When I started to think about the *hit-chance* system for combat, I wanted to address the ‘consecutive hit/miss’ issue that pops up in turn-based games. Even some of my own favourites games, like X-COM have players complaining of their questionable bad luck (naturally, no one complains of good luck).

Citizen is a *real-time* game. The random-hit issue presents itself differently from a turn-based game. I think the issue is more glaring in a turn-based game because every shot is felt. Nevertheless, as my iterative test showed, this issue is still relevantly noticeable in real-time game.

## Luck vs skill

I think that the root of the issue with this game design is the distinction between luck vs skill. If we say that I have a 25% *chance of hitting*, and then proceed to roll a d8, and hope to get <= 2, then, that’s the concept of *luck* as all dice rolls are.

But in combat, it’s not all about luck; rather, it’s more about skill. When we say that we can hit a bulls-eye 25% of the time — contingent on factors affecting accuracy — we are likely referring to a *fact*, not a chance. To say that I can hit so-and-so 25% of the time means that I would have gone to a firing range, shot some rounds, and observed how many rounds have gone in the #1 ring and how many have landed outside. Then I would repeat this process until I get an average percentage, which becomes a quantitative representation of my skill level. This is the principle of *skill*, which I wished to represent in the Give-Me-A-Chance (GMAC) system.

## Randomness

Some folks think that the problem with pseudo-random numbers (also referred to RNG — random number generation) is that they are ‘pseudo’, rather than ‘true’ random numbers. For the purposes of rolling for a hit that technical distinction is irrelevant. The important aspect about RNG is that whether they are ‘pseudo’ or ‘true’, they they depict luck rather than skill.

When you view a graphical representation of random numbers, they do not form any coherent shape, making them suitable for unpredictability.

But in a combat system *some* unpredictability is necessary. But the unpredictability needs to be felt in the details of combat to give it an organic touch. But unpredictability shouldn’t be felt on the wider scope of the whole combat system, which is the complaint of most players.

## Give-Me-A-Chance

Enter GMAC, which tries to balance the hit-chance based on previous hits/misses. This means that the hit-chance (i.e. the skill level) is being modified based on the success rate of hits. In short, GMAC is intended to make hit-chance *feel* like the percentage it is depicting.

As an example of why RNG without modifications feels like luck, we run a random number generator for 100 iterations. For each iteration, it compares a random number to 75%; if the random number falls below 75%, then that’s considered a hit. Then the average percentage for those 100 iterations is shown. Then we run it 10 more times (10 cycles). This is an example of the results:

Each line represents a single cycle. Remember that the percentages are *averages* of 100 comparisons per single cycle. This means that for cycle # 3, the average percentage was 7% higher than the target. And at cycle #9 it was 5% lower, giving a total range of 12% difference, which is rather a big deal.

## Success rate

The principle behind GMAC is counting the success rate of shots. The basic principle is this: when you shoot the first round, you roll against your hit-chance, which is your basic skill level, which we’ll set as 50%. If you hit the target, you would have had a 100% success rate (1 out of 1 shot). Because you are 100% successful so far, and your skill level is 50%, your next hit-chance would be *penalised* to, say, 1%. If you make the second shot (roll below 1% — yes it’s actually possible!), then you would continue to have a 100% success rate, and your hit-chance continues to be penalised to 1%, which you will *likely* not keep on hitting for long.

On the flip-side, if you missed the first shot, your success rate is 0%, and your hit-chance is given a slight *bonus* so as to make you more likely to hit.

Like a true socialist system, it helps you when you’re down, and when you’re getting too successful, it shuts you down.

Compared to the previous random hit-chance test, the above image shows GMAC modifying the hit-chance. `hit_chance`

is incremented, and `average`

is the result of the GMAC operation. The closer `average`

is to `hit_chance`

means that it is working.

However, you can see that in the `hit_chance:12`

there is a large 3% discrepancy. This occurs in the lower percentages (< 20%). GMAC represents higher percentages far more accurately than low ones.

## Shot count

I had to decide how many shots I wanted to track in order to compute the percentages accurately. As I’m tracking each shot that fires, I have to know when to ‘give up’ and reset the counter. The primary reason for this is the assumption that the hit-chance changes over time. For example, if the Player is moving towards the enemy, the hit-chance increases. If I track too many shots, then I would potentially be comparing the success rate of another hit-chance that is drastically different from the current one.

Of course, the downside of tracking too little is that I won’t be able to represent the accuracy of certain the percentages because there wouldn’t be enough ‘resolution’ for the math to compute.

In the actual GMAC v1 algorithm, however, once properly tweaked, it seemed like 10 shots satisfied all requirements; resolution was good especially when I simulated the shot series over a thousand times.

## Low percentage

There was a peculiarity with the algorithm, which I think was related to the fact that I decided on counting 10 shots.

The lowest percentage I could track was 10%, which is logical, since any hit-chance above 0% is going to be adjusted to have at least *once* in 10 shots, giving it always a minimum of 10%. Thus, combat skills should always resolve to anything above 10%.

## Hit-chance and GMAC

Note that GMAC is a modifier. The actual hit-chance is calculated by the factors governing the combat mechanics; weapon accuracy, weapon range, Player skills, etc. Then that ‘base’ hit-chance is passed onto GMAC which takes care of the balancing for success rate.

I think the GMAC modifier is a good RPG combat concept. It allows randomisation on a shot-by-shot basis, but will endeavour to reflect your actual skill level by increasing or decreasing likelihood of hitting based on on your success rate. Hopefully, this replaces the feeling of being unlucky with the feeling of being unskilled.