's look at this part:
So the probability of -in actual play- winning a series of 50-50 (or whatever) encounters is higher, because in order to have a series (more than one), one of those encounters has to have gone your way, and then each comes as 50-50 individually
Completely and utterly wrong.
Let's take this through with baby steps through an example here. The DM plans a series of four encounters, each 50-50, because that makes the math easy. Let's assume a loss stops you.
Encounter 1: 50% chance of loss, 50% chance to go on to encounter 2.
Encounter 2: If you see it, you have a 50% chance to go on to encounter 3, and a 50% chance to lose. Because your chance of having lost already and never actually seeing this encounter is 50%, to take into account that possibility, you have to multiply all of the chances here by 0.5. Half the time, you've lost before you get to see this encounter, and half the time when you haven't (a total of 25% of the time), you lose here (75% of the time total).
Encounter 3: You have a 25% chance of seeing this encounter. If you see it, you have a 50% chance to see encounter 4. Taking your losses into account, that means that you have a 1-in-8 chance of seeing encounter 4. From a perspective at the start, you have a 6-in-8 chance (3-in-4, but I'm keeping denominators consistent within an encounter) of not even getting here, and a 1-in-8 chance of not making it past here (half of the remaining chance).
Encounter 4: If you do see this encounter, you have a 1-in-2 chance of winning. Taking your chances of loss into account, you have a 1-in-16 chance of winning. Looking from the beginning, you have a 14-in-16 (7-in-8) chance of not making it here, and a 1-in-16 chance of failing here.
If you play 1,600 groups through this adventure, and they fall roughly according to probability distribution, then only about 100 of those groups will have made it through. More than 90% of your playerbase never will make it to the end.
A series of 50-50 chances means that half the time (half of all groups, in our sample) you don't get a series of encounters from the players' perspective, yes, because you got stabbed to death in the face in the first one. You still have a series of encounters from the DM's perspective, because the DM had to write their notes, or read the adventure, or whatever. From their perspective, there is a series of encounters even if the PCs are a pile of corpses in a roadside drainage ditch after the first encounter.
"No, you can't burn the inn down. It's made of solid fire."
