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For simplicity, assume that there are no special effects on criticals, other than a doubling of damage. Without agile is good enough, but it would be welcome.
(there are no circumstance penalties, and the enemy is fully visible)

Do I cause more damage (and how much more) if instead of Attacking 3 times, I cast True Strike first?

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    \$\begingroup\$ What kind of weapon user are we talking about here? The answer will probably be very different for a Flurry Ranger than a Fighter. It might also vary depending on Agile vs Non-Agile, and the size of the damage dice (although I don't suspect the latter to actually matter all that much). \$\endgroup\$
    – ESCE
    Mar 1 at 20:39
  • \$\begingroup\$ @ESCE the damage die does change the answer. In DnD 5e it would, but in PF2 the full damage is doubled. MAP does matter, but Flurry Ranger is an edge case. \$\endgroup\$
    – András
    Mar 1 at 22:08
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It Depends a Lot on the Specifics

The relative value of true strike depends entirely on the value of the action you trade away to use it. If that action is a Strike, it has direct DPR value depending on:

  • The MAP for the Strike
  • The chance to hit for your first attack
  • Damage for each of your Strikes on a successful hit and crit.

Note that this doesn't even consider the effective value of not taking a strike. Moving, recalling knowledge, and many other actions can often have a far more significant effect on the outcome of a fight than making a 3rd attack with a low % chance of success.


However, we can make some assumptions.

Lets assume we're using a non-agile weapon without any special bonus damage on critical hits. With a base chance to hit of 60% and a MAP of -5, the base effectiveness of a first attack is 0.7 * X and the base effectiveness of a third attack is 0.15 * X, where X is the raw average damage dealt by a successful strike. The "effectiveness" here combines the chance to hit with the attack and the multiplier of critically hitting. True strike on the first attack does the following to the distribution of critfail/fail/success/critsuccess:

No True Strike True Strike
Crit Success 10% 19%
Success 50% 65%
Failure/ Crit Fail 40% 16%

Therefore the base effectiveness of a first strike with true strike and these assumptions is 1.03 * X. True strike is getting us 0.33 * X more damage over just making the first strike alone. Repeating this exercise for other base chances to hit, we see the following:

Base Chance to hit "effectiveness" of 3rd strike "effectiveness" of true strike
90% 0.45 0.33
85% 0.40 0.35
80% 0.35 0.37
75% 0.30 0.38
70% 0.25 0.37
65% 0.20 0.35
60% 0.15 0.33
55% 0.10 0.30
50% 0.05 0.30
45% 0.05 0.30
40% 0.05 0.29
35% 0.05 0.28
30% 0.05 0.26

If you do an average of 10 damage on a successful hit and have a 60% chance to hit your intended target, true strike adds 3.3 DPR, and making a third Strike instead adds 1.5 DPR. As you can see from this table, true strike provides the biggest edge over making a 3rd strike when your chance to hit is ~50% for your first attack.

Agile weapons and other MAP reducers weigh this calculation toward the 3rd attack. For example, an agile weapon's 3rd attack is better than true strike when you have a 75% chance to hit with your first attack, rather than the 85% chance for a normal weapon. Fatal and Deadly weapons weigh this calculation significantly toward true strike, as do one-off or 1/round riders like a Ranger's precision bonus damage.

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Casting True Strike does multiple things: first, it gives you what is essentially "advantage" in other systems (rolling two dice and taking the higher), which is worth +3.325 on average. Second, it ignores circumstance penalties to the roll. Third, it ignores any flat check to hit on concealed or hidden targets.

Let's break those down.

For the first effect, a +3.325 is valuable, but not necessarily better than an extra attack. It depends on how likely you are to hit and how much damage you deal.

For the second effect, the value is obviously dependent on whether you are taking any penalties.

The third effect is deceptively powerful. On a hidden creature, you're ignoring an instant 50% chance to miss, and on a concealed creature, you're ignoring an instant 20% chance to miss. That is extremely powerful when it's relevant.

So, True Strike is particularly valuable against stealthed enemies. That's a particularly good time to use it. Otherwise, you would consider using it if you really need one particular attack to hit (for sneak attack, poison, etc.) or if your attack (especially a third attack) is likely to miss otherwise.

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    \$\begingroup\$ Good analysis, it made me realise I need to change the question. \$\endgroup\$
    – András
    Mar 1 at 22:32
  • \$\begingroup\$ Please do not downvote this, the question was changed under it \$\endgroup\$
    – András
    Mar 2 at 8:51
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tldr : I believe the True Strike option is always better

Checking the assertions of another answer, I arrived at an average increase in rolled value of 3.825 when rolling 2d20s and taking the higher result. I also calculated a 9.75% chance of a Nat 20, rather than the 5% chance when using a single die. Using those values, and an 18 attack bonus stat (eventually improved to 22 at level 20), and standard Ranger proficiency numbers, and a d6 weapon (with Runes at appropriate levels), I wrote a spreadsheet (which is too large to reproduce here) that calculated the average DPR for either 3 attacks (assuming Flurry and Hunted Target with an Agile weapon, for the least MAP) or 2 attacks with True Strike on the first, against the Moderate creature AC by level (based on the Gamemastery Guide values). In all cases, the average Damage Per Round was higher for the True Strike routine, ranging from a low of about 1.2 times the DPR at level 4 to 1.98 times the DPR at level 3.

A large contributing factor to this result is that, under 2nd ed, better accuracy directly translates to more frequent critical hits, and critical hits cause double damage.

The question originally talked about rangers, but I also decided to test a flurry ranger for the simple reason that they have the smallest Multiple Attack Penalty in the game - only a -2 per attack when attacking a Hunted target with an Agile weapon. The numbers show that, even in this ideal situation, using True Strike is almost always going to be a more successful choice, which also implies it will be a better choice for most character builds.

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  • \$\begingroup\$ Flurry Rangers lose the most by giving up an attack, as their 3rd action is most likely to hit compared to other classes. Not at all representative of the classes that could get True Strike \$\endgroup\$
    – András
    Mar 2 at 17:53
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    \$\begingroup\$ @András which suggests that since he found True Strike to be universally superior for flurry rangers, it would be even that much more valuable for everyone else. \$\endgroup\$
    – Ben Barden
    Mar 2 at 20:44

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