XCOM: Enemy Unknown

[Jarmam]

Let me also share a train of thought I've had, which might help everyone avoid the mistake I've made more often than I wish to admit. Concerning Overwatch squads/traps and how likely they are to not get your people murdered, and how unfathomable a single point of health can be in terms of overthrowing previous correct conclusions.

I dislike a number of maps, the long narrow train in the station-map is high on that dislike-list for a variety of reasons. Mostly I just can't see any way to advance on it without either relying on shootouts or hoping that your cover doesn't get blown up by the notorious clown car of spawns this map has. Consequently I decided on the following strategy on it: I put my Support in front of the train, peaking out over the right flank. My squaddie Sniper and a Rookie took position inside the driver's room of the train, taking each piece of hardcover that's available there, and my Assault would edge up, grab the first MELD canister that happened to be that way, and trigger a pack of 3 Sectoids. Now my reasoning was this: With 3 Sectoids, one of them will almost certainly mind merge. That leaves a maximum of 2 Sectoids advancing. If they both advance inside the train, they will block eachother due to lack of cover, so I guessed that one would take the train and one would take the right flank (the left flank up to the map edge would be walking into a very angry concealed Assault which they knew about). Thus, the flank-Sectoid would be susceptible to three Overwatch-shots, and the train-one to two, one of which is a Sniper (+10 Aim, +1 damage from a Rookie-Overwatch). Sounds good, right? Even if they don't kill the little bugger he only has 35% chance to hit me back. And I am all out of good ideas for this stupid map, so I went for it.

Here's the issue I didn't consider: I've been tracking damage spread for a while, since I had gotten the idea that it was top-heavy (3-5 would yield more 5's than 3's). My data pool is still too small to conclude anything, but it seems to be completely random. I can't say that it isn't, so we'll assume that it is for now. All numbers are averaged slightly to the point of insignificance.

A Sectoid has 4 health. This means that my Rookie has a 45% chance to hit the guy, and 33% of those will be 4's, giving her a 15% chance to outright kill the alien. My Sniper has 55% hit chance and 66% of those will be 4+ hits, giving him 36,3% chance to outright kill. On top of that if they both hit the Sectoid it will die no matter what the damagespread, which is a 24,7% chance of happening. There is some overlap with their independant solo killing chance. All in all this leaves me with:
15% (Rookie)
+
36,3% (Sniper)
+
24,7%(overlap)
-
(0,15+0,363)*(0,247)=12,6% overlap on killing blows (took me a while to realize my own incompetence there :p)
=
63,76 chance of killing the little bugger if he wanders into the trap in the train. (Edit: Plan was good, I was bad at math) Now in those 35%some of cases that I don't just outright kill him he now has 35% hit chance for 2-4 damage of the plasma pistol, and 10% crit chance of a guaranteed lethal blow. With 4 health on both Sniper and Rookie this gives him a mere 11,55% chance of instantly killing someone with a hit, and a 2,3% chance of turning a 2 or 3 hit into a crit. Or:
(0,35*0,10)= 3,5% (the crits)
+
(0,35-0,035)*(0,33)=10,3% (the hit-and-kill-chance minus the crits)
=
13,8% chance to kill. Since he dies 2 out of 3 times, this is less than 5% likely to happen. Now 1 out of 20 is still kind of a lot for every single Sectoid but oh my I will taketh this any day with no better plan.

"But... what if he is the one getting the mind merge?", you correctly ask. Incorrectly my initial reaction was "well how much could it change? I have a plan, I will do said plan, now hush". This, my honorable forumers, is what is known as "delusion". It ruins everything.

With 5 health, my firing squad is now subject to the following chances: My Sniper's 55% hit chance gives him 18,15% chance for a 5. My Rookie cannot deal 5 damage on Overwatch, so she has 0% chance of killing the merged Sectoid alone. If they both hit, then once again damagespread is irrelevant since their combined minimal damage is 2+3. Chances of that are the same - 24,7%. But this still overlaps with some of the Sniper's solo killing chance (if he hits a 5 and the Rookie hits, this is overkill). Because of this, only the Sniper 5's without the Rookie will increase the likelihood of a kill:
18,15% (Sniper chance)
+
(55%*0,66) (Sniper non-lethal hits)=36,3% times the Rookie's hit chance (overlap kill chance) = (36,3%*0,45)= 16,3%
=
34,45% chance to kill. Yes, ladies and gentlemen, this single point of health has reduced the odds of a successful trap by roughly half

And it gets so much worse. With the mindmerge's +25% critical chance the Sectoid now has the following return fire chances: He still hits 35% of the time. Now he has 35% crit chance, meaning that 12,25% of his shots will connect and crit for a kill.
The remaining 65% of his hits still have the same 2-4 chance, so 33% of those will also kill:
(23,45*0,33)=7,74% "4 hits"
+
12,25 (crits)
=
20% chance to kill. Since he now only dies 1 out of 3 times, he will return kill 13,35% of the time. Or more than twice as often. Add to this that even if he should miss he will be much harder to kill on my next turn with his innate extra hit point and the situation is arguable 3-4 times worse than if he were not merged.

Of course this would be different stats on Classic since Sectoids have one less health, but the concept is the same. So heed my warning, ye fellow fighters of ETs. Health and mindmerge matters beyond what I had even bothered to consider.

You could almost say this indicates that mind... over-matters...?
YEAAAAAAAAHHHHHH