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# True hit

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True hit, also referred to as 2RN (short for "two random numbers"), is a calculation that determines whether or not a unit's attack will hit their opponent. As its name suggests, true hit differs from the displayed hit rate.

All games up to Thracia 776 do not use true hit; the displayed hit rate is the same as the actual hit rate. The game will only roll for one random number from 0 to 99, and if this random number is less than the hit rate, the attack will land. This is colloquially called "1RN" ("one random number").

## The Binding Blade through Awakening and Three Houses

True hit was first introduced in The Binding Blade and is featured in every game following up to and including Awakening. It was absent in Fates and Shadows of Valentia, which instead use a "hybrid" system, before returning in Three Houses.[1] In these games, instead of rolling just one random number, the game will instead roll two. These two random numbers are then averaged, and this resulting average is what is compared to the displayed hit rate; if the average number is less than the hit rate, the attack will land.

As a result of this double random number system, the likelihood of landing hit rates below 50% is lower than what is shown, while the likelihood of landing hit rates above 50% is higher than what is shown. In effect, this makes higher hit rates more reliable than in previous games, and makes lower hit rates even more likely to miss, making avoiding attacks more reliable. Classes with high avoid such as Swordmasters benefit greatly from this, as opponents will naturally have low hit rates against them already.

The following table shows the discrepancies:[2]

Note that in The Binding Blade, due to an error in how random numbers are generated, the actual hit rates are slightly lower, resulting in the possibility of missing attacks with a displayed hit of 100.
Displayed hit rate vs. actual hit rate
Hit rate True hit Hit rate True hit Hit rate True hit Hit rate True hit Hit rate True hit
0 0.00 20 8.20 40 32.40 60 68.40 80 92.20
1 0.03 21 9.03 41 34.03 61 69.97 81 92.97
2 0.10 22 9.90 42 35.70 62 71.50 82 93.70
3 0.21 23 10.81 43 37.41 63 72.99 83 94.39
4 0.36 24 11.76 44 39.16 64 74.44 84 95.04
5 0.55 25 12.75 45 40.95 65 75.85 85 95.65
6 0.78 26 13.78 46 42.78 66 77.22 86 96.22
7 1.05 27 14.85 47 44.65 67 78.55 87 96.75
8 1.36 28 15.96 48 46.56 68 79.84 88 97.24
9 1.71 29 17.11 49 48.51 69 81.09 89 97.69
10 2.10 30 18.30 50 50.50 70 82.30 90 98.10
11 2.53 31 19.53 51 52.47 71 83.47 91 98.47
12 3.00 32 20.80 52 54.40 72 84.60 92 98.80
13 3.51 33 22.11 53 56.29 73 85.69 93 99.09
14 4.06 34 23.46 54 58.14 74 86.74 94 99.34
15 4.65 35 24.85 55 59.95 75 87.75 95 99.55
16 5.28 36 26.28 56 61.72 76 88.72 96 99.72
17 5.95 37 27.75 57 63.45 77 89.65 97 99.85
18 6.66 38 29.26 58 65.14 78 90.54 98 99.94
19 7.41 39 30.81 59 66.79 79 91.39 99 99.99
20 8.20 40 32.40 60 68.40 80 92.20 100 100.00

## Fates, Shadows of Valentia, and Engage

Fates introduced a new "hybrid" system between the 1 RN and 2 RN hit rate systems, and two subsequent games—Shadows of Valentia and Engage—have used it as well. If the displayed hit rate is lower than 50%, the game will use the 1 RN system where Displayed Hit equals True Hit; if the hit rate is 50% or higher, the game rolls a single random number, but it is compared against the below mathematical function:[3]

Game Notes Formula Fates, Shadows of Valentia,[3] Engage[4] Hits if < random number 0–9999.Sine function expects degree input.

The result of this system makes hit rates above 50% higher than the displayed hit, but slightly lower than hit rates in the 2 RN system. Meanwhile Hit Rates below 50% are higher than the usual 2 RN system, making dodging less reliable than in some other games. This makes enemy classes such as Berserkers more threatening, as their attacks are harder to avoid than what may be expected.

The following table shows the effected hit rates:[3]

Displayed hit rate vs. actual hit rate (for hit rates 50% and above)
Hit rate True hit Hit rate True hit Hit rate True hit Hit rate True hit Hit rate True hit
50 50 60 64.70 70 78.87 80 90.14 90 97.05
51 51.42 61 66.18 71 80.16 81 91.04 91 97.50
52 52.86 62 67.65 72 81.42 82 91.89 92 97.90
53 54.32 63 69.12 73 82.65 83 92.69 93 98.27
54 55.79 64 70.57 74 83.84 84 93.45 94 98.61
55 57.26 65 72.01 75 85.00 85 94.16 95 98.91
56 58.74 66 73.43 76 86.11 86 94.83 96 99.18
57 60.23 67 74.82 77 87.18 87 95.45 97 99.42
58 61.72 68 76.20 78 88.21 88 96.03 98 99.63
59 63.21 69 77.55 79 89.20 89 96.56 99 99.82

## References

1. u/dee-ee, Three Houses absolutely uses 2RN; a technical analysis, Reddit, Published: September 14, 2019, Retrieved: November 14, 2019
2. True Hit, Serenes Forest, Retrieved: June 2, 2018
3. u/dee-ee, Echoes absolutely uses Fates RN (bonus explanation as to how Fates RN works), Reddit, Published: January 9, 2019, Retrieved: April 16, 2019
4. @DeathChaos25, DeathChaos on Twitter, Twitter, Published: January 26, 2023, Retrieved: January 27, 2023