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But there is a trick. The RNG change every time you do an action. So just move a soldier, fire with another one with better chances to hit or do something and the RNG outcome will change.
Don't calculate percentages in a row, because that's technically gambler's fallacy. Every shot with a 65% chance has a 35% chance to miss. The chances of you missing an individual shot don't decrease the more you miss, they remain the same.
this is extremely misleading post since it is written without mentioning about the Xcom EW 2nd wave mods.
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here is the Xcom EW walkthrough which is a guide
https://gamefaqs.gamespot.com/pc/728011-xcom-enemy-within/faqs/68373
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in Xcom EW, there is the 2nd wave mods
and one of them is called "save scum", once you enable it, you can just save and reload prior to taking shots when you in a mission.
actually, your maths is somewhat inaccurate.
due to RNG being involved, chances of missing shots with 65 % accuracy is actually 50%.
but if your accuracy is as high as 99% or higher especially your sniper, then you will never miss your shots.
even if accuracy is 90% also, chances of missing shots can still be counted as 50%.
same with 95% too.
but once it goes to 99% and beyond, then chances of missing shots becomes 0%.
sniper is the only one that can go 99% and beyond.
it does apply to OP's post.
don't forget about the RNG.
even if Save Scum is enabled, that doesn't mean you shots will hit all the time.
there is always a 50% chance of missing shots due to 65% accuracy even if Save Scum enabled.
1) if you are playing the first 2 difficulties in Xcom EU or Xcom EW, if you miss your shot, in your next turn, you will be given an accuracy buff until you hit your enemy.
Obiouvlsy you didn't have read my post well and don't know how RNG seeds works.
The RNG in this game is just a torture sometimes, to the point that, I have the "you think you are playing the game, but no, you are playing by the game" feeling.