Rework "Sight" functionality

[Heroesflorian]

Current Situation

• At the moment, the sight increases the accuracy of a single shot by ((100% - current accuracy) / 3), and costs 6 XP. This makes the sight kind of useless right now, in general.

• But besides the cost/reward imbalance, sight has the general issue of being not much use in higher levels at all, while having (in comparison) a rather large effect in lower levels, which might make it hard to balance it globally - unless the duration (either in time or shots) of a sight varies depending on the hunter level.

Proposal

• The sight's effect should generally last for more than just a single shot. At a cost of 6 XP, probably about 4-5 shots (ignoring the (low) possibility of superducks) would be required to make the expected outcome of using a sight vs not using a sight positive even for very low level hunters which profit the most from the sight's effect due to their low regular accuracy. However, for higher-level hunters, the benefits of sight shrink dramatically as their base accuracy increases (see https://api-d.com/snaps/progression_table_en.html).

Example: A level 4 hunter at 58% accuracy would gain (100-58)/3 = 42/3 = 14% accuracy, i.e. would have 58% "vanilla" accuracy VS 58+14 = 72% accuracy with sight. XP gained with sight after N shots would be: N * 0.72 * 10 - N * 0.28 * 1 - sightXPCost; XP gained without sight after N shots would be: N * 0.58 * 10 - N * 42 * 1; At a cost of 6 XP for a sight, the advantage of sight is: 1.4 * N + 0.14 * N - 6, so the break even point is at N = 6 / 1.54 = 3.896... that means at least 4 shots have to be affected by sight for the sight's benefit to be non-negative (ignoring clover and super duck effects).

A level 14 hunter at 74% accuracy would gain (100-74)/3 = 26/3 = 8.7% accuracy, and according to the formulas above would need N = 6 / (0.87+0.887) = 6 / 0.957 = 6.270... i.e. minimum 7 shots affected by sight in order to have a non-negative XP outcome from using a sight. A level 24 hunter at 84% accuracy would gain 16/3 = 5.3% accuracy, and need N = 6 / (0.53+0.053) = 6/0.583 = 10,291... i.e. minimum 11 shots affected by sight in order to have a non-negative outcome from using a sight. A level 34 hunter at 94% accuracy would gain 6/3 = 2% accuracy, and need N = 6 / 0.22 = 27.272... i.e. minimum 28 shots affected by sight in order to have a non-negative outcome from using a sight. A level 41 hunter at 98% accuracy would gain 2/3 = 0.7% accuracy, and need N = 6 / 0.077 = 77.922... i.e. 78 shots affected by sight in order to have a non-negative outcome from using a sight.

• One idea to fix the issue of sights being obsolete in higher level could be some sort of "durability" for the sight, with the sight getting "damaged" somehow (losing durability) whenever preventing a miss, and not getting damaged when not preventing a miss. That way, lower level hunters (who naturally would miss more often) would damage their sight more quickly, while higher level hunters would only rarely damage their sight as they rarely miss without a sight. Then, the sight would have greater effect per shot for lower levels, but also a shorter lifetime (in shots), and on higher levels it would have a longer lifetime (in shots) with a lesser effect per shot.

Reasoning Besides the general buff to the sight's effect duration which is required to make the sight any use at any level at all, especially the durability concept provides benefits over the current way sights work.

With this mechanic change, it would be possible to balance the cost-reward-ratio of the sight for all levels a lot more easily, and the sight would be useful on a much wider level range.