I used to get so many comments about how the computer opponent in a tile-based board game of mine cheats and got all the high numbers while they always got low numbers, and I'd be like "that's mathematically impossible. I divide the number of spaces on the board in half, generate a deck of tiles to go into a 'bag', and then give a copy of those same tiles to the other player.

So over the course of the game you'll get the exact same tiles, just in a different random order.

Now to be fair, I didn't make that clear to the player that's what was happening, they were just seeing numbers come up, but it was still amazing to see how they perceived themselves as getting lower numbers overall compared to the opponent all the time.

Meanwhile on the base game difficulty I was beating the computer opponent pretty much every game because it had such basic A.I. where it was placing its tiles almost totally at random (basically I built an array of all possible moves where it would increase its score, and it would pick one at random from all those possibilities, not the best possibility out of those).

My Dad used to play a lot of online poker, and he used to complain when other players got lucky with their hands, be like 'I know the chances are like 5% of them getting that! They shouldn't have gotten that!' and it always reminded me of those people.

The better option would be to just increase the flat odds. DQM: The Dark Prince is brutal with it's odds, but fair. A 45% chance is 45%.

In games like Civ/EU/Stellaris/Sins/etc It makes sense that a 3:1 battle wouldn't scale linearly, especially if you have higher morale/tech/etc. Bullets have a miss ratio, 3x as many bullets at the same target narrows that gap and gives the larger side an advantage at more quickly destroying the other side. So just give it an oversized ratio to scale the base (1:1) odds at.

That keeps "losing" realistic...a once in an occasion happenstance of luck/bad tactics/etc but also a generally very favorable and reliable outcome for your side.

I worked on a game where we added a "fairness" factor to randomness. If you were unlucky in one battle, you were lucky in the next, and vice versa. Mathematically you ended up completely fair. (The game designer hated it, though, and it wasn't shipped like that)

Games like Battle for Wesnoth which have it implemented right, you’ll look at a 90-10 scenario with 2 attacks and end up with the 1% scenario. Enough to make a man rage. I have degrees in Mathematics, I am aware of statistics, and all that. And yet when I played that game I would still have an instant “wait what, that’s super unlikely” before I had to mentally control for the fact that so many battles happen in a single map.

Was good because it identified a personal mental flaw.

Dispatch too. If your odds are above a certain threshold, the mission is a gimme.

I think XCOM does this as well.