Why it's bad to mess with probability in turn-based games

(This is basically just a summary of my arguments on Battle for Wesnoth forums over the same thing)

In games with luck, it's common for users to complain about situations where they have bad luck, and it's also common for users to suggest ways to compensate for bad luck by screwing with the RNG to "prevent" streaks of bad luck. This is generally a horrible idea.

1. The first problem is that probability is no longer constant. Instead of Hydro Pump being 80% accurate, its accuracy now depends on how good your luck was up until that point. Instead of thinking "I'll win unless he crits, so I have a 94% chance of winning", you now have to think "He hasn't critted in a while... should I be worried?"

I once compared the hit probability calculation for one proposed "luck compensation" system in Wesnoth. It was something like:

Let D be a unit's terrain defense, let K() be the karma function, and let H[n] be a unit's previous hits.

In the old system, the unit's accuracy (barring marksman/magical) would be:

1-D

In the new system, the unit's accuracy would be:

1-D+K(H[-1])+K(H[-2])+K(H[-3])+K(H[-4])+...

You shouldn't have to spend an hour doing calculus to figure out Hydro Pump's accuracy.

2. The second problem is that luck compensation doesn't deal with why hax is a problem in the first place.

Hax is localized extremal rolls, but luck compensation systems only compensate for global extremal rolls, which aren't ever a problem. Problematic situations are things like: Dugtrio misses Stone Edge and Volc OHKOs with Bug Buzz. A luck compensation that would have made the second Stone Edge hit is pointless since Dugtrio's already dead before the second Stone Edge. If this sort of thing happens enough times in one game, we complain about it.

Hax isn't having bad rolls on average. Everyone has average rolls on average, that's just the way luck works. Hax is having bad rolls when it matters and good rolls when it doesn't, and no luck compensation system can account for that.

3. The third problem is that luck compensation comes with its own metagame. A good analogy is poker. In poker, the deck is sort of like a luck compensator: each time an ace comes out, the probability of getting an ace goes down, until there are no more aces. Players who want to take advantage of that are called card counters, and card counting is generally considered a bad thing for the game, since it replaces strategy with a mathematical formula.

Online games have an even worse problem: They're played on a computer, and computers also happen to be good at using mathematical formulas. A lot of online poker systems actually remove the luck compensator by removing the idea of a deck, to prevent people from using card counting programs to gain an advantage.

And you want to add a luck compensator?

4. The fourth problem is that luck compensation actually makes luck a worse problem. Remember when I said: "Instead of Hydro Pump being 80% accurate, its accuracy now depends on how good your luck was up until that point"? Think about that for a moment: Now your luck affects your luck. That's more luck, not less.

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